Related papers: Quantum Simulation of Markov Chains
The simulation of quantum processes is a key goal for the grand programme aiming at grounding quantum technologies as the way to explore complex phenomena that are inaccessible through standard, classical calculators. Some interesting steps…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Randomness comes in two qualitatively different forms. Apparent randomness can result both from ignorance or lack of control of degrees of freedom in the system. In contrast, intrinsic randomness should not be ascribable to any such cause.…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
A digital quantum simulator is an envisioned quantum device that can be pro- grammed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions.…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus…
We implement in a reactive programming framework a simulation of three aspects of quantum mechanics: self-interference, state superposition, and entanglement. The simulation basically consists in a cellular automaton embedded in a…
Quantum simulation is of great importance in quantum information science. Here, we report an experimental quantum channel simulator imbued with an algorithm for imitating the behavior of a general class of quantum systems. The reported…
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a…
We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
Quantum systems are notoriously difficult to simulate with classical means. Recently, the idea of using another quantum system - which is experimentally more controllable - as a simulator for the original problem has gained significant…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…