We derive a closed-form achievable rate for entanglement-assisted classical communication over a lossy thermal-noise bosonic channel, where the entanglement is in the form of a Two-Mode Squeezed Vacuum (TMSV) modulation restricted to Phase Shift Keying (PSK). The achievable rate is non-asymptotic in terms of the mean signal photon number, mean noise photon number, and transmissivity defining the communication channel, which provides insights into the interplay of these physical parameters and bridges recent experimental demonstrations of entanglement-assisted communications with the coding theorems used in information-theoretic proofs. The key challenge we address is deriving an analytical bound for the von Neumann entropy of the non-Gaussian mixed state resulting from the phase modulation of one arm of a TMSV. Our approach hinges on two key observations: 1) as the size of the PSK modulation increases, the resulting mixed state converges in trace distance to a diagonal state in the Fock basis; 2) the Fock-basis representation of the diagonal state involves hypergeometric functions that can be appropriately bounded to offer a tractable lower bound for the Holevo information.
Efficient and systematic numerical methods for robust control design are highly desired in the study of quantum systems, since system imperfections such as uncertainties or disturbances inevitably exist. By modeling uncertainties as combinations of random variables following prescribed distributions, the expectation of infidelity can be used to quantify the level of robustness as a performance index in various control problems. Inspired by sample-based algorithms, we consider the level of robustness as a weighted tensor product quadrature, and take advantage of Smolyak's sparse grid algorithm to develop a parametric robust quantum control scheme, with the purpose of reducing computation cost and improving accuracy. Furthermore, the features and strengths of the scheme proposed in this paper have been illustrated in the context of robust control problems, including state transfer and realization of quantum gates, where ultrahigh fidelity can be achieved with strong robustness using Smolyak algorithm-assisted gradient-based methods. Therefore, our results can contribute to reliable and secure quantum computing as well as communication.
We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation. In purity estimation, we are to estimate $tr(\rho^2)$ of an unknown quantum state $\rho$ to additive error $\epsilon$. Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate $tr(\rho\sigma)$ to additive error $\epsilon$ given copies of unknown quantum state $\rho$ and $\sigma$ using classical communication and restricted quantum communication. In this paper, we show a strong connection between the sample complexity of purity estimation with bounded quantum memory and inner product estimation with bounded quantum communication and unentangled measurements. We propose a protocol that solves quantum inner product estimation with $k$-qubit one-way quantum communication and unentangled local measurements using $O(median\{1/\epsilon^2,2^{n/2}/\epsilon,2^{n-k}/\epsilon^2\})$ copies of $\rho$ and $\sigma$. Our protocol can be modified to estimate the purity of an unknown quantum state $\rho$ using $k$-qubit quantum memory with the same complexity. We prove that arbitrary protocols with $k$-qubit quantum memory that estimate purity to error $\epsilon$ require $\Omega(median\{1/\epsilon^2,2^{n/2}/\sqrt{\epsilon},2^{n-k}/\epsilon^2\})$ copies of $\rho$. This indicates the same lower bound for quantum inner product estimation with one-way $k$-qubit quantum communication and classical communication, and unentangled local measurements. For purity estimation, we further improve the lower bound to $\Omega(\max\{1/\epsilon^2,2^{n/2}/\epsilon\})$ for any protocols using an identical single-copy projection-valued measurement. Additionally, we investigate a decisional variant of quantum distributed inner product estimation without quantum communication for mixed state and provide a lower bound on the sample complexity.
Kieren A. Harkins, Cooper Selco, Christian Bengs, David Marchiori, Leo Joon Il Moon, Zhuo-Rui Zhang, Aristotle Yang, Angad Singh, Emanuel Druga, Yi-Qiao Song, Ashok Ajoy Floquet prethermalization is observed in periodically driven quantum many-body systems where the system avoids heating and maintains a stable, non-equilibrium state, for extended periods. Here we introduce a novel quantum control method using off-resonance and short-angle excitation to significantly extend Floquet prethermal lifetimes. This is demonstrated on randomly positioned, dipolar-coupled, 13C nuclear spins in diamond, but the methodology is broadly applicable. We achieve a lifetime $T_2'~800 s at 100 K while tracking the transition to the prethermal state quasi-continuously. This corresponds to a >533,000-fold extension over the bare spin lifetime without prethermalization, and constitutes a new record both in terms of absolute lifetime as well as the total number of Floquet pulses applied (here exceeding 7 million). Using Laplace inversion, we develop a new form of noise spectroscopy that provides insights into the origin of the lifetime extension. Finally, we demonstrate applications of these extended lifetimes in long-time, reinitialization-free quantum sensing of time-varying magnetic fields continuously for ~10 minutes at room temperature. Our work facilitates new opportunities for stabilizing driven quantum systems through Floquet control, and opens novel applications for continuously interrogated, long-time responsive quantum sensors.
Quantum illumination (QI) provides entanglement-enabled target-detection enhancement, despite operating in an entanglement-breaking environment. Existing experimental studies of QI have utilized a Bayesian approach, assuming that the target is equally likely to be present or absent before detection, to demonstrate an advantage over classical target detection. However, such a premise breaks down in practical operational scenarios in which the prior probability is unknown, thereby hindering QI's applicability to real-world target-detection scenarios. In this work, we adopt the Neyman-Pearson criterion in lieu of the error probability for equally likely target absence or presence as our figure of merit for QI. We demonstrate an unconditional quantum advantage over the optimal classical-illumination protocol as benchmarked by the receiver operating characteristic, which examines detection probability versus false-alarm probability without resorting to known prior probabilities. Our work represents a critical advancement in adapting quantum-enhanced sensing to practical operational settings.
Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, measuring improvement of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50 kHz range - a blind spot for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions.
Bang Liu, Li-Hua Zhang, Ya-Jun Wang, Jun Zhang, Qi-Feng Wang, Yu Ma, Tian-Yu Han, Zheng-Yuan Zhang, Shi-Yao Shao, Qing Li, Han-Chao Chen, Jia-Dou Nan, Dong-Yang Zhu, Yi-Ming Yin, Bao-Sen Shi, Dong-Sheng Ding Higgs and Goldstone modes manifest as fluctuations in the order parameter of system, offering insights into its phase transitions and symmetry properties. Exploring the dynamics of these collective excitations in a Rydberg atoms system advances various branches of condensed matter, particle physics, and cosmology. Here, we report an experimental signature of Higgs and Goldstone modes in a U(1) symmetry-broken Rydberg atomic gases. By constructing two probe fields to excite atoms, we observe the distinct phase and amplitude fluctuations of Rydberg atoms collective excitations under the particle-hole symmetry. Due to the van der Waals interactions between the Rydberg atoms, we detect a symmetric variance spectrum divided by the divergent regime and phase boundary, capturing the full dynamics of the additional Higgs and Goldstone modes. Studying the Higgs and Goldstone modes in Rydberg atoms allows us to explore fundamental aspects of quantum phase transitions and symmetry breaking phenomena, while leveraging the unique properties of these highly interacting systems to uncover new physics and potential applications in quantum simulation.
Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction. Despite intensive study, most existing works focus on learning Pauli noise channels associated with some specific gates rather than treating the gate set as a whole. A learning algorithm that is self-consistent, complete, and efficient at the same time is yet to be established. In this work, we study the task of gate set Pauli noise learning, where a set of quantum gates, state preparation, and measurements all suffer from unknown Pauli noise channels with a customized noise ansatz. Using tools from algebraic graph theory, we analytically characterize the self-consistently learnable degrees of freedom for Pauli noise models with arbitrary linear ansatz, and design experiments to efficiently learn all the learnable information. Specifically, we show that all learnable information about the gate noise can be learned to relative precision, under mild assumptions on the noise ansatz. We then demonstrate the flexibility of our theory by applying it to concrete physically motivated ansatzs (such as spatially local or quasi-local noise) and experimentally relevant gate sets (such as parallel CZ gates). These results not only enhance the theoretical understanding of quantum noise learning, but also provide a feasible recipe for characterizing existing and near-future quantum information processing devices.
