Complexity of several constraint satisfaction problems using the heuristic, classical, algorithm, WalkSAT

Solving boolean satisfiability problems with the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to optimization problems. We focus on the fundamental boolean satisfiability problem, in the form of random $k$-SAT. We develop analytic bounds on the average success probability of QAOA over random boolean formulae at the satisfiability threshold, as the number of variables $n$ goes to infinity. The bounds hold for fixed parameters and when $k$ is a power of 2. We c…

Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical" instances. We find that at large sizes N, the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm the harder it is also for the quantum adiabatic algorithm.

利用混合量子-经典MCMC算法公平采样基态配置

Fair sampling of ground-state configurations using hybrid quantum-classical MCMC algorithms

本文提出混合量子-经典MCMC算法用于公平采样基态配置，通过实验验证其在组合优化问题中的有效性。

3-Regular 3-XORSAT Planted Solutions Benchmark of Classical and Quantum Heuristic Optimizers

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving Quadratic Unconstrained Binary Optimization (QUBO) problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a…

Faster than Classical Quantum Algorithm for dense Formulas of Exact Satisfiability and Occupation Problems

We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: First, the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the XSAT; Second, a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query comple…

使用量子Grover搜索算法解决段显示问题

Solving Segment Display Problems Using Quantum Grover's Search Algorithm

本文提出了一种基于量子Grover算法的段显示问题求解方法，利用二进制可逆电路和Stesso算子构建量子 oracle，并通过实验验证其在匹配火柴问题中的有效性。