Wan‐Su Bao

He-Liang Huang, Xiao-Yue Xu, Chu Guo et al.

Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field.

Chen Ding, Xiao-Yue Xu, Yun-Fei Niu et al.

Training a quantum machine learning model generally requires a large labeled dataset, which incurs high labeling and computational costs. To reduce such costs, a selective training strategy, called active learning (AL), chooses only a subset of the original dataset to learn while maintaining the trained model's performance. Here, we design and implement two AL-enpowered variational quantum classifiers, to investigate the potential applications and effectiveness of AL in quantum machine learning. Firstly, we build a programmable free-space photonic quantum processor, which enables the programmed implementation of various hybrid quantum-classical computing algorithms. Then, we code the designed variational quantum classifier with AL into the quantum processor, and execute comparative tests for the classifiers with and without the AL strategy. The results validate the great advantage of AL in quantum machine learning, as it saves at most $85\%$ labeling efforts and $91.6\%$ percent computational efforts compared to the training without AL on a data classification task. Our results inspire AL's further applications in large-scale quantum machine learning to drastically reduce training data and speed up training, underpinning the exploration of practical quantum advantages in quantum physics or real-world applications.

Yun-Fei Niu, Shuo Zhang, Chen Ding et al.

Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the incompatibility with backpropagation and the cost of a large number of measurements, posing a great challenge to the large-scale development of VQAs. Here, we propose a parameter-parallel distributed variational quantum algorithm (PPD-VQA), to accelerate the training process by parameter-parallel training with multiple quantum processors. To maintain the high performance of PPD-VQA in the realistic noise scenarios, a alternate training strategy is proposed to alleviate the acceleration attenuation caused by noise differences among multiple quantum processors, which is an unavoidable common problem of distributed VQA. Besides, the gradient compression is also employed to overcome the potential communication bottlenecks. The achieved results suggest that the PPD-VQA could provide a practical solution for coordinating multiple quantum processors to handle large-scale real-word applications.

Jie Lin, Dan-Bo Zhang, Shuo Zhang et al.

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.

He-Liang Huang, You-Wei Zhao, Tan Li et al.

Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.

Xiangqun Fu, Wansu Bao, Jianhong Shi et al.

Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about what the parameter effects the problem solving difficulty. Then we pointed out that the index-calculus algorithm is not suitable for the problem, and two sufficient conditions of resistance to the quantum algorithm for the hidden subgroup problem are given.

Heliang Huang, Wansu Bao

Solving systems of m multivariate quadratic equations in n variables (MQ-problem) over finite fields is NP-hard. The security of many cryptographic systems is based on this problem. Up to now, the best algorithm for solving the underdefined MQ-problem is Hiroyuki Miura et al.'s algorithm, which is a polynomial-time algorithm when \[n \ge m(m + 3)/2\] and the characteristic of the field is even. In order to get a wider applicable range, we reduce the underdefined MQ-problem to the problem of finding square roots over finite field, and then combine with the guess and determine method. In this way, the applicable range is extended to \[n \ge m(m + 1)/2\], which is the widest range until now. Theory analysis indicates that the complexity of our algorithm is \[O(q{n^ω}m{(\log {\kern 1pt} {\kern 1pt} q)^2}){\kern 1pt} \] when characteristic of the field is even and \[O(q{2^m}{n^ω}m{(\log {\kern 1pt} {\kern 1pt} q)^2})\] when characteristic of the field is odd, where \[2 \le ω\le 3\] is the complexity of Gaussian elimination.

Wansu Bao, Heliang Huang

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based algebraic attacks, namely, any information won't be got if we couldn't work out the Grobner bases of the polynomial equations system. In this paper, firstly, a generalized model of Grobner basis algorithms is presented, which provides us a platform to analyze and solve common problems of the algorithms. Secondly, we give and prove the degree bound of the polynomials appeared during the computation of Grobner basis after field polynomials is added. Finally, by detecting the temporary basis during the computation of Grobner bases and then extracting the univariate polynomials contained unique solution in the temporary basis, a heuristic strategy named Middle-Solving is presented to solve these polynomials at each iteration of the algorithm. Farther, two specific application mode of Middle-Solving strategy for the incremental and non-incremental Grobner bases algorithms are presented respectively. By using the Middle-Solving strategy, even though we couldn't work out the final Grobner bases, some information of the variables still leak during the computational process.

Xiangqun Fu, Wansu Bao, Jianhong Shi et al.

In order to research the security of the knapsack problem under quantum algorithm attack, we study the quantum algorithm for knapsack problem over Z_r based on the relation between the dimension of the knapsack vector and r. First, the oracle function is designed based on the knapsack vector B and S, and the quantum algorithm for the knapsack problem over Z_r is presented. The observation probability of target state is not improved by designing unitary transform, but oracle function. Its complexity is polynomial. And its success probability depends on the relation between n and r. From the above discussion, we give the essential condition for the knapsack problem over Z_r against the existing quantum algorithm attacks, i.e. r<O(2^n). Then we analyze the security of the Chor-Rivest public-key crypto.

Heliang Huang, Wansu Bao

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Faugere's F4 is a well-known Grobner bases algorithm to solve this problem. However, a serious drawback exists in the Grobner bases based algebraic attacks, namely, any information won't be got if we couldn't work out the Grobner bases of the polynomial equations system. In this paper, we in-depth research the F4 algorithm over GF(2). By using S-polynomials to replace critical pairs and computing the normal form of the productions with respect to the field equations in certain steps, many "redundant" reductors are avoided during the computation process of the F4 algorithm. By slightly modifying the logic of F4 algorithm, we solve the univariate polynomials appeared in the algorithm and then back-substitute the values of the solved variables at each iteration of the algorithm. We call our improvements Middle-Solving F4. The heuristic strategy of Middle-Solving overcomes the drawback of algebraic attacks and well suits algebraic attacks. It has never been applied to the Grobner bases algorithm before. Experiments to some Hidden Field Equation instances and some classical benchmarks (Cyclic 6, Gonnet83) show that Middle-Solving F4 is faster and uses less memory than Faugere's F4.