In trapped-atom quantum computers, high-fidelity control of optical qubits is challenging due to the motion of atoms in the trap. If not corrected, the atom motion gets entangled with the qubit degrees of freedom through two fundamental mechanisms, (i) photon recoil and (ii) thermal motion, both leading to a reduction of the gate fidelity. We develop motion-insensitive pulses that suppress both sources of infidelity by modulating the phase of the driving laser field in time. To eliminate photon recoil, we use bang-bang pulses$-$derived using time-optimal control$-$which shorten the gate duration by about 20 times compared to conventional pulses. However, even when photon recoil is eliminated, we find that the gate error does not vanish, but is rather limited by a bound arising from thermal motion-induced entanglement. Remarkably, this bound is independent of the Rabi frequency, meaning that, unlike for photon recoil, operating in the resolved sideband regime does not mitigate this source of infidelity. To overcome this bound, we derive smooth-phase pulses, which allow for a further reduction of the gate error by more than an order of magnitude for typical thermal atoms. Motion-insensitive pulses can be refined to compensate for laser inhomogeneities, enhancing the gate performance in practical situations. Our results are validated through simulations of one-qubit gates operating on the optical clock transition of ${}^{88}$Sr atoms trapped in an optical tweezers array.
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace verification and explore several stabilizer code subspaces of practical significance. First, we present two efficient verification strategies for general stabilizer code subspaces, utilizing measurements of their stabilizer generators and stabilizer groups, respectively. Then, building on the observation that certain tests can be conducted in parallel when the subspace exhibits specific structural properties, we propose a coloring strategy tailored to graph code subspaces and an XZ strategy tailored to Calderbank-Shor-Steane (CSS) code subspaces. Compared to stabilizer-based strategies, these new strategies require significantly fewer measurement settings and consume fewer state copies, approaching near-global optimality. Notably, all the strategies employ a limited number of Pauli measurements, are non-adaptive, and work on mixed states, enabling efficient experimental certification of both logical qubits and logical operations in noisy quantum computers. This work contributes to the first systematic study of efficient verification of stabilizer code subspaces with local measurements.
The evolution of superconducting quantum processors is driven by the need to reduce errors and scale for fault-tolerant computation. Reducing physical qubit error rates requires further advances in the microscopic modeling and control of decoherence mechanisms in superconducting qubits. Piezoelectric interactions contribute to decoherence by mediating energy exchange between microwave photons and acoustic phonons. Centrosymmetric materials like silicon and sapphire do not display piezoelectricity and are the preferred substrates for superconducting qubits. However, the broken centrosymmetry at material interfaces may lead to piezoelectric losses in qubits. While this loss mechanism was predicted two decades ago, interface piezoelectricity has not been experimentally observed in superconducting devices. Here, we report the observation of interface piezoelectricity at an aluminum-silicon junction and show that it constitutes an important loss channel for superconducting devices. We fabricate aluminum interdigital surface acoustic wave transducers on silicon and demonstrate piezoelectric transduction from room temperature to millikelvin temperatures. We find an effective electromechanical coupling factor of $K^2\approx 2 \times 10^{-5}\%$ comparable to weakly piezoelectric substrates. We model the impact of the measured interface piezoelectric response on superconducting qubits and find that the piezoelectric surface loss channel limits qubit quality factors to $Q\sim10^4-10^8$ for designs with different surface participation ratios and electromechanical mode matching. These results identify electromechanical surface losses as a significant dissipation channel for superconducting qubits, and show the need for heterostructure and phononic engineering to minimize errors in next-generation superconducting qubits.
Jun Zhang, Ya-Jun Wang, Bang Liu, Li-Hua Zhang, Zheng-Yuan Zhang, Shi-Yao Shao, Qing Li, Han-Chao Chen, Yu Ma, Tian-Yu Han, Qi-Feng Wang, Jia-Dou Nan, Yi-Ming Yin, Dong-Yang Zhu, Bao-Sen Shi, Dong-Sheng Ding Study of phase transitions provide insights into how a many-body system behaves under different conditions, enabling us to understand the symmetry breaking, critical phenomena, and topological properties. Strong long-range interactions in highly excited Rydberg atoms create a versatile platform for exploring exotic emergent topological phases. Here, we report the experimental observation of dynamical topological phase transitions in cold Rydberg atomic gases under a microwave field driving. By measuring the system transmission curves while varying the probe intensity, we observe complex hysteresis trajectories characterized by distinct winding numbers as they cross the critical point. At the transition state, where the winding number flips, the topology of these hysteresis trajectories evolves into more non-trivial structures. The topological trajectories are shown to be robust against noise, confirming their rigidity in dynamic conditions. These findings contribute to the insights of emergence of complex dynamical topological phases in many-body systems.
Hagedorn wavepackets have been used with local harmonic approximation to partially capture the anharmonic effects on single vibronic level (SVL) spectra in model potentials. To make the Hagedorn approach practical for realistic anharmonic polyatomic molecules, here we combine local harmonic Hagedorn wavepacket dynamics with on-the-fly ab initio dynamics. We then test this method by computing the SVL fluorescence spectra of difluorocarbene, a small, floppy molecule with a very anharmonic potential energy surface. Our time-dependent approach obtains the emission spectra of all initial vibrational levels from a single anharmonic semiclassical wavepacket trajectory without the need to fit individual anharmonic vibrational wavefunctions and to calculate the Franck--Condon factors for all vibronic transitions. We show that, whereas global harmonic models are inadequate for CF$_2$, the spectra computed with the on-the-fly local harmonic Hagedorn wavepacket dynamics agree well with experimental data, especially for low initial excitations.
Absorption estimation, the base of spectroscopy, is crucial for probing the composition and dynamics of matter. Conventional methods of estimation rely on coherent laser sources, and in turn suffer from inherent limitations in estimating weak absorption. Here we propose a new measurement strategy with correlated photons to determine the weak absorption by distinguishing the output with and without photons, dubbed as the on-off measurement. Our implementation within the strategy allows the estimation precision to reach the ultimate quantum limit. We demonstrate that absorption spectroscopy that incorporates quantum correlations is capable of estimating weak absorption down to a single-photon level, even in noisy environments, achieving a precision comparable to that obtained through several hundred photons in conventional absorption spectroscopy. By introducing the quantum correlations, our work avoids the occurrence of light-induced damage while breaking the classical inherent limitations in spectroscopy.
Hagedorn wavepacket dynamics yields exact single vibronic level (SVL) fluorescence spectra from any initial vibrational level in displaced, squeezed, and Duschinsky-rotated global harmonic models. Real molecules, however, have anharmonic potential energy surfaces. To partially describe effects of anharmonicity on the spectra, we combine the Hagedorn approach to spectroscopy with the local harmonic approximation of the potential. We compute the SVL spectra for several anharmonic Morse-type potentials in one, two, and twenty dimensions and compare them to the results of global harmonic approximations and, where possible, of exact quantum calculations. We show that the local harmonic approach yields more accurate results than global harmonic approximations, especially for the emission spectra from higher initial vibrational levels.
Yu Ma, Bang Liu, Li-Hua Zhang, Ya-Jun Wang, Zheng-Yuan Zhang, Shi-Yao Shao, Qing Li, Han-Chao Chen, Jun Zhang, Tian-Yu Han, Qi-Feng Wang, Jia-Dou Nan, Yi-Ming Yin, Dong-Yang Zhu, Bao-Sen Shi, Dong-Sheng Ding The interactions between Rydberg atoms and microwave fields provide a valuable framework for studying the complex dynamics out of equilibrium, exotic phases, and critical phenomena in many-body physics. This unique interplay allows us to explore various regimes of nonlinearity and phase transitions. Here, we observe a phase transition from the state in the regime of bistability to that in multistability in strongly interacting Rydberg atoms by varying the microwave field intensity, accompanying with the breaking of Z3-symmetry. During the phase transition, the system experiences a hidden critical point, in which the multistable states are difficult to be identified. Through changing the initial state of system, we can identify a hidden multistable state and reveal a hidden trajectory of phase transition, allowing us to track to a hidden critical point. In addition, we observe multiple phase transitions in spectra, suggesting higher-order symmetry breaking. The reported results shed light on manipulating multistability in dissipative Rydberg atoms systems and hold promise in the applications of non-equilibrium many-body physics.
