A fast quantum search algorithm by controlled measurement and qubit comparison implying the complexity class inclusion NP in BQP

Multi-layer quantum search and inclusion of NP into BQP

In this work, we present a multi-layer quantum search method that generates an exponential speedup of the standard Grover's algorithm. As direct applications, any NP problems can be solved efficiently on a quantum circuit with only polynomial gate complexity. In particular, such multi-layer search can solve the factoring problem with an exponential speedup, providing an alternative to Shor's algorithm. Our results show that the exponential speedup of quantum circuits is ubiquitous, and Grover's search is much more powerful than that has been demonstrated. With no contradiction to the quadratic…

A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes

We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In particular, we show that while (*) is doable in quantum randomized polynomial time when m=2 (and no classical randomized polynomial time algorithm is known), (*) is nearly NP-hard for general m: Under a plausible hypothesis involving primes in arithmetic progression (implied by the Generalized Riemann Hypothesis for certain cyclotomic fields), a randomized polyn…

量子计算复杂性与对称性

Quantum Computational Complexity and Symmetry

本文研究量子态与信道对称性测试的计算复杂性，证明多类对称性测试问题对 BQP、QMA、QSZK、QIP(2)、QIP_EB(2) 和 QIP 完备，并证明两个哈密顿量对称性测试问题分别属于 QMA 与 QAM，揭示了对称性与量子计算复杂性之间的深层联系。

Computation in generalised probabilistic theories

From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that BQP is in AWPP. This work investigates limits on computational power that are imposed by physical principles. To this end, we define a circuit-based model of computation in a class of operationally-defined theories more general than quantum theory, and ask: what is the minimal set of physical assumptions under which the above inclusion still holds? …

区分幂等量子通道

Discriminating idempotent quantum channels

研究二元区分幂等量子通道，当两个通道共享共同全秩不变态时，图像包含条件决定渐进行为，所有误差指数可显式计算，且无适应优势，从而获得该通道族的强反向性质。

关于量子态之间的Schatten范数和幂距离的估计

On estimating Schatten norm and power distances between quantum states

研究估计量子Schatten α-范数距离的计算复杂性，对于α>1提出高效量子估计器，并揭示量子态区分问题的计算复杂性二分性。