While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field.
Quantum computing is a promising paradigm for efficiently solving large and high-complexity problems. To protect quantum computing privacy, pioneering research efforts proposed to redefine differential privacy (DP) in quantum computing, i.e., quantum differential privacy (QDP), and harvest inherent noises generated by quantum computing to implement QDP. However, such an implementation approach is limited by the amount of inherent noises, which makes the privacy budget of the QDP mechanism fixed and uncontrollable. To address this issue, in this paper, we propose to leverage quantum error correction (QEC) techniques to reduce quantum computing errors, while tuning the privacy protection levels in QDP. In short, we gradually decrease the quantum noise error rate by deciding whether to apply QEC operations on the gate in a multiple single qubit gates circuit. We have derived a new calculation formula for the general error rate and corresponding privacy budgets after QEC operation. Then, we expand to achieve further noise reduction using multi-level concatenated QEC operation. Through extensive numerical simulations, we demonstrate that QEC is a feasible way to regulate the degree of privacy protection in quantum computing.
Quantum computing revolutionizes the way of solving complex problems and handling vast datasets, which shows great potential to accelerate the machine learning process. However, data leakage in quantum machine learning (QML) may present privacy risks. Although differential privacy (DP), which protects privacy through the injection of artificial noise, is a well-established approach, its application in the QML domain remains under-explored. In this paper, we propose to harness inherent quantum noises to protect data privacy in QML. Especially, considering the Noisy Intermediate-Scale Quantum (NISQ) devices, we leverage the unavoidable shot noise and incoherent noise in quantum computing to preserve the privacy of QML models for binary classification. We mathematically analyze that the gradient of quantum circuit parameters in QML satisfies a Gaussian distribution, and derive the upper and lower bounds on its variance, which can potentially provide the DP guarantee. Through simulations, we show that a target privacy protection level can be achieved by running the quantum circuit a different number of times.
Quantum computing has been widely applied in various fields, such as quantum physics simulations, quantum machine learning, and big data analysis. However, in the domains of data-driven paradigm, how to ensure the privacy of the database is becoming a vital problem. For classical computing, we can incorporate the concept of differential privacy (DP) to meet the standard of privacy preservation by manually adding the noise. In the quantum computing scenario, researchers have extended classic DP to quantum differential privacy (QDP) by considering the quantum noise. In this paper, we propose a novel approach to satisfy the QDP definition by considering the errors generated by the projection operator measurement, which is denoted as shot noises. Then, we discuss the amount of privacy budget that can be achieved with shot noises, which serves as a metric for the level of privacy protection. Furthermore, we provide the QDP of shot noise in quantum circuits with depolarizing noise. Through numerical simulations, we show that shot noise can effectively provide privacy protection in quantum computing.
Quantum computing holds tremendous potential for processing high-dimensional data, capitalizing on the unique capabilities of superposition and parallelism within quantum states. As we navigate the noisy intermediate-scale quantum (NISQ) era, the exploration of quantum computing applications has emerged as a compelling frontier. One area of particular interest within the realm of cyberspace security is Behavior Detection and Evaluation (BDE). Notably, the detection and evaluation of internal abnormal behaviors pose significant challenges, given their infrequent occurrence or even their concealed nature amidst vast volumes of normal data. In this paper, we introduce a novel quantum behavior detection and evaluation algorithm (QBDE) tailored for internal user analysis. The QBDE algorithm comprises a Quantum Generative Adversarial Network (QGAN) in conjunction with a classical neural network for detection and evaluation tasks. The QGAN is built upon a hybrid architecture, encompassing a Quantum Generator ($G_Q$) and a Classical Discriminator ($D_C$). $G_Q$, designed as a parameterized quantum circuit (PQC), collaborates with $D_C$, a classical neural network, to collectively enhance the analysis process. To address the challenge of imbalanced positive and negative samples, $G_Q$ is employed to generate negative samples. Both $G_Q$ and $D_C$ are optimized through gradient descent techniques. Through extensive simulation tests and quantitative analyses, we substantiate the effectiveness of the QBDE algorithm in detecting and evaluating internal user abnormal behaviors. Our work not only introduces a novel approach to abnormal behavior detection and evaluation but also pioneers a new application scenario for quantum algorithms. This paradigm shift underscores the promising prospects of quantum computing in tackling complex cybersecurity challenges.
Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence N(C), where C is a coherence measurement. In virtue of the constraint of large N and Shannon's maximum entropy principle, a surprising complementary relationship between the coherence and the success probability of GSA is obtained. Namely, P_s(t)+N(C(t))≃1, where C is in terms of the relative entropy of coherence and l_1 norm of coherence, t is the number of the search iterations in GSA. Moreover, the equation holds no matter in ideal or noisy environments. Considering the number of qubits is limited in the recent noisy intermediate-scale quantum (NISQ) era, some exact numerical calculation experiments are presented for different database sizes N with different types of noises. The results show that the complementary between the success probability and the coherence almost always hold. This work provides a new perspective to improve the success probability by manipulating its complementary coherence, and vice versa. It has an excellent potential for helping quantum algorithms design in the NISQ era.
For the goal of strong artificial intelligence that can mimic human-level intelligence, AI systems would have the ability to adapt to ever-changing scenarios and learn new knowledge continuously without forgetting previously acquired knowledge. When a machine learning model is consecutively trained on multiple tasks that come in sequence, its performance on previously learned tasks may drop dramatically during the learning process of the newly seen task. To avoid this phenomenon termed catastrophic forgetting, continual learning, also known as lifelong learning, has been proposed and become one of the most up-to-date research areas of machine learning. As quantum machine learning blossoms in recent years, it is interesting to develop quantum continual learning. This paper focuses on the case of quantum models for quantum data where the computation model and the data to be processed are both quantum. The gradient episodic memory method is incorporated to design a quantum continual learning scheme that overcomes catastrophic forgetting and realizes knowledge backward transfer. Specifically, a sequence of quantum state classification tasks is continually learned by a variational quantum classifier whose parameters are optimized by a classical gradient-based optimizer. The gradient of the current task is projected to the closest gradient, avoiding the increase of the loss at previous tasks, but allowing the decrease. Numerical simulation results show that our scheme not only overcomes catastrophic forgetting, but also realize knowledge backward transfer, which means the classifier's performance on previous tasks is enhanced rather than compromised while learning a new task.
Grover's search algorithm (GSA) is known to experience a loss of its quadratic speedup when exposed to quantum noise. In this study, we partially agree with this result and present our findings. First, we examine different typical diagonalizable noises acting on the oracles in GSA and find that the success probability decreases and oscillates around $1/2$ as the number of iterations increases. Secondly, our results show that the performance of GSA can be improved by certain types of noise, such as bit flip and bit-phase flip noise. Finally, we determine the noise threshold for bit-phase flip noise to achieve a desired success probability and demonstrate that GSA with bit-phase flip noise still outperforms its classical counterpart. These results suggest new avenues for research in noisy intermediate-scale quantum (NISQ) computing, such as evaluating the feasibility of quantum algorithms with noise and exploring their applications in machine learning.
Entanglement is considered to be one of the primary reasons for why quantum algorithms are more efficient than their classical counterparts for certain computational tasks. The global multipartite entanglement of the multiqubit states in Grover's search algorithm can be quantified using the geometric measure of entanglement (GME). Rossi \em et al. (Phys. Rev. A \textbf87, 022331 (2013)) found that the entanglement dynamics is scale invariant for large $n$. Namely, the GME does not depend on the number $n$ of qubits; rather, it only depends on the ratio of iteration $k$ to the total iteration. In this paper, we discuss the optimization of the GME for large $n$. We prove that ``the GME is scale invariant'' does not always hold. We show that there is generally a turning point that can be computed in terms of the number of marked states and their Hamming weights during the curve of the GME. The GME is scale invariant prior to the turning point. However, the GME is not scale invariant after the turning point since it also depends on $n$ and the marked states.
Braneshop, and
the US National Science Foundation.
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