Quantum recursive programming has been recently introduced for describing sophisticated and complicated quantum algorithms in a compact and elegant way. However, implementation of quantum recursion involves intricate interplay between quantum control flows and recursive procedure calls. In this paper, we aim at resolving this fundamental challenge and develop a series of techniques to efficiently implement quantum recursive programs. Our main contributions include: 1. We propose a notion of quantum register machine, the first purely quantum architecture (including an instruction set) that supports quantum control flows and recursive procedure calls at the same time. 2. Based on quantum register machine, we describe the first comprehensive implementation process of quantum recursive programs, including the compilation, the partial evaluation of quantum control flows, and the execution on the quantum register machine. 3. As a bonus, our efficient implementation of quantum recursive programs also offers automatic parallelisation of quantum algorithms. For implementing certain quantum algorithmic subroutine, like the widely used quantum multiplexor, we can even obtain exponential parallel speed-up (over the straightforward implementation) from this automatic parallelisation. This demonstrates that quantum recursive programming can be win-win for both modularity of programs and efficiency of their implementation.
Quench experiments on a unitary Bose gas around a broad Feshbach resonance have led to the discovery of universal dynamics. This universality is manifested in the measured atomic momentum distributions where, asymptotically, a quasi-equilibrated metastable state is found in which both the momentum distribution and the time scales are determined by the particle density. In this paper we present counterpart studies but for the case of a very narrow Feshbach resonance of $^{133}$Cs atoms having a width of 8.3 mG. In dramatic contrast to the behavior reported earlier, a rapid quench of an atomic condensate to unitarity is observed to ultimately lead to coherent oscillations involving dynamically produced condensed and non-condensed molecules and atoms. The same characteristic frequency, determined by the Feshbach coupling, is observed in all types of particles. To understand these quench dynamics and how these different particle species are created, we develop a beyond Hartree-Fock-Bogoliubov dynamical framework including a new type of cross correlation between atoms and molecules. This leads to a quantitative consistency with the measured frequency. Our results, which can be applied to the general class of bosonic superfluids associated with narrow Feshbach resonances, establish a new paradigm for universal dynamics dominated by quantum many-body interactions.
Zhiyuan Zhang, Ziwei Dou, Anqi Wang, Cuiwei Zhang, Yu Hong, Xincheng Lei, Yue Pan, Zhongchen Xu, Zhipeng Xu, Yupeng Li, Guoan Li, Xiaofan Shi, Xingchen Guo, Xiao Deng, Zhaozheng Lyu, Peiling Li, Faming Qu, Guangtong Liu, Dong Su, Kun Jiang, et al (4) P-wave superconductors hold immense promise for both fundamental physics and practical applications due to their unusual pairing symmetry and potential topological superconductivity. However, the exploration of the p-wave superconductors has proved to be a complex endeavor. Not only are they rare in nature but also the identification of p-wave superconductors has been an arduous task in history. For example, phase-sensitive measurement, an experimental technique which can provide conclusive evidence for unconventional pairing, has not been implemented successfully to identify p-wave superconductors. Here, we study a recently discovered family of superconductors, A2Cr3As3 (A = K, Rb, Cs), which were proposed theoretically to be a candidate of p-wave superconductors. We fabricate superconducting quantum interference devices (SQUIDs) on exfoliated K2Cr3As3, and perform the phase-sensitive measurement. We observe that such SQUIDs exhibit a pronounced second-order harmonic component sin(2\phi) in the current-phase relation, suggesting the admixture of 0- and \pi-phase. By carefully examining the magnetic field dependence of the oscillation patterns of critical current and Shapiro steps under microwave irradiation, we reveal a crossover from 0- to \pi-dominating phase state and conclude that the existence of the \pi-phase is in favor of the p-wave pairing symmetry in K2Cr3As3.
We study the task of agnostic tomography: given copies of an unknown $n$-qubit state $\rho$ which has fidelity $\tau$ with some state in a given class $C$, find a state which has fidelity $\ge \tau - \epsilon$ with $\rho$. We give a new framework, stabilizer bootstrapping, for designing computationally efficient protocols for this task, and use this to get new agnostic tomography protocols for the following classes: Stabilizer states: We give a protocol that runs in time $\mathrm{poly}(n,1/\epsilon)\cdot (1/\tau)^{O(\log(1/\tau))}$, answering an open question posed by Grewal, Iyer, Kretschmer, Liang [40] and Anshu and Arunachalam [6]. Previous protocols ran in time $\mathrm{exp}(\Theta(n))$ or required $\tau>\cos^2(\pi/8)$. States with stabilizer dimension $n - t$: We give a protocol that runs in time $n^3\cdot(2^t/\tau)^{O(\log(1/\epsilon))}$, extending recent work on learning quantum states prepared by circuits with few non-Clifford gates, which only applied in the realizable setting where $\tau = 1$ [30, 37, 46, 61]. Discrete product states: If $C = K^{\otimes n}$ for some $\mu$-separated discrete set $K$ of single-qubit states, we give a protocol that runs in time $(n/\mu)^{O((1 + \log (1/\tau))/\mu)}/\epsilon^2$. This strictly generalizes a prior guarantee which applied to stabilizer product states [39]. For stabilizer product states, we give a further improved protocol that runs in time $(n^2/\epsilon^2)\cdot (1/\tau)^{O(\log(1/\tau))}$. As a corollary, we give the first protocol for estimating stabilizer fidelity, a standard measure of magic for quantum states, to error $\epsilon$ in $n^3 \mathrm{quasipoly}(1/\epsilon)$ time.
Zhao Zhang, Léo Van Damme, Marco Rossignolo, Lorenzo Festa, Max Melchner, Robin Eberhard, Dimitrios Tsevas, Kevin Mours, Eran Reches, Johannes Zeiher, Sebastian Blatt, Immanuel Bloch, Steffen J. Glaser, Andrea Alberti We propose a scheme to perform optical pulses that suppress the effect of photon recoil by three orders of magnitude compared to ordinary pulses in the Lamb-Dicke regime. We derive analytical insight about the fundamental limits to the fidelity of optical qubits for trapped atoms and ions. This paves the way towards applications in quantum computing for realizing $>1000$ of gates with an overall fidelity above 99\%.
Jun Zhang, En-Ze Li, Ya-Jun Wang, Bang Liu, Li-Hua Zhang, Zheng-Yuan Zhang, Shi-Yao Shao, Qing Li, Han-Chao Chen, Yu Ma, Tian-Yu Han, Qi-Feng Wang, Jia-Dou Nan, Yi-Ming Ying, Dong-Yang Zhu, Bao-Sen Shi, Dong-Sheng Ding The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an additional dissipation channel, resulting in non-Hermitian many-body dynamics and the emergence of exceptional points in spectrum. Here, we report experimental observation of interaction-induced exceptional points in cold Rydberg atomic gases, revealing the breaking of charge-conjugation parity symmetry. By measuring the transmission spectrum under increasing and decreasing probe intensity, the interaction-induced hysteresis trajectories are observed, which give rise to non-Hermitian dynamics. We record the area enclosed by hysteresis loops and investigate the dynamics of hysteresis loops. The reported exceptional points and hysteresis trajectories in cold Rydberg atomic gases provide valuable insights into the underlying non-Hermitian physics in many-body systems, allowing us to study the interplay between long-range interactions and non-Hermiticity.
Cat-state qubits formed by photonic coherent states are a promising candidate for realizing fault-tolerant quantum computing. Such logic qubits have a biased noise channel that the bit-flip error dominates over all the other errors. In this manuscript, we propose an optimally robust protocol using the control method of shortcuts to adiabaticity to realize a nearly perfect population inversion in a cat-state qubit. We construct a shortcut based on the Lewis-Riesenfeld invariant and examine the stability versus different types of perturbations for the fast and robust population inversion. Numerical simulations demonstrate that the population inversion can be mostly insensitive to systematic errors in our protocol. Even when the parameter imperfection rate for bit-flip control is $20\%$, the final population of the target state can still reach $\geq 99\%$. The optimally robust control provides a feasible method for fault-tolerant and scalable quantum computation.
We propose an efficient circuit-based quantum state tomography (QST) scheme to reconstruct $n$-qubit states with $k$ nonzero entries using measurements of $|\psi\rangle$ and $U_1|\psi\rangle, \dots, U_{2m}|\psi\rangle$, where $m \le k$. Each $U_j$ involves CNOT gates followed by a single-qubit gate, either Hadamard $H$ or $HD$, where $D = {\rm diag}(1,i)$, targeting a specific qubit. We provide an upper limit on the number of CNOT gates based on the nonzero entries' positions in $|\psi\rangle$. This approach, applied to both state and process tomography, was tested using the Qiskit simulator.
