arXiv:2210.15922 · Entropy

Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics

Andreas Burger, L. C. Kwek, Dario Poletti

Published Dec 2, 2022• 15 citations

Abstract

Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator.

DOI: 10.3390/e24121766

Related papers

Digital Quantum Simulation of Open Quantum Systems Using Quantum Imaginary–Time Evolution

Hirsh Kamakari, Shi-Ning Sun, Mário Motta +1 more

Quantum simulation on emerging quantum hardware is a topic of intense interest.While many studies focus on computing ground-state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior.However, their nonunitary dynamics are also not natural to simulate on digital quantum devices.Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary-time evolution algorithm.We demonstrate the algorithms on IBM Quantum's hardware with simulations of the spontaneous emission of a two-level system and the dissipative transverse field Ising model.Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.

arXiv:2104.07823PRX QuantumFeb 4, 2022141 citations

Simulation, characterisation and control of open quantum systems dynamics

Giorgio Zicari

In this thesis, we discuss aspects of the simulation, characterisation, and control of the dynamics of open quantum systems. The latter are systems governed by quantum mechanical laws and interacting with an environment, which is typically much larger than the system itself. According to the standard approach, one is usually able to perform a suitable average over the environmental degrees of freedom, resulting in an effective description of the main system dynamics, which accounts for the effects of the interaction with the surroundings. In standard scenarios, usually studied within the so-called Born-Markov approximation, the system-environment coupling is weak and such that we can perform a neat separation of timescales: the environmental dynamics is assumed to be fast compared to the typical evolution timescale of the system of interest. However, nowadays we are able to inspect physical scenarios where the usual Born-Markov approximation breaks down: the interaction between system and environment can be strong, likely leading to non-negligible memory (non-Markovian) effects. In this work, we discuss some instances in which we cannot work in the standard Born-Markov regime. We introduce and analyse some numerical and analytical techniques to characterise and simulate non-standard scenarios. We show that, even in the Markovian regime, the traditional formulation of thermodynamic irreversibility shows flaws and inconsistencies. We thus use phase-space methods to assess the role of initial correlations shared by the two parties of a bipartite harmonic system in the entropy production rate, including non-Markovian effects. Furthermore, we show that certain interactions enable to redraw the boundaries between the system and the environment in an effective manner, resulting in a new picture where the system degrees of freedom are augmented, while the residual environment is rearranged in such a way that the Born-Markov approximation is recovered. This analytical technique, known as reaction coordinate mapping approach, is employed in this work to show that, upon an accurate choice of the parameter regime, a spin-boson model can serve as a quantum analogue simulator of non-Markovian multiphoton Jaynes-Cummings models. These systematic studies shed light on the thermodynamic characterisation of open quantum systems, as well as on their numerical simulation.

Oct 1, 20260 citations

Efficiently Solving Spin-Boson Dynamics Via Non-Markovian Quantum Trajectories

Zeng-Zhao Li, Cho‐Tung Yip, Hai-Yao Deng +4 more

We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an important application, we consider a real-time simulation of a spin-boson model in a strong coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schrodinger equation can be efficiently implemented as a real--time simulation for this model, so as to give an accurate description of spin-boson dynamics beyond the rotating-wave approximation.

Jun 6, 20140 citations

Verifying quantum memory in the dynamics of spin-boson models

Charlotte Bäcker, Valentin Link, Walter T. Strunz

We investigate the nature of memory effects in the non-Markovian dynamics of spin-boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We focus on two such criteria, one based on the dynamical map and the other on single-intervention process tensors, and discuss their connection. We apply these criteria to quench dynamics in spin-boson and two-spin-boson models, computed using a numerically exact method for non-Markovian open-system dynamics based on matrix product operator influence functionals. This method is ideally suited to simulate quantum multitime processes in spin-boson models across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, it is still possible to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.

arXiv:2505.13067Physical Review ResearchNov 25, 20253 citations

Objectivity in the non-Markovian spin-boson model

Aniello Lampo, Jan Tuziemski, Maciej Lewenstein +1 more

Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. In the present paper we study the emergence of such a state structure in one of the canonical models of the condensed-matter theory: the spin-boson model, describing the dynamics of a two-level system coupled to an environment made up by a large number of harmonic oscillators. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the surfacing of a spectrum broadcast structure.

arXiv:1702.08427Physical Review AJul 18, 201743 citations

Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models

Ricardo Puebla, Giorgio Zicari, Íñigo Arrazola +3 more

The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms.

arXiv:1904.07037SymmetryMay 20, 201920 citations