Related papers: The performance of the quantum adiabatic algorithm…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…
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…
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…
We present a 2-local quantum algorithm for graph isomorphism GI based on an adiabatic protocol. By exploiting continuous-time quantum-walks, we are able to avoid a mere diffusion over all possible configurations and to significantly reduce…
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…
Quantum computing holds promise for outperforming classical computing in specialized applications such as optimization. With current Noisy Intermediate Scale Quantum (NISQ) devices, only variational quantum algorithms like the Quantum…
A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly…
The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…
We describe a general methodology for enhancing the efficiency of adiabatic quantum computations (AQC). It consists of homotopically deforming the original "Hamiltonian surface" in a way that the redistribution of the Gaussian curvature…
Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers…
Perturbed Hamming weight problems serve as examples of optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work we study the efficiency of the adiabatic algorithm for solving…
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…
Obtaining exact solutions to combinatorial optimization problems using classical computing is computationally expensive. The current tenet in the field is that quantum computers can address these problems more efficiently. While promising…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
Hardware accelerators like quantum annealers or neuromorphic chips are capable of finding the ground state of a Hamiltonian. A promising route in utilizing these devices is via methods from automated reasoning: The problem at hand is first…
The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from an approximation to the Quantum Adiabatic Algorithm (QAA). In solving…
The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$ and the allowable error $\epsilon$ [PRX Quantum…