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A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…
Current and near term quantum computers (i.e. NISQ devices) are limited in their computational power in part due to qubit decoherence. Here we seek to take advantage of qubit decoherence as a resource in simulating the behavior of real…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible.…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Computational physics is an important tool for analysing, verifying, and -- at times -- replacing physical experiments. Nevertheless, simulating quantum systems and analysing quantum data has so far resisted an efficient classical treatment…
A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this paper, I describe a…
We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several…