Related papers: Generalized Quantum Turing Machine and its Applica…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…
A quantum algorithm is proposed to solve the Satisfiability problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit Exact Cover problem. The time cost of this…
The electronic structure problem is one of the main problems in modern theoretical chemistry. While there are many already-established methods both for the problem itself and its applications like semi-classical or quantum dynamics, it…
The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called "search space expansion", which modifies the…
We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits,…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a…
Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries--where n denotes the number of…