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The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…
Quantum annealing has emerged as a promising approach for solving NP-hard optimization problems, leveraging quantum phenomena such as quantum tunneling to navigate complex energy landscapes. However, the extent to which quantum tunneling…
The standard quantum annealing algorithm tries to approach the ground state of a classical system by slowly decreasing the hopping rates of a quantum random walk in the configuration space of the problem, where the on-site energies are…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are…
Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a high-level user interface developed on Mathematica\copyright which is connected to C++ code in order to…
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:…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed…
We introduce a planar embedding of the k-regular k-XORSAT problem, in which solutions are encoded in the ground state of a classical statistical mechanics model of reversible logic gates arranged on a square grid and acting on bits that…
A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…