Silicon nanomechanical resonators display ultra-long lifetimes at cryogenic temperatures and microwave frequencies. Achieving quantum control of single-phonons in these devices has so far relied on nonlinearities enabled by coupling to ancillary qubits. In this work, we propose using atomic forces to realize a silicon nanomechanical qubit without coupling to an ancillary qubit. The proposed qubit operates at 60 MHz with a single-phonon level anharmonicity of 5 MHz. We present a circuit quantum acoustodynamics architecture where electromechanical resonators enable dispersive state readout and multi-qubit operations. The combination of strong anharmonicity, ultrahigh mechanical quality factors, and small footprints achievable in this platform could enable quantum-nonlinear phononics for quantum information processing and transduction.
Joshua E. Castro, Eber Nolasco-Martinez, Paolo Pintus, Zeyu Zhang, Boqiang Shen, Theodore Morin, Lillian Thiel, Trevor J. Steiner, Nicholas Lewis, Sahil D. Patel, John E. Bowers, David M. Weld, Galan Moody In the last decade, remarkable advances in integrated photonic technologies have enabled table-top experiments and instrumentation to be scaled down to compact chips with significant reduction in size, weight, power consumption, and cost. Here, we demonstrate an integrated continuously tunable laser in a heterogeneous gallium arsenide-on-silicon nitride (GaAs-on-SiN) platform that emits in the far-red radiation spectrum near 780 nm, with 20 nm tuning range, <6 kHz intrinsic linewidth, and a >40 dB side-mode suppression ratio. The GaAs optical gain regions are heterogeneously integrated with low-loss SiN waveguides. The narrow linewidth lasing is achieved with an extended cavity consisting of a resonator-based Vernier mirror and a phase shifter. Utilizing synchronous tuning of the integrated heaters, we show mode-hop-free wavelength tuning over a range larger than 100 GHz (200 pm). To demonstrate the potential of the device, we investigate two illustrative applications: (i) the linear characterization of a silicon nitride microresonator designed for entangled-photon pair generation, and (ii) the absorption spectroscopy and locking to the D1 and D2 transition lines of 87-Rb. The performance of the proposed integrated laser holds promise for a broader spectrum of both classical and quantum applications in the visible range, encompassing communication, control, sensing, and computing.
J. A. Li, H. Han, X. P. Huang, B.Y. Tang, K. Guo, J. Q. Huang, S. Y. Xiong, W. R. Yu, Z. J. Zhang, J. B. Yang, B. Liu, H. Chen, Z. K. Lu In this paper, we propose a quantum clock synchronization (QCS) network scheme with silicon-chip dual-pumped entangled photon source. This scheme couples two pump beams into the silicon-based waveguide, where degenerate and non-degenerate spontaneous four-wave mixing (SFWM) occurs, generating entanglement between one signal channel and three idler channels. The entangled photons are distributed to remote users through the wavelength division multiplexing strategy to construct an entanglement distribution network, and the round-trip QCS is adopted to realize a QCS network that can serve multiple users. A proof-of-principle QCS network experiment is implemented among the server and multiple users (Alice, Bob, and Charlie) for 11.1 hours, where Alice and Charlie are 10 km away from the server and Bob is 25 km away from the server. The lowest time deviations (TDEV) between the server and each user (Alice, Bob, and Charlie) are 1.57 ps, 0.82 ps and 2.57 ps at the average time of 8000 s, 8000 s and 800 s respectively. The results show that the QCS network scheme with dual-pumped SFWM photon source proposed by us achieves high accuracy, and the channel resources used by n users are reduced by about 30% compared with other round-trip QCS schemes.
The development of quantum networks is paramount towards practical and secure communications. Quantum digital signatures (QDS) offer an information-theoretically secure solution for ensuring data integrity, authenticity, and non-repudiation, rapidly growing from proof-of-concept to robust demonstrations. However, previous QDS systems relied on expensive and bulky optical equipment, limiting large-scale deployment and reconfigurable networking construction. Here, we introduce and verify a chip-based QDS network, placing the complicated and expensive measurement devices in the central relay while each user needs only a low-cost transmitter. We demonstrate the network with a three-node setup using an integrated encoder chip and decoder chip. By developing a 1-decoy-state one-time universal hash-QDS protocol, we achieve a maximum signature rate of 0.0414 times per second for a 1 Mbit file over fiber distances up to 200 km, surpassing all current state-of-the-art QDS experiments. This study validates the feasibility of chip-based QDS, paving the way for large-scale deployment and integration with existing fiber infrastructure.
We study the Lamb shift by considering the steady-state heat current through two coupled two-level atoms, which, respectively, interact with a heat reservoir at a certain temperature. It is found that the Lamb shift significantly alters the energy levels. In particular, it is shown that the heat current will approach an upper bound if the Lamb shift isn't considered, while the heat current will break the upper bound if the Lamb shift is considered. This finding can deepen our understanding of Lamb shift in the quantum thermodynamic field.
Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear equations with $N$ variables and condition number $\kappa$ can be solved on a quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially faster than any classical algorithms, its improvements and applications have been extensively investigated. The state-of-the-art quantum algorithm for this problem is due to Costa, An, Sanders, Su, Babbush, and Berry (2022), with optimal query complexity $\Theta(\kappa)$. An important question left is whether parallelism can bring further optimization. In this paper, we study the limitation of parallel quantum computing on this problem. We show that any quantum algorithm for solving systems of linear equations with time complexity $\operatorname{poly}(\log(N), \kappa)$ has a lower bound of $\Omega(\kappa)$ on the depth of queries, which is tight up to a constant factor.
The advantage distillation (AD) method has proven effective in improving the performance of quantum key distribution (QKD). In this paper, we introduce the AD method into a recently proposed asynchronous measurement-device-independent (AMDI) QKD protocol, taking finite-key effects into account. Simulation results show that the AD method significantly enhances AMDIQKD, e.g., extending the transmission distance by 16 km with a total pulse count of N = 7.24*10^13, and enables AMDI-QKD, previously unable to generate keys, to generate keys with a misalignment error rate of 10%. As the AD method can be directly integrated into the current system through refined post-processing, our results facilitate the practical implementation of AMDI-QKD in various applications, particularly in scenarios with high channel losses and misalignment errors.
The Goos-Hänchen (GH) shift is a specifical optical phenomenon that describes a shift parallel to the reflected light inside the plane of incidence, when a finite-width light undergoes total internal reflection at the interface of medium. Although the GH shift in optics has been widely observed experimentally, its generalization remains uncovered completely in relativistic quantum mechanics for the existence of Klein's paradox. Recently, Wang has solved Klein's paradox based on the different solutions adpoted for Dirac's equation with step potential in corresponding energy regions \hrefhttps://dx.doi.org/10.1088/2399-6528/abd340[J. Phys. Commun. \bf 4, 125010 (2020)]. In the light of Wang's method, we calculate the GH shift for Dirac fermions under relativistic conditions when they are incident obliquely on a three-dimensional infinite potential barrier. Furthermore, we find that the relativistic quantum GH shift can be negative, which is different from the non-relativistic case.
Quantum illumination is an entanglement-based target detection protocol that provides quantum advantages despite the presence of entanglement-breaking noise. However, the advantage of traditional quantum illumination protocols is limited to impractical scenarios with low transmitted power and simple target configurations. In this work, we propose a quantum illumination network to overcome the limitations, via designing a transmitter array and a single receiver antenna. Thanks to multiple transmitters, quantum advantage is achieved even with a high total transmitted power. Moreover, for single-parameter estimation, the advantage of network over a single transmitter case increases with the number of transmitters before saturation. At the same time, complex target configurations with multiple unknown transmissivity or phase parameters can be resolved. Despite the interference of different returning signals at the single antenna and photon-loss due to multiple-access channel, we provide two types of measurement design, one based on parametric-amplification and one based on the correlation-to-displacement conversion (CtoD) to achieve a quantum advantage in estimating all unknown parameters. We also generalize the parameter estimation scenario to a general hypothesis testing scenario, where the six-decibel quantum illumination advantage is achieved at a much greater total probing power.
