Related papers: Experimental Evidence about "A factorisation algor…
Much attention has been drawn to quantum computing and the exponential speed-up in computation the technology would be able to provide. Various claims have been made about what aspect of quantum mechanics causes this speed-up. Formulations…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
One of the most exciting quantum emulation [1] breakthroughs was the first analog signal-based emulation of a universal quantum computer [2]. This yielded a very interesting paper, but no practical use - even for theorists. The reason for…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
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…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Commercial quantum annealers from D-Wave Systems can find high quality solutions of quadratic unconstrained binary optimization problems that can be embedded onto its hardware. However, even though such devices currently offer up to 2048…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
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…
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…
Recent advances bring within reach the viability of solving combinatorial problems using a quantum annealing algorithm implemented on a purpose-built platform that exploits quantum properties. However, the question of how to tune the…
Wave-particle duality of quantum objects is one of the most striking features of quantum physics and has been widely studied in past decades. Developments of quantum technologies enable us to experimentally realize several quantum…
We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments…
The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports P\'olya's and Hilbert's conjecture to prove Riemann's hypothesis. The energies of this system, being…
We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…
In the evaluation of quantum annealers, metrics based on ground state success rates have two major drawbacks. First, evaluation requires computation time for both quantum and classical processors that grows exponentially with problem size.…
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…