Simulating non-Markovian open quantum dynamics by exploiting physics-informed neural network
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心）；State Key Laboratory of Porous Materials for Separation and Conversion & MOE Key Laboratory of Computational Physical Sciences & Department of Chemistry, Fudan University（复旦大学化学系多孔材料分离转化国家重点实验室及计算物理教育部重点实验室）；Hefei National Laboratory（合肥国家实验室）
Long Cao, Liwei Ge, Daochi Zhang, Yao Wang, Rui-Xue Xu, YiJing Yan, Xiao Zheng
This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics, to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.
Simulating Non-Markovian Open Quantum Dynamics with Neural Quantum States
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（合肥微尺度物质科学国家研究中心，中国科学技术大学）；Department of Chemistry, Fudan University（复旦大学化学系）；Hefei National Laboratory（合肥国家实验室）
Simulating the Dynamics of Markovian Quantum Processes by Quantum Collision Models on Quantum Computers
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Q-CTRL；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute（理化学研究所先导研究本部）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
Forked Physics-Informed Neural Networks for Non-Markovian Open Quantum Dynamics and Control
College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与光电工程学院）；China Mobile (Suzhou) Software Technology Co., Ltd（中国移动（苏州）软件技术有限公司）；School of Information Management and School of Artificial Intelligence, Qingdao University of Technology（青岛理工大学信息管理学院和人工智能学院）；Engineering Research Center of Advanced Marine Physical Instruments and Equipment of Ministry of Education, Ocean University of China（教育部海洋先进物理仪器装备工程研究中心）；Qingdao Key Laboratory of Optics and Optoelectronics, Ocean University of China（青岛市光学与光电技术重点实验室）
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction: one basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the…
We propose an all-optical experiment to quantify non-Markovianity in an open quantum system through quantum coherence of a single quantum bit. We use an amplitude damping channel implemented by an optical setup with an intense laser beam simulating a single-photon polarization. The optimization over initial states required to quantify non-Markovianity is analytically evaluated. The experimental results are in a very good agreement with the theoretical predictions.
Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and classify its complexity in the many-body setting. In this paper, we identify a general class of non-Markovian memory kernels, described by complex-valued radon measures, and define their dynamics through a regularization procedure constructing the corresponding system-environment unitary groups. Building on this definition, we then consider $k-$local many-bo…
Faster Quantum Simulation Of Markovian Open Quantum Systems Via Randomisation
University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）；Stellenbosch University（斯坦伦布什大学）
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the embeddability problem for stochastic matrices, we show that quantum memoryless dynamics can simulate classical processes that necessarily require memory. Second, by extending the notion of space-time cost of a stochastic process $P$ to the quantum domain, we prove an advantage of the quantum cost of simulating $P$ over the classical cost. Third, we demonstrate tha…
Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases, such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations for the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we …
Efficient construction of time-invariant process tensors for simulating high-dimensional non-Markovian open quantum systems
Département de Physique de l’ENS Lyon, ENS de Lyon（里昂高等师范学校物理系）；SUPA, School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院）；Sorbonne Université, Institut des NanoSciences de Paris（索邦大学巴黎纳米科学研究所）；CNRS, Institut des NanoSciences de Paris（法国国家科学研究中心巴黎纳米科学研究所）
An all-optical scheme for simulating non-Markovian evolution of a quantum system is proposed. It uses only linear optics elements and by controlling the system parameters allows one to control the presence or absence of information backflow from the environment. A sufficient and necessary condition for the non-Markovianity of our channel based on Gaussian inputs is proved. Various criteria for detecting non-Markovianity are also investigated by checking the dynamical evolution of the channel.
The advent of Noisy Intermediate-Scale Quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum …
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space and it is shown, that this method is capable of simulating quantum master equations with negative transition rates. Non-Markovian effects in the reduced systems dynamics can be treated within this approach by employing the time-convolutionless projection operator technique. This ansatz yields a systematic perturbative expansion of the reduced systems dynamic…
We consider the problem of constructing a "universal set" of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of processes from the universal set. In particular, for quantum systems of dimension $d$, we explicitly construct a universal set of semigroup generators, parametrized by $d^2-3$ continuous parameters, and prove that a necessary and sufficient condition for the dynamical simulation of a $d$ dimensional Markovian quantum system is the ability to implement a) quant…
Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心）；State Key Laboratory of Porous Materials for Separation and Conversion & MOE Key Laboratory of Computational Physical Sciences & Department of Chemistry, Fudan University（复旦大学化学系多孔材料分离转化国家重点实验室及计算物理科学教育部重点实验室）；Hefei National Laboratory（合肥国家实验室）
A Lie-algebraic approach to non-Markovian quantum dynamics
The University of Hong Kong（香港大学）；Tsinghua University（清华大学）；Materials Innovation Institute for Life Sciences and Energy (MILES)（生命科学与能源材料创新研究所）；HKU-SIRI, Shenzhen（香港大学深圳研究院）
There is presently considerable interest in accurately simulating the evolution of open systems for which Markovian master equations fail. Examples are systems that are time-dependent and/or strongly damped. A number of elegant methods have now been devised to do this, but all use a bath consisting of a continuum of harmonic oscillators. While this bath is clearly appropriate for, e.g., systems coupled to the EM field, it is not so clear that it is a good model for generic many-body systems. Here we explore a different approach to exactly simulating open-systems: using a finite bath chosen to …
We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space, but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical …
We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. We propose to work with mixed-species crystals such that one species serves to …
Markovian heat engine boosted by quantum coherence
Centre for Bioinformatics and Photonics—CIBioFi（生物信息学与光子学中心）；Departamento de Física, Universidad del Valle（国立谷大学物理系）；Department of Physics, University of Oslo（奥斯陆大学物理系）
We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E {\bf73}, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by num…
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems. The circuits use ancilla qubits to simulate the environment, and memory effects are induced by storing information about the system on extra qubits. We simulate the amplitude damping channel and dephasing channel as examples …
We consider the natural generalization of the Schrödinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$ within precision $ε$. If the Lindbladian consists of $\mathrm{poly}(n)$ operators that can each be expressed as a linear combination of $\mathrm{poly}(n)$ tensor products of Pauli operators then the gate cost of our algorithm is $O(t\, \mathrm{polylog}(t/ε)\mathrm{poly}(n))$. We also obtain similar bounds for the cases where the Lindbladian consists of local operato…
A long-standing open problem in non-Markovian quantum state diffusion (QSD) approach to open quantum systems is to establish the non-Markovian QSD equations for multiple qubit systems. In this paper, we settle this important question by explicitly constructing a set of exact time-local QSD equations for $N$-qubit systems. Our exact time-local (convolutionless) QSD equations have paved the way towards simulating quantum dynamics of many-body open systems interacting with a common bosonic environment. The applicability of this multiple-qubit stochastic equation is exemplified by numerically solv…
Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use s…
For complex molecules, nuclear degrees of freedom can act as an environment for the electronic `system' variables, allowing the theory and concepts of open quantum systems to be applied. However, when molecular system-environment interactions are non-perturbative and non-Markovian, numerical simulations of the complete system-environment wave function become necessary. These many body dynamics can be very expensive to simulate, and extracting finite-temperature results - which require running and averaging over many such simulations - becomes especially challenging. Here, we present numerical …
Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a gener…
Non-Markovian dynamics in nonstationary Gaussian baths: a hierarchy of pure states approach
Universität Hamburg（汉堡大学）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；Max Planck Institute for the Structure and Dynamics of Matter（马普学会物质结构与动力学研究所）