Wonjae Lee, Vincent S. Liu, Zhelun Zhang, Sangha Kim, Ruotian Gong, Xinyi Du, Khanh Pham, Thomas Poirier, Zeyu Hao, James H. Edgar, Philip Kim, Chong Zu, Emily J. Davis, Norman Y. Yao The negatively charged boron vacancy ($\mathrm{V}_{\mathrm{B}}^-$) in hexagonal boron nitride (hBN) has garnered significant attention among defects in two-dimensional materials. This owes, in part, to its deterministic generation, well-characterized atomic structure, and optical polarizability at room temperature. We investigate the latter through extensive measurements probing both the ground and excited state polarization dynamics. We develop a semiclassical model based on these measurements that predicts a near-unity degree of spin polarization, surpassing other solid-state spin defects under ambient conditions. Building upon our model, we include the presence of nuclear spin degrees of freedom adjacent to the $\mathrm{V}_{\mathrm{B}}^-$ and perform a comprehensive set of Lindbladian numerics to investigate the hyperfine-induced polarization of the nuclear spins. Our simulations predict a number of important features that emerge as a function of magnetic field which are borne out by experiment.
Mid-circuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement (SPAM) noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest.
The reference-frame-independent quantum key distribution (RFI-QKD) protocol enables QKD systems to function effectively despite slowly varying reference frames, offering a distinct advantage in practical scenarios, particularly in mobile platforms. In this study, we successfully distribute secure key bits over a 250 km optical fiber distance by developing an RFI-QKD system with a repetition rate of 150 MHz. Benefiting from high repetition rate, we achieve a finite-key secret key rate of 49.65 bit/s at a distance of 200 km, which is more than three times higher than state-of-the-art systems. Our work dramatically extends the transmission distance and enhances the secret key rate of RFI-QKD, significantly promoting its practical application.
We propose an optomechanical scheme for reaching quantum entanglement in vibration polaritons. The system involves $N$ molecules, whose vibrations can be fairly entangled with plasmonic cavities. We find that the vibration-photon entanglement can exist at room temperature and is robust against thermal noise. We further demonstrate the quantum entanglement between the vibrational modes through the plasmonic cavities, which shows a delocalized nature and an incredible enhancement with the number of molecules. The underlying mechanism for the entanglement is attributed to the strong vibration-cavity coupling which possesses collectivity. Our results provide a molecular optomechanical scheme which offers a promising platform for the study of noise-free quantum resources and macroscopic quantum phenomena.
The rich information of electron energy-loss spectroscopy (EELS) comes from the complex inelastic scattering process whereby fast electrons transfer energy and momentum to atoms, exciting bound electrons from their ground states to higher unoccupied states. To quantify EELS, the common practice is to compare the cross-sections integrated within an energy window or fit the observed spectrum with theoretical differential cross-sections calculated from a generalized oscillator strength (GOS) database with experimental parameters. The previous Hartree-Fock-based and DFT-based GOS are calculated from Schrödinger's solution of atomic orbitals, which does not include the full relativistic effects. Here, we attempt to go beyond the limitations of the Schrödinger solution in the GOS tabulation by including the full relativistic effects using the Dirac equation within the local density approximation, which is particularly important for core-shell electrons of heavy elements with strong spin-orbit coupling. This has been done for all elements in the periodic table (up to Z = 118) for all possible excitation edges using modern computing capabilities and parallelization algorithms. The relativistic effects of fast incoming electrons were included to calculate cross-sections that are specific to the acceleration voltage. We make these tabulated GOS available under an open-source license to the benefit of both academic users as well as allowing integration into commercial solutions.
We study the dynamical evolution of cold atoms in crossed optical dipole trap theoretically and experimentally. The atomic transport process is accompanied by two competitive kinds of physical mechanics, atomic loading and atomic loss. The loading process normally is negligible in the evaporative cooling experiment on the ground, while it is significant in the preparation of ultra-cold atoms in the space station. Normally, the atomic loading process is much weaker than the atomic loss process, and the atomic number in the center region of the trap decreases monotonically, as reported in previous research. However, when the atomic loading process is comparable to the atomic loss process, the atomic number in the center region of the trap will initially increase to a maximum value and then slowly decrease, and we have observed the phenomenon first. The increase of atomic number in the center region of the trap shows the presence of the loading process, and this will be significant especially under microgravity conditions. We build a theoretical model to analyze the competitive relationship, which coincides with the experimental results well. Furthermore, we have also given the predicted evolutionary behaviors under different conditions. This research provides a solid foundation for further understanding of the atomic transport process in traps. The analysis of loading process is of significant importance for the preparation of ultra-cold atoms in a crossed optical dipole trap under microgravity conditions.
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully used to solve the time-dependent Schrödinger equation exactly in harmonic systems and variationally in anharmonic systems. For evaluating typical observables, such as position or kinetic energy, it is sufficient to consider orthonormal Hagedorn functions with a single Gaussian center. Here, we instead derive various relations between Hagedorn bases associated with different Gaussians, including their overlaps, which are necessary for evaluating quantities nonlocal in time, such as time correlation functions needed for computing spectra. First, we use the Bogoliubov transformation to obtain commutation relations between the ladder operators associated with different Gaussians. Then, instead of using numerical quadrature, we employ these commutation relations to derive exact recurrence relations for the overlap integrals between Hagedorn functions with different Gaussian centers. Finally, we present numerical experiments that demonstrate the accuracy and efficiency of our algebraic method as well as its suitability to treat problems in spectroscopy and chemical dynamics.
Semi-quantum key distribution (SQKD) allows sharing random keys between a quantum user and a classical user. However, implementing classical user operations is challenging, posing a hurdle to achieving the Single-state protocol. By using the "selective modulation" method, the feasibility of SQKD is verified in principle. The proposal of the selective modulation method enables the realization of other protocols for SQKD. To advance experimental progress in SQKD, we propose and implement a phase-encoded semi-quantum key distribution system based on the Single-state protocol and the "selective modulation" method. The system operates at a frequency of 100MHz and an average photon number of 0.1. The interference contrast achieved 96.52%, the average quantum bit error rate was 1.19%, and the raw key rate reached 88Kbps. Our experimental results demonstrate the feasibility and stability of the proposed phase-encoded semi-quantum key distribution system. Furthermore, by leveraging the "selective modulation" scheme proposed in this paper, we develop a comprehensive theoretical description of selective modulation. Through an analysis of quantum state evolution, we assess the security of our system, ultimately demonstrating its resilience against attacks targeting quantum states. The classical user of our system requires only two optical devices, significantly reducing the equipment requirements and enhancing its application potential. This work validates the feasibility of semi-quantum key distribution experiments and provides ideas for future research on semi-quantum key distribution experiments and security studies.
We revisit the Feynman approach to the Josephson effect, which employs a pair of linear coupling equations for its modeling. It is found that while the exact solutions can account for the AC Josephson effect when the coupling strength is significantly less than the voltage, they fail to produce the DC Josephson effect in any practical scenario. To address this fundamental discrepancy, we derive the coupled Ginzburg-Landau (GL) equations for two interconnected superconductors based on BCS theory. These equations reveal that the nonlinear coupling, which is overlooked in the Feynman method, is crucial in describing the spontaneous symmetry breaking in superconductors, a critical factor for achieving the DC Josephson effect. When the coupled GL equations are applied to a double junction, a sawtooth current pattern emerges, a result unattainable via the Feynman approach.
Recently, both global and local classical randomness-assisted projective measurement protocols have been employed to share Bell nonlocality of an entangled state among multiple sequential parties. Unlike Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering exhibits distinct asymmetric characteristics and serves as the necessary quantum resource for one-sided device-independent quantum information tasks. In this work, we propose a projective measurement protocol and investigate the shareability of EPR steering with steering radius criterion theoretically and experimentally. Our results reveal that arbitrarily many independent parties can share one-way steerability using projective measurements, even when no shared randomness is available. Furthermore, by leveraging only local randomness, asymmetric two-way steerability can also be shared. Our work not only deepens the understanding of the role of projective measurements in sharing quantum correlations but also opens up a new avenue for reutilizing asymmetric quantum correlations.
Certain pure-state symmetry-protected topological orders (SPT) can be used as a resource for transmitting quantum information. Here, we investigate the ability to transmit quantum information using decohered SPT states, and relate this property to the "strange correlation functions" which diagnose quantum many-body orders in these mixed-states. This perspective leads to the identification of a class of quantum channels -- termed symmetry-decoupling channels -- which do not necessarily preserve any weak or strong symmetries of the SPT state, but nevertheless protect quantum many-body order in the decohered mixed-state. We quantify the ability to transmit quantum information in decohered SPT states through the coherent quantum information, whose behavior is generally related to a decoding problem, whereby local measurements in the system are used to attempt to "learn" the symmetry charge of the SPT state before decoherence.
