OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors.

Open quantum systems and study of decoherence are important for our fundamental understanding of quantum physical phenomena. For practical purposes, a large number of quantum protocols exist that exploit quantum resources, e.g., entanglement, which allows us to go beyond what is possible to achieve by classical means. We combine concepts from open quantum systems and quantum information science and give a proof-of-principle experimental demonstration---with teleportation---that it is possible to implement efficiently a quantum protocol via a non-Markovian open system. The results show that, at the time of implementation of the protocol, it is not necessary to have the quantum resource in the degree of freedom used for the basic protocol---as long as there exists some other degree of freedom or the environment of an open system, which contains useful resources. The experiment is based on a pair of photons, where their polarizations act as open system qubits and frequencies as their environments, while the path degree of freedom of one of the photons represents the state of Alice's qubit to be teleported to Bob's polarization qubit.

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 fulfill the gap of studying such dynamics by (1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and (2) developing an efficient quantum algorithm for simulating such dynamics with cost $${\mathcal {O}}(t\, \textrm{polylog}(t/\epsilon ))$$ for evolution time t and precision $$\epsilon $$ . Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with open quantum systems as well.

We study the optimal control problem in a non-Markovian open quantum system. The quantum system of interest is coupled to its local environment, which is dissipative in nature and tends to decay the quantum system. Based on the non-Markovian master equation, we study the non-Markovian effects on the system dynamics. The non-Markovian environment has dual effects on the quantum system: the dissipation and the backaction. The dissipation effect makes the system lose of quantum features, whereas the backaction revives it. We further design quantum control laws to control the system. The optimal control principle is studied to steer to quantum state to a target state. Finally, as an example, we used the optimal control method to control the quantum decoherence.

The weak-coupled two-level open quantum system described by non-Markovian Time-convolution-less master equation is investigated in this paper. The cut-off frequency, coupling constant and transition frequency, which impact on the system's decay rate, coherence factor and purity, are investigated. The appropriate parameters used in system simulation experiments are determined by comparing analysis results of different values of parameters for the effects of system performance. The control laws used to transfer the system states are designed on the basis of the Lyapunov stability theorem. Numerical simulation experiments are implemented under the MATLAB environment. The features of the free evolution trajectory of the non-Markovian systems and the states transfer from a pure state to a desired pure state under the action of the proposed control laws are studied, respectively. By comparing the experimental results, the effectiveness of the proposed quantum Lyapunov control method applied to the state transfer in non-Markovian open quantum systems is verified. Meanwhile, the influences of different control parameters and cut-off frequencies on the system performance are analyzed.

We introduce a general numerical method to compute the dynamics and multitime correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time-evolving block decimation for one-dimensional chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. We illustrate the power of this method by studying two examples. First, we study the thermalization of individual spins of a short XYZ Heisenberg chain with strongly coupled thermal leads. Our results confirm the complete thermalization of the chain when coupled to a single bath, and they reveal distinct effective temperatures in low-, mid-, and high-frequency regimes when the chain is placed between a hot and a cold bath. Second, we study the dynamics of diffusion in a longer XY chain, when each site couples to its own bath.

We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall causing insurmountable difficulties in the effective modelling of the controlled system. We show that the only way to avoid these problems is a full microscopic description of the controlled system in presence of noise. We illustrate our findings with a paradigmatic example.

We describe a general-purpose computational toolkit for simulating open quantum systems, which provides numerically exact solutions for composites of zero-dimensional quantum systems that may be strongly coupled to multiple, quite general non-Markovian environments. It is based on process tensor matrix product operators (PT-MPOs), which efficiently encapsulate environment influences. The code features implementations of several PT-MPO algorithms, in particular Automated Compression of Environments for general environments comprised of independent modes as well as schemes for generalized spin boson models. The latter includes a divide-and-conquer scheme for periodic PT-MPOs, which enable million time step simulations for realistic models. PT-MPOs can be precalculated and reused for efficiently probing different time-dependent system Hamiltonians. They can also be stacked together and combined to provide numerically complete solutions of small networks of open quantum systems. The code is written in C++ and is fully controllable by configuration files, for which we have developed a versatile and compact human-readable format.

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry and quantum information. In close analogy to a classical Markov process, the interaction of an open quantum system with a noisy environment is often modelled by a dynamical semigroup with a generator in Lindblad form, which describes a memoryless dynamics leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence and correlations. Here, recent results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of memory effects. The general theory is illustrated by a series of examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This article further explores the various physical sources of non-Markovian quantum dynamics, such as structured spectral densities, nonlocal correlations between environmental degrees of freedom and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments on the detection, quantification and control of non-Markovian quantum dynamics are also discussed.

Solving non-Markovian open quantum systems with multi-channel reservoir coupling

In this study, we reexamine a recent optimal control simulation targeting the preparation of a superposition of two excited electronic states in the UV range in a complex molecular system. We revisit this control from the perspective of reinforcement learning, offering an efficient alternative to conventional quantum control methods. The two excited states are addressable by orthogonal polarizations and their superposition corresponds to a right or left localization of the electronic density. The pulse duration spans tens of femtoseconds to prevent excitation of higher excited bright states what leads to a strong perturbation by the nuclear motions. We modify an open source software by L. Giannelli et al., Phys. Lett. A, 434, 128054 (2022) that implements reinforcement learning with Lindblad dynamics, to introduce non-Markovianity of the surrounding either by timedependent rates or more exactly by using the hierarchical equations of motion with the QuTiP-BoFiN package. This extension opens the way to wider applications for non-Markovian environments, in particular when the active system interacts with a highly structured noise.

Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems. We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems. Open quantum systems with pure stationary states of linear oscillator are suggested. We consider stationary states for the Lindblad equation. We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations.

Information scrambling refers to the phenomenon in which local quantum information in a many-body system becomes dispersed throughout the entire system under unitary evolution. It has been extensively studied in closed quantum systems, where it is quantified by operator size growth, revealing deep connections between condensed matter physics, high-energy physics, and quantum information. However, when extending the study of operator size dynamics to open quantum systems, two different definitions of operator size distributions emerge. These definitions are based on different treatments of the bath. In this work, we aim to establish a unified picture for operator size dynamics in open quantum systems, using the solvable Brownian SYK models at generic system size. In particular, we provide the conditions under which the signature of scrambling transition — discovered using one particular definition — appears in operator size dynamics under the other definition. Additionally, we extend previous studies by exploring finite-size effects that are not captured by the scramblon theory. Our results provide a refined understanding of operator size dynamics in open quantum systems.

Open quantum systems (OQS) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. Here, we give an overview of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. We emphasize the physical interpretation and derivation of the various approaches, explore how they are connected and examine how different methods may be suitable for solving different problems.

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this Letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.

We investigate the preparation of a target initial state for a two-level (qubit) system from a system-environment equilibrium or correlated state by an external field. The system-environment equilibrium or correlated state results from the inevitable interaction of the system with its environment. An efficient method in an extended auxiliary Liouville space is introduced to describe the dynamics of the non-Markovian open quantum system in the presence of a strong field and an initial system-environment correlation. By using the time evolutions of the population difference, the state trajectory in the Bloch sphere representation and the trace distance between two reduced system states of the open quantum system, the effect of initial system-environment correlations on the preparation of a system state is studied. We introduce an upper bound and a lower bound for the trace distance within our perturbation formalism to describe the diverse behaviors of the dynamics of the trace distance between various correlated states after the system state preparation. These bounds that are much more computable than similar bounds in the literature give a sufficient condition and a necessary condition for the increase of the trace distance and are related to the witnesses of non-Markovianity and initial system-bath correlation.