Related papers: An adiabatic quantum algorithm for the Frobenius p…
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…
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…
Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster…
We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both…
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim…
The Closest String Problem is an NP-complete problem which appears more commonly in bioinformatics and coding theory. Less surprisingly, classical approaches have been pursued with two prominent algorithms being the genetic algorithm and…
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…
Quantum information processing is likely to have far-reaching impact in the field of artificial intelligence. While the race to build an error-corrected quantum computer is ongoing, noisy, intermediate-scale quantum (NISQ) devices provide…
By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic…
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…
We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the `period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its…
Given a set of three positive integers {a1, a2, a3}, denoted A, the Frobenius problem in three variables is to find the greatest integer which cannot be expressed in the following form, where x1, x2 and x3 are non-negative integers: x1*a1 +…
In previous implementations of adiabatic quantum algorithms using spin systems, the average Hamiltonian method with Trotter's formula was conventionally adopted to generate an effective instantaneous Hamiltonian that simulates an adiabatic…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…