We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a noiseless shallow quantum circuit and rigorously prove that any classical neural network with bounded connectivity requires logarithmic depth to output correctly with a larger-than-exponentially-small probability. This unconditional near-optimal quantum-classical separation originates from the quantum nonlocality property that distinguishes quantum circuits from their classical counterparts. We further derive the noise thresholds for demonstrating such a separation on near-term quantum devices under the depolarization noise model. We prove that this separation will persist if the noise strength is upper bounded by an inverse polynomial with respect to the system size, and vanish if the noise strength is greater than an inverse polylogarithmic function. In addition, for quantum devices with constant noise strength, we prove that no super-polynomial classical-quantum separation exists for any classification task defined by shallow Clifford circuits, independent of the structures of the circuits that specify the learning models.
Matrix geometric means between two positive definite matrices can be defined equivalently from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain optimisation problems. This diversity already suggests the potential for varied applications, as well as acting as a bridge between different domains. Here we devise new quantum subroutines to efficiently prepare quantum unitary operators that embed the standard matrix geometric mean and its generalisations called the weighted matrix geometric mean. This enables the construction of solutions to the algebraic Riccati equation, which is an important class of nonlinear systems of equations that appears in machine learning, optimal control, estimation, and filtering. Using these subroutines, we present a new class of quantum learning algorithms called quantum geometric mean metric learning. This has applications in efficiently finding the best distance measure and solving classification problems in the weakly supervised limit and for anomaly detection, for both classical and quantum problems. We also show how our method can be generalised to a particular p^th-order system of nonlinear equations. These quantum subroutines for matrix geometric means are also useful in other areas of quantum information. For example, we show how to use them in the estimation of geometric Renyi relative entropies and the Uhlmann fidelity by means of the Fuchs-Caves observable. In particular, our quantum algorithms for estimating the Uhlmann and Matsumoto fidelities have optimal dependence on the precision. Finally, we provide a BQP-complete problem based on matrix geometric means that can be solved by our subroutines, thus characterising their computational capability.
Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing, although atomicity is still commonly assumed, it has not been seriously studied, and a rigorous basis for it is missing. Classical results on atomicity do not directly carry over to distributed quantum computing, due to new challenges caused by quantum entanglement and the measurement problem from the underlying quantum mechanics. In this paper, we initiate the study of atomicity in distributed quantum computing. A formal model of (non-atomic) distributed quantum system is established. Based on the Dijkstra-Lamport condition, the system dynamics and observable dynamics of a distributed quantum system are defined, which correspond to the quantum state of and classically observable events in the system, respectively. Within this framework, we prove that local actions can be regarded as if they were atomic, up to the observable dynamics of the system.
Richen Xiong, Samuel L. Brantly, Kaixiang Su, Jacob H. Nie, Zihan Zhang, Rounak Banerjee, Hayley Ruddick, Kenji Watanabe, Takashi Taniguchi, Sefaattin Tongay, Cenke Xu, Chenhao Jin Spin and charge are the two most important degrees of freedom of electrons. Their interplay lies at the heart of numerous strongly correlated phenomena including Hubbard model physics and high temperature superconductivity. Such interplay for bosons, on the other hand, is largely unexplored in condensed matter systems. Here we demonstrate a unique realization of the spin-1/2 Bose-Hubbard model through excitons in a semiconducting moiré superlattice. We find evidence of a transient in-plane ferromagnetic (FM-$xy$) order of exciton spin - here valley pseudospin - around exciton filling $\nu_{ex}$ = 1, which transitions into a FM-$z$ order both with increasing exciton filling and a small magnetic field of 10 mT. The phase diagram is different from the fermion case and is qualitatively captured by a simple phenomenological model, highlighting the unique consequence of Bose-Einstein statistics. Our study paves the way for engineering exotic phases of matter from spinor bosons, as well as for unconventional devices in optics and quantum information science.
We review our progress in developing a frequency reference with singly ionized lutetium and give estimates of the levels of inaccuracy we expect to achieve in the near future with both the $^1S_0\leftrightarrow{}^3D_1$ and $^1S_0\leftrightarrow{}^3D_2$ transitions. Based on established experimental results, we show that inaccuracies at the low $10^{-19}$ level are readily achievable for the $^1S_0\leftrightarrow{}^3D_1$ transition, and the frequency ratio between the two transitions is limited almost entirely by the BBR shift. We argue that the frequency ratio measured within the one apparatus provides a well-defined metric to compare and establish the performance of remotely located systems. For the measurement of an in situ frequency ratio, relativistic shifts drop out and both transitions experience the same electromagnetic environment. Consequently, the uncertainty budget for the ratio is practically identical to the uncertainty budgets for the individual transitions. If the ratios for two or more systems disagree we can be certain at least one of the clock assessments is incorrect. If they agree, subsequent comparisons on one transition would only differ by relativistic effects. Since motional effects are easily assessed and typically small for a heavy ion, only the differential gravitational red-shift will significantly contribute and this can be confirmed by comparison on the second transition.
Lillian B. Hughes, Simon A. Meynell, Weijie Wu, Shreyas Parthasarathy, Lingjie Chen, Zhiran Zhang, Zilin Wang, Emily J. Davis, Kunal Mukherjee, Norman Y. Yao, Ania C. Bleszynski Jayich Systems of spins with strong dipolar interactions and controlled dimensionality enable new explorations in quantum sensing and simulation. In this work, we investigate the creation of strong dipolar interactions in a two-dimensional ensemble of nitrogen-vacancy (NV) centers generated via plasma-enhanced chemical vapor deposition (PECVD) on (111)-oriented diamond substrates. We find that diamond growth on the (111) plane yields high incorporation of spins, both nitrogen and NV centers, where the density of the latter is tunable via the miscut of the diamond substrate. Our process allows us to form dense, preferentially aligned, 2D NV ensembles with volume-normalized AC sensitivity down to $\eta_{AC}$ = 810 pT um$^{3/2}$ Hz$^{-1/2}$. Furthermore, we show that (111) affords maximally positive dipolar interactions amongst a 2D NV ensemble, which is crucial for leveraging dipolar-driven entanglement schemes and exploring new interacting spin physics.
Explicit mathematical reconstructions of quantum networks play a significant role in developing quantum information science. However, tremendous parameter requirements and physical constraint implementations have become computationally non-ignorable encumbrances. In this work, we propose an efficient method for quantum network tomography by learning isometries on the Stiefel manifold. Tasks of reconstructing quantum networks are tackled by solving a series of unconstrained optimization problems with significantly fewer parameters. The stepwise isometry estimation shows the capability for providing information of the truncated quantum network while processing the tomography. Remarkably, this method enables the dimension-reduced quantum network tomography by reducing the ancillary dimensions of isometries with bounded error. As a result, our proposed method exhibits high accuracy and efficiency.
Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal verification of the correctness of recursively defined quantum circuits. The soundness and (relative) completeness of the proof system are established. To demonstrating its effectiveness, a series of application examples of the proof system are given, including (multi-qubit) controlled gates, a quantum circuit generating (multi-qubit) GHZ (Greenberger-Horne-Zeilinger) states, recursive definition of quantum Fourier transform, quantum state preparation, and quantum random-access memories (QRAM).
