Effects of noise, correlations, and errors in the preparation of initial states in quantum simulations

Abstract

In principle, a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which are difficult to simulate on a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be readily measured or controlled in an experiment. The system will interact with the surrounding environment and with the other particles in the system, and be implemented using imperfect controls, making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing. However, the effects of noise in quantum simulations are not well understood and how best to treat them in most cases is not known. In this paper we study an existing quantum algorithm for simulating the one-dimensional Fano-Anderson model using a liquid-state NMR device. We examine models of noise in the evolution using different initial states in the original model. We also add interacting spins to simulate a realistic situation where an environment of spins is present. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled, have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.

Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm

“…However, in real situations, the physical system under consideration is continuously interacting with its environment, causing its time evolution to be non-unitary. In some cases, the noise from open dynamics can contribute significantly to errors in the computational output, leading to lower experimental fidelity and a reduction in the quality of the quantum device [10]. A duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system was proposed where the time evolution is realized using Kraus operators [11,12].…”

Adiabatic Control of Decoherence-Free-Subspaces in an Open Collective System

“…However, the investigation of such controlled quantum systems as platforms for quantum computation, memory, metrology, and simulation is often limited experimentally due to decoherence induced by the system's coupling to its environment [15][16][17][18][19][20][21][22][23][24][25][26][27]. As a result, many schemes have been developed to evolve the system in a dark state so that the system does not undergo any nonunitary evolution [28].…”

Determination of the hardness of drinking packaged water of Kalyani area, West Bengal

“…The effect is explicitly seen when one considers transmission spectrum of one dimensional quantum wire (QW) systems with a single quantum dot (QD), or a cluster of them is attached to the QW from one side [7,8,10,11]. Needless to say, the studies so far has gone well beyond mere theoretical interest, thanks to the present advanced stage of lithographic techniques and nanotechnology, and has incorporated the studies of nonequilibrium dynamics in optical transition [13], quantum simulation [14] and tunneling in a Kondo hole system [15] to name a few.…”