Yu-Ao Chen

Yin Mo, Lei Zhang, Yu-Ao Chen et al.

Quantum combs play a vital role in characterizing and transforming quantum processes, with wide-ranging applications in quantum information processing. However, obtaining the explicit quantum circuit for the desired quantum comb remains a challenging problem. We propose PQComb, a novel framework that employs parameterized quantum circuits (PQCs) or quantum neural networks to harness the full potential of quantum combs for diverse quantum process transformation tasks. This method is well-suited for near-term quantum devices and can be applied to various tasks in quantum machine learning. As a notable application, we present two streamlined protocols for the time-reversal simulation of unknown qubit unitary evolutions, reducing the ancilla qubit overhead from six to three compared to the previous best-known method. We also extend PQComb to solve the problems of qutrit unitary transformation and channel discrimination. Furthermore, we demonstrate the hardware efficiency and robustness of our qubit unitary inversion protocol under realistic noise simulations of IBM-Q superconducting quantum hardware, yielding a significant improvement in average similarity over the previous protocol under practical regimes. PQComb's versatility and potential for broader applications in quantum machine learning pave the way for more efficient and practical solutions to complex quantum tasks.

Yu-Ao Chen, Xiao-Shan Gao, Chun-Ming Yuan

In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field or a bounded interval of integers. The quantum algorithms can solve these problems with any given success probability and have polynomial runtime complexities in the size of the input, the degree of the inequality constraints, and the condition number of certain matrices derived from the problem. So, we achieved exponential speedup for these problems when their condition numbers are small. As applications, quantum algorithms are given to three basic computational problems in cryptography: the polynomial system with noise problem, the short integer solution problem, the shortest vector problem, as well as the cryptanalysis for the lattice based NTRU cryptosystem. It is shown that these problems and NTRU can against quantum computer attacks only if their condition numbers are large, so the condition number could be used as a new criterion for the lattice based post-quantum cryptosystems.

Yu-Ao Chen, Xiao-Shan Gao

Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if FS does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of FS and the condition number of FS. As a consequence, we give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are small, say polynomial in the size of FS. We apply our quantum algorithm for solving Boolean equations to the cryptanalysis of several important cryptosystems: the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large. This leads to a new criterion for designing cryptosystems that can against the attack of quantum computers: their corresponding equation systems must have large condition numbers.