We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an optimal (over all global testers) local tester acting only on the other part. This suggests a canonical local tester for entanglement spectra (i.e., Schmidt coefficients), and reveals that purified samples offer no advantage in property testing of mixed states. As applications, we show new sample lower bounds, e.g.: - The first general lower bound $\Omega(r/\epsilon^2)$ for testing whether the Schmidt rank of a bipartite state is at most $r$ or $\epsilon$-far, settling an open question raised in Montanaro and de Wolf (ToC 2016). - A lower bound $\Omega((\sqrt n+\sqrt r)\cdot\sqrt r/\epsilon^2)$ for testing whether an $n$-partite state is a matrix product state of bond dimension $r$ or $\epsilon$-far, improving the prior lower bound $\Omega(\sqrt n/\epsilon^2)$ by Soleimanifar and Wright (SODA 2022) and $\Omega(\sqrt r)$ by Aaronson et al. (ITCS 2024). Further, when perfect completeness is required, we provide a matching lower bound $\Omega(r^2/\epsilon^2)$ with respect to $r$ and $\epsilon$. - A matching lower bound $\Omega(d/\epsilon^2)$ for testing whether a $d$-dimensional bipartite state is maximally entangled or $\epsilon$-far, showing that the algorithm of O'Donnell and Wright (STOC 2015) is optimal for this task. Beyond sample complexity, we also contribute new query lower bounds: - A query lower bound $\tilde\Omega(\sqrt{d/\Delta})$ for the $d$-dimensional entanglement entropy problem with gap $\Delta$, improving the prior best $\Omega(\sqrt[4]{d})$ by She and Yuen (ITCS 2023) and $\tilde\Omega(1/\sqrt\Delta)$ by Wang and Zhang (2023) and Weggemans (2024). Further, our central result can be extended when the tested state is mixed: one-way LOCC is sufficient to realize the optimal tester.
Quantum cluster state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum cluster states among physically distant nodes has gained increasing popularity owing to its potential in expanding current quantum applications in scale. Existing research on this topic relies on a two-step approach: first distributing low-dimension elementary entanglement to target nodes, and then fusing them into a high-dimension quantum cluster state. However, most existing studies focus solely on minimizing costs (e.g., the number of elementary entanglements consumed) to entangle target nodes, while neglecting the structure of the final quantum cluster state. This can easily result in weak system entanglement, jeopardizing the cluster state under partial measurement or noises. In this paper, we aim to establish any arbitrary quantum cluster states of strong entanglement structures at a much lower cost than the state of the art. The method is to search for and establish an alternative state to the target state that is of lowest cost in creation. Subsequently, we transform such an alternative state back to the target state via compressed single-qubit Clifford operations. To verify the performance of our developed algorithm, we conduct comprehensive simulations based on an open dataset containing all cluster state structures up to 8 qubits. The results demonstrate fast algorithm convergence, an increased success probability in distributing any cluster states, and 53.57% saving in ERP cost compared with the state-of-the-art baseline.
It is well known that a constant energy density of the vacuum produces a negative pressure. We show that, in the presence of special boundaries for the photon field, the virtual photons in the quantum vacuum may induce a negative pressure of this type. In this context, we find in particular that an anomalous quantum vacuum radiation is responsible for the appearance of this negative pressure in a system, which generates the tangential Casimir force [Z. Zhang, New J. Phys. 24 (2022) 113036] experienced by parallel conducting plates.
Single vibronic level (SVL) fluorescence spectroscopy contributes to the understanding of molecular vibrational structures and relaxation processes. Here, we present a practical method for computing SVL fluorescence spectra of polyatomic molecules from arbitrary initial vibrational levels. This method, which combines a time-dependent approach using Hagedorn wavepackets with accurate evaluation of electronic structure, captures both mode distortion and Duschinsky rotation. We apply the method to compute SVL spectra of anthracene by performing wavepacket dynamics on a 66- dimensional harmonic potential energy surface constructed from density functional theory calculations. With the Hagedorn approach, we not only reproduce the previously reported simulation results for singly excited $12^{1}$ and $\overline{11}^{1}$ levels, but also are able to compute SVL spectra from multiply excited levels in good agreement with experiments. All spectra were obtained from the same wavepacket trajectory without any additional propagation beyond what is required for ground-state emission spectra.
In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Whereas computing all contributing Franck-Condon factors individually becomes impractical in large systems, a time-dependent formalism has not been applied to simulate emission from arbitrary initial vibrational levels. Here, we use Hagedorn functions, which are products of a Gaussian and carefully generated polynomials, to represent SVL initial states. In systems where the potential is at most quadratic, the Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket. Having developed an efficient recursive algorithm to compute the overlaps between two Hagedorn wavepackets, we can now evaluate emission spectra from arbitrary vibronic levels using a single trajectory. We validate the method in two-dimensional global harmonic models by comparing it with quantum split-operator calculations. Additionally, we study the effects of displacement, distortion (squeezing), and Duschinsky rotation on SVL spectra. Finally, we demonstrate the applicability of the Hagedorn approach to high-dimensional systems on an example of displaced, distorted, and Duschinsky-rotated harmonic model with 100 degrees of freedom.
We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique over traditional sideband spectroscopy allows us to detect stray fields of $0.01\,\mathrm{V/m}$ on a timescale of a few minutes and detect differential phases of $5\,\mu\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in the vibrational ground-state. The technique we introduce can be readily implemented in any ion trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way
The performance of superconducting quantum circuits is primarily limited by dielectric loss due to interactions with two-level systems (TLS). State-of-the-art circuits with engineered material interfaces are approaching a limit where dielectric loss from bulk substrates plays an important role. However, a microscopic understanding of dielectric loss in crystalline substrates is still lacking. In this work, we show that boron acceptors in silicon constitute a strongly coupled TLS bath for superconducting circuits. We discuss how the electronic structure of boron acceptors leads to an effective TLS response in silicon. We sweep the boron concentration in silicon and demonstrate the bulk dielectric loss limit from boron acceptors. We show that boron-induced dielectric loss can be reduced in a magnetic field due to the spin-orbit structure of boron. This work provides the first detailed microscopic description of a TLS bath for superconducting circuits, and demonstrates the need for ultrahigh purity substrates for next-generation superconducting quantum processors.
The spin polarization of photoelectrons induced by an intense linearly polarized laser field is investigated using numerical solutions of the time-dependent Schrödinger equation in companion with our analytic treatment via the spin-resolved strong-field approximation and classical trajectory Monte Carlo simulations. We demonstrate that, even though the total polarization vanishes upon averaging over the photoelectron momentum, momentum-resolved spin polarization is significant, typically exhibiting a vortex structure relative to the laser polarization axis. The polarization arises from the transfer of spin-orbital coupling in the bound state to the spin-correlated quantum orbits in the continuum. The rescattering of photoelectrons at the atomic core plays an important role in forming the polarization vortex structure, while there is no significant effect of the spin-orbit coupling during the continuum dynamics. Furthermore, spin-polarized electron holography is demonstrated, feasible for extracting fine structural information about the atom.
Zong-Kai Liu, Kong-Hao Sun, Albert Cabot, Federico Carollo, Jun Zhang, Zheng-Yuan Zhang, Li-Hua Zhang, Bang Liu, Tian-Yu Han, Qing Li, Yu Ma, Han-Chao Chen, Igor Lesanovsky, Dong-Sheng Ding, Bao-Sen Shi Quantum many-body systems near phase transitions respond collectively to externally applied perturbations. We explore this phenomenon in a laser-driven dissipative Rydberg gas that is tuned to a bistable regime. Here two metastable phases coexist, which feature a low and high density of Rydberg atoms, respectively. The ensuing collective dynamics, which we monitor in situ, is characterized by stochastic collective jumps between these two macroscopically distinct many-body phases. We show that the statistics of these jumps can be controlled using a dual-tone microwave field. In particular, we find that the distribution of jump times develops peaks corresponding to subharmonics of the relative microwave detuning. Our study demonstrates the control of collective statistical properties of dissipative quantum many-body systems without the necessity of fine-tuning or of ultra cold temperatures. Such robust phenomena may find technological applications in quantum sensing and metrology.
As an essential component of state-of-the-art quantum technologies, fast and efficient quantum measurements are in persistent demand over time. We present a proof-of-principle experiment on a new dimensionless pseudo-spin pointer based on weak measurement. In the context of optical parameter estimation, we demonstrate that the parametric distribution's moment is obtained experimentally by employing the dimensionless pointer without measuring the distribution literally. In addition to the sheer liberation of experimental expense, the photon-countering-based pointer is well-calibrated for the detection of weak signals. We show that for signals $3$-$4$ orders of weaker in strength than the area-array camera method, an order of improvement in precision is achieved experimentally.
The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT problems (All-SAT). G-QAOA is less resource-intensive and more adaptable for 3-SAT and Max-SAT than Grover's algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.
