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arXiv:1608.01317 · Physical Review Letters

Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise

Aurélia Chenu, Mathieu Beau, Jianshu Cao, Adolfo del Campo

Published Apr 5, 2017• 160 citations
arXivHTMLPDF

Abstract

We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N^{-2k} with the system size N. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.

DOI
10.1103/physrevlett.118.140403

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We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N^{-2k} with the system size N. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.
We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by kkk-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N−2kN^{-2k}N−2k with the system size NNN. Our proposal can be readily implemented on a variety of quantum platforms including optical lattices, superconducting circuits and trapped ions.
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.
We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.
ABSTRACT Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrödinger equation (SSE), and the stochastic Liouville equation (SLE). These approaches replace the explicit system–environment coupling with an effective system‐only dynamics, where dissipative behavior emerges from ensemble averaging. Stochastic Hamiltonians, in particular, have long served as phenomenological tools in physical chemistry to include environmental effects without recourse to an explicit microscopic derivation. In this work, we aim at a self‐contained and accessible presentation of these approaches to further elaborate on their common roots in essential concepts of stochastic calculus and to delineate the conditions under which they are equivalent. We also discuss how different formulations naturally lead to different numerical time‐integration schemes, better suited for either classical simulation platforms, based on finite‐difference approximations, or quantum algorithms, that employ random unitary maps. Our analysis aims at providing a unified perspective and actionable recipes for classical and quantum implementations of stochastic evolution in the simulation of open quantum systems.
As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed system models (described by a Hamiltonian) or open system models (described by a Lindbladian), have been developed, it remains less well understood whether similar protocols for non-Markovian models exist. In this paper, we consider geometrically local lattice models with both quantum and classical non-Markovian noise and show that, under a Gaussian assumption on the noise, we can learn the noise with sample complexity scaling logarithmically with the system size. Our protocol requires preparing the simulator qubits initially in a product state, introducing a layer of single-qubit Clifford gates and measuring product observables.