Related papers: Reducing NEXP-complete problems to DQBF
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…
We introduce the entangled quantum polynomial hierarchy $\mathsf{QEPH}$ as the class of problems that are efficiently verifiable given alternating quantum proofs that may be entangled with each other. We prove $\mathsf{QEPH}$ collapses to…
We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom NE, a logic known to be both convex and union closed. We…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
Widely employed Near-Edge X-Ray Absorption Fine Structure (NEXAFS) spectroscopy probes a system by excitation of core electrons to unoccupied states. A variety of different methodologies are available to simulate corresponding spectra from…
We analyze the complexity of decision problems for Boolean Nonassociative Lambek Calculus admitting empty antecedent of sequents ($\mathsf{BFNL^*}$), and the consequence relation of Distributive Full Nonassociative Lambek Calculus…
Current algorithms for bounded model checking use SAT methods for checking satisfiability of Boolean formulae. These methods suffer from the potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulae…
Quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study sufficient conditions for a convex hull result that immediately implies that…
We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does…
Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…
Quantifier elimination (qelim) is used in many automated reasoning tasks including program synthesis, exist-forall solving, quantified SMT, Model Checking, and solving Constrained Horn Clauses (CHCs). Exact qelim is computationally…
Finding a quantum computing method to solve nondeterministic polynomial time (NP)-complete problems is currently of paramount importance in quantum information science. Here an experiment is presented to demonstrate the use of Rydberg atoms…