Stochastic master equations are often used to describe conditional spin squeezing of atomic ensemble, but are limited so far to the systems with few atoms due to the exponentially increased Hilbert space. In this article, we present an exact numerical solution of these equations for systems with identical atoms by mapping identical density matrix elements to a single quantity characterized by collective quantum numbers, and apply it to the system with hundred atoms in a bad cavity subject to a homodyne detection. We demonstrate that the spin squeezing can be vividly illustrated by the Gaussian-like distribution of the collective density matrix elements, and we examine the influence of the probe field strength and polarization, the detection efficiency, the spontaneous emission rate and the number of atoms. Our exact approach can play an important role in gauging the approximate approaches applied for systems with more atoms, such as Gaussian-state formalism and stochastic mean-field approach, and it permits also exploration of entanglement effects beyond these approaches.
Subsystems of a composite system in a pure state generally exist in mixed states and undergo changes with the overall state. This phenomenon arises from the coherence of the entire system and represents a crucial distinction between quantum and classical systems. Such a quantum property can enhance the work of an Otto heat engine, where two coupled qubits serve as the working substance, allowing situations in which negative work output initially occurred to now yield positive work. We utilize the imagery of Maxwell's demon to explain the reason for positive work in this Otto cycle, attributing it to the increased coherence after the mutual measurement of the two subsystems. Conversely, the quantum measurement-erase cycle typically outputs negative work, attributed to the decoherence of the instrument during the measurement process.
We study charge pumping in generic non-Hermitian settings and show that quantized charge pumping is only guaranteed under a biorthogonal formalism therein, where the charge transport is evaluated using the left and right eigenvectors of the non-Hermitian Hamiltonian. Specifically, for biorthogonal charge pumping in generic one-dimensional non-Hermitian models, we demonstrate how quantized transport is related to the Chern number in the parameter space. When the non-Hermitian model possesses the non-Hermitian skin effect, under which Bloch states in the bulk are deformed and localize toward boundaries, we propose a scenario where the pumped charge is related to the non-Bloch Chern number defined in the parameter space involving the generalized Brillouin zone. We illustrate the validity of our analytic results using concrete examples and, in the context of the biorthogonal charge pumping, discuss in detail a recent experiment where quantized charge pumping was observed in a lossy environment.
Entropy is a measure of the randomness of a system. Estimating the entropy of a quantum state is a basic problem in quantum information. In this paper, we introduce a time-efficient quantum approach to estimating the von Neumann entropy $S(\rho)$ and Rényi entropy $S_\alpha(\rho)$ of an $N$-dimensional quantum state $\rho$, given access to independent samples of $\rho$. Specifically, we provide the following: 1. A quantum estimator for $S(\rho)$ with time complexity $\tilde O(N^2)$, improving the prior best time complexity $\tilde O(N^6)$ by Acharya, Issa, Shende, and Wagner (2020) and Bavarian, Mehraba, and Wright (2016). 2. A quantum estimator for $S_\alpha(\rho)$ with time complexity $\tilde O(N^{4/\alpha-2})$ for $0<\alpha<1$ and $\tilde O(N^{4-2/\alpha})$ for $\alpha>1$, improving the prior best time complexity $\tilde O(N^{6/\alpha})$ for $0<\alpha<1$ and $\tilde O(N^6)$ for $\alpha>1$ by Acharya, Issa, Shende, and Wagner (2020), though at a cost of a slightly larger sample complexity. Moreover, these estimators are naturally extensible to the low-rank case. We also provide a sample lower bound for estimating $S_{\alpha}(\rho)$. Technically, our method is quite different from the previous ones that are based on weak Schur sampling and Young diagrams. At the heart of our construction, is a novel tool called samplizer, which can "samplize" a quantum query algorithm to a quantum algorithm with similar behavior using only samples of quantum states; this suggests a unified framework for estimating quantum entropies. Specifically, when a quantum oracle $U$ block-encodes a mixed quantum state $\rho$, any quantum query algorithm using $Q$ queries to $U$ can be samplized to a $\delta$-close (in the diamond norm) quantum algorithm using $\tilde\Theta(Q^2/\delta)$ samples of $\rho$. Moreover, this samplization is proven to be optimal, up to a polylogarithmic factor.
Parameterized Quantum Circuits (PQC) have obtained increasing popularity thanks to their great potential for near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Achieving quantum advantages usually requires a large number of qubits and quantum circuits with enough capacity. However, limited coherence time and massive quantum noises severely constrain the size of quantum circuits that can be executed reliably on real machines. To address these two pain points, we propose QuantumSEA, an in-time sparse exploration for noise-adaptive quantum circuits, aiming to achieve two key objectives: (1) implicit circuits capacity during training - by dynamically exploring the circuit's sparse connectivity and sticking a fixed small number of quantum gates throughout the training which satisfies the coherence time and enjoy light noises, enabling feasible executions on real quantum devices; (2) noise robustness - by jointly optimizing the topology and parameters of quantum circuits under real device noise models. In each update step of sparsity, we leverage the moving average of historical gradients to grow necessary gates and utilize salience-based pruning to eliminate insignificant gates. Extensive experiments are conducted with 7 Quantum Machine Learning (QML) and Variational Quantum Eigensolver (VQE) benchmarks on 6 simulated or real quantum computers, where QuantumSEA consistently surpasses noise-aware search, human-designed, and randomly generated quantum circuit baselines by a clear performance margin. For example, even in the most challenging on-chip training regime, our method establishes state-of-the-art results with only half the number of quantum gates and ~2x time saving of circuit executions. Codes are available at https://github.com/VITA-Group/QuantumSEA.
Weitang Li, Zhi Yin, Xiaoran Li, Dongqiang Ma, Shuang Yi, Zhenxing Zhang, Chenji Zou, Kunliang Bu, Maochun Dai, Jie Yue, Yuzong Chen, Xiaojin Zhang, Shengyu Zhang Quantum computing, with its superior computational capabilities compared to classical approaches, holds the potential to revolutionize numerous scientific domains, including pharmaceuticals. However, the application of quantum computing for drug discovery has primarily been limited to proof-of-concept studies, which often fail to capture the intricacies of real-world drug development challenges. In this study, we diverge from conventional investigations by developing \reva hybrid quantum computing pipeline tailored to address genuine drug design problems. Our approach underscores the application of quantum computation in drug discovery and propels it towards more scalable system. We specifically construct our versatile quantum computing pipeline to address two critical tasks in drug discovery: the precise determination of Gibbs free energy profiles for prodrug activation involving covalent bond cleavage, and the accurate simulation of covalent bond interactions. This work serves as a pioneering effort in benchmarking quantum computing against veritable scenarios encountered in drug design, especially the covalent bonding issue present in both of the case studies, thereby transitioning from theoretical models to tangible applications. Our results demonstrate the potential of a quantum computing pipeline for integration into real world drug design workflows.
Kunliang Bu, Sainan Huai, Zhenxing Zhang, Dengfeng Li, Yuan Li, Jingjing Hu, Xiaopei Yang, Maochun Dai, Tianqi Cai, Yi-Cong Zheng, Shengyu Zhang The unique property of tantalum (Ta), particularly its long coherent lifetime in superconducting qubits and its exceptional resistance to both acid and alkali, makes it promising for superconducting quantum processors. It is a notable advantage to achieve high-performance quantum processors with neat and unified fabrication of all circuit elements, including coplanar waveguides (CPW), qubits, and airbridges, on the tantalum film-based platform. Here, we propose a reliable tantalum airbridges with separate or fully-capped structure fabricated via a novel lift-off method, where a barrier layer with aluminium (Al) film is first introduced to separate two layers of photoresist and then etched away before the deposition of tantalum film, followed by cleaning with piranha solution to remove the residual photoresist on the chip. We characterize such tantalum airbridges as the control line jumpers, the ground plane crossovers and even coupling elements. They exhibit excellent connectivity, minimal capacitive loss, effectively suppress microwave and flux crosstalk and offer high freedom of coupling. Besides, by presenting a surface-13 tunable coupling superconducting quantum processor with median $T_1$ reaching above 100 $\mu$s, the overall adaptability of tantalum airbridges is verified. The median single-qubit gate fidelity shows a tiny decrease from about 99.95% for the isolated Randomized Benchmarking to 99.94% for the simultaneous one. This fabrication method, compatible with all known superconducting materials, requires mild conditions of film deposition compared with the commonly used etching and grayscale lithography. Meanwhile, the experimental achievement of non-local coupling with controlled-Z (CZ) gate fidelity exceeding 99.2% may further facilitate qLDPC codes, laying a foundation for scalable quantum computation and quantum error correction with entirely tantalum elements.
Braneshop, and
the US National Science Foundation.
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