We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as a two-dimensional grid of plaquettes, detailing the use of gauge fixing to reduce the degrees of freedom and simplify the Hamiltonian. We demonstrate how the system dynamics, ground states, and energy gaps can be computed using the continuous-variable approach to quantum computing. Our results indicate that it is feasible to study non-Abelian gauge theories with continuous variables, providing new avenues for understanding the real-time dynamics of quantum field theories.
We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ Majorana fermions with $q$-body fermion interaction with $q=4,6,8$ for a range of sparse parameter $k$. Using the peak of the Krylov complexity as a probe, we find change in behavior as we vary $k$ for various $q$. We argue that this captures the change from holographic to non-holographic behavior in the sparse SYK-type models such that model is holographic for all $k \ge k_{\text{min}}$.
We present a functional-based approach to compute thermal expectation values for actions expressed in the $G-\Sigma$ formalism, applicable to any time sequence ordering. Utilizing this framework, we analyze the linear response to an electric field in various Sachdev-Ye-Kitaev (SYK) chains. We consider the SYK chain where each dot is a complex $q/2$-body interacting SYK model, and we allow for $r/2$-body nearest-neighbor hopping where $r=\kappa q$. We find exact analytical expressions in the large-$q$ limit for conductivities across all temperatures at leading order in $1/q$ for three cases, namely $\kappa = \{ 1/2, 1, 2\}$. When $\kappa = \{1/2, 1\}$, we observe linear-in-temperature $T$ resistivities at low temperatures, indicative of strange metal behavior. Conversely, when $\kappa = 2$, the resistivity diverges as a power law at low temperatures, namely as $1/T^2$, resembling insulating behavior. As $T$ increases, there is a crossover to Fermi liquid behavior ($\sim T^2$) at the minimum resistivity. Beyond this, another crossover occurs to strange metal behavior ($\sim T$). In comparison to previous linear-in-$T$ results in the literature, we also show that the resistivity behavior exists even below the MIR bound, indicating a true strange metal instead of a bad metal. In particular, we find for the $\kappa = 2$ case a smooth crossover from an insulating phase to a Fermi liquid behavior to a true strange metal and eventually becoming a bad metal as temperature increases. We extend and generalize previously known results on resistivities to all temperatures, do a comparative analysis across the three models where we highlight the universal features and invoke scaling arguments to create a physical picture out of our analyses. Remarkably, we find a universal maximum DC conductivity across all three models when the hopping coupling strength becomes large.
We study the preparation of thermal states of the dense and sparse Sachdev-Ye-Kitaev (SYK) model using a variational quantum algorithm for $6 \le N \le 12$ Majorana fermions over a wide range of temperatures. Utilizing IBM's 127-qubit quantum processor, we perform benchmark computations for the dense SYK model with $N = 6$, showing good agreement with exact results. The preparation of thermal states of a non-local random Hamiltonian with all-to-all coupling using the simulator and quantum hardware represents a significant step toward future computations of thermal out-of-time order correlators in quantum many-body systems.
The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k\ll N^{3}/24$ (where $k$ is the total number of interaction terms times 1/$N$) using second-order Trotter method and Jordan-Wigner encoding is found to be $\widetilde{\mathcal{O}}(k^{p}N^{3/2} \log N (\mathcal{J}t)^{3/2}\varepsilon^{-1/2})$ where $t$ is the simulation time, $\varepsilon$ is the desired error in the implementation of the unitary $U = \exp(-iHt)$, $\mathcal{J}$ is the disorder strength, and $p < 1$. This complexity implies that with less than a hundred logical qubits and about $10^{6}$ gates, it will be possible to achieve an advantage in this model and simulate real-time dynamics up to scrambling time.
Krylov complexity has recently gained attention where the growth of operator complexity in time is measured in terms of the off-diagonal operator Lanczos coefficients. The operator Lanczos algorithm reduces the problem of complexity growth to a single-particle semi-infinite tight-binding chain (known as the Krylov chain). Employing the phenomenon of Anderson localization, we propose the phenomenology of inverse localization length on the Krylov chain that undergoes delocalization/localization transition on the Krylov chain while the physical system undergoes ergodicity breaking. On the Krylov chain we find delocalization in an ergodic regime, as we show for the SYK model, and localization in case of a weakly ergodicity-broken regime. Considering the dynamics beyond scrambling, we find a collapse across different operators in the ergodic regime. We test for two settings: (1) the coupled SYK model, and (2) the quantum East model. Our findings open avenues for mapping ergodicity/weak ergodicity-breaking transitions to delocalization/localization phenomenology on the Krylov chain.
It has been known that the large-$q$ complex SYK model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-$q$ complex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-$q$ limit at low temperatures, adhering to the Maldacena-Shenker-Stanford bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the "very" low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be taken to make the connection robust.
We study the SYK model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the gate complexity of the time evolution using the first-order product formula for $N$ Majorana fermions is $\mathcal{O}(N^5 J^{2}t^2/\epsilon)$ where $J$ is the dimensionful coupling parameter, $t$ is the evolution time, and $\epsilon$ is the desired precision. With this improved resource requirement, we perform the time evolution for $N=6, 8$ with maximum two-qubit circuit depth of 343. We perform different error mitigation schemes on the noisy hardware results and find good agreement with the exact diagonalization results on classical computers and noiseless simulators. In particular, we compute return probability after time $t$ and out-of-time order correlators (OTOC) which is a standard observable of quantifying the chaotic nature of quantum systems.
We formulate the $O(3)$ non-linear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We expect that the methods developed in this work will be useful for exploring interesting dynamics for a wide class of sigma models and gauge theories, as well as for simulating scattering events on quantum hardware in the coming decades.
We discuss fundamentals of quantum computing and information - quantum gates, circuits, algorithms, theorems, error correction, and provide collection of QISKIT programs and exercises for the interested reader.
We propose a system for guiding plasmon-enhanced polarized single photons into optical nanowire (ONW) guided modes. It is shown that spontaneous emission properties of quantum emitters (QEs) can be strongly enhanced in the presence of gold nanorod dimer (GNRD) leading to the emission of highly polarized and bright single photons. We have calculated that a high Purcell factor of 279, coupling efficiency of 11 %, and degree of polarization (DOP) of single photons is estimated to be as high as 99.57% in the guided modes of ONW by suitably placing a QE on an optimized location of the GNRD system. This proposed hybrid quantum system can be in-line with fiber networks, opening the door for possible quantum information processing and quantum cryptography applications.
Quantum computers can potentially solve problems that are computationally intractable on a classical computer in polynomial time using quantum-mechanical effects such as superposition and entanglement. The N-Queens Problem is a notable example that falls under the class of NP-complete problems. It involves the arrangement of N chess queens on an N x N chessboard such that no queen attacks any other queen, i.e. no two queens are placed along the same row, column or diagonal. The best time complexity that a classical computer has achieved so far in generating all solutions of the N-Queens Problem is of the order O(N!). In this paper, we propose a new algorithm to generate all solutions to the N-Queens Problem for a given N in polynomial time of order O(N^3) and polynomial memory of order O(N^2) on a quantum computer. We simulate the 4-queens problem and demonstrate its application to satellite communication using IBM Quantum Experience platform.
Braneshop, and
the US National Science Foundation.
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