Showing papers on "Master equation published in 2022"
TL;DR: In this paper , the authors present an extensive introduction to quantum collision models (CMs), also known as repeated interactions schemes: a class of microscopic system-bath models for investigating open quantum systems dynamics whose use is currently spreading in a number of research areas.
44 citations
TL;DR: In this paper , a set of quantitative constraints on the minimum complexity necessary to reproduce gene coexpression patterns using synchronized burst models are derived, and they validate these findings by analyzing long-read sequencing data, where they find evidence of expression patterns largely consistent with these constraints.
20 citations
05 Sep 2022
TL;DR: In this article , the authors apply the master-equation program to a model that is exactly solvable, and which consists of two linearly coupled scalar fields evolving on a cosmological background.
Abstract: Abstract Master equations are commonly employed in cosmology to model the effect of additional degrees of freedom, treated as an “environment”, onto a given “system”. However, they rely on assumptions that are not necessarily satisfied in cosmology, where the environment may be out of equilibrium and the background is dynamical. In this work, we apply the master-equation program to a model that is exactly solvable, and which consists of two linearly coupled scalar fields evolving on a cosmological background. The light field plays the role of the system and the heavy field is the environment. By comparing the exact solution to the output of the master equation, we can critically assess its performance. We find that the master equation exhibits a set of “spurious” terms that explicitly depend on the initial conditions, and which arise as a consequence of working on a dynamical background. Although they cancel out in the perturbative limit of the theory (i.e. at leading orders in the interaction strength), they spoil resummation. However, when those terms are removed, the master equation performs impressively well to reproduce the power spectra and the amount of the decoherence of the light field, even in the strongly decohered regime. We conclude that master equations are able to perform late-time resummation, even though the system is far from the Markovian limit, provided spurious contributions are suppressed.
16 citations
TL;DR: In this paper , it was shown that the Redfield form of the Lindblad equation cannot preserve complete positivity in most cases, leading to physical inconsistencies such as inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, and violation of local conservation laws at the nonequilibrium steady state.
Abstract: It is very common in the literature to write a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in a system-bath coupling is of the so-called Redfield form, which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundamental requirements for any further approximations to the Redfield equation, which, if violated, leads to physical inconsistencies such as inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, and violation of local conservation laws at the nonequilibrium steady state. We argue that one or more of these conditions will generically be violated in all the weak system-bath-coupling Lindblad descriptions existing in the literature to our knowledge. As an example, we study the recently derived universal Lindblad equation and use these conditions to show the violation of local conservation laws due to inaccurate coherences but accurate populations in the energy eigenbasis. Finally, we exemplify our analytical results numerically in an interacting open quantum spin system.
15 citations
TL;DR: In this paper , a level-resolved protocol in a hybrid architecture for connecting a superconducting qubit and a magnon mode contained within a microwave cavity (resonator) to generate the local and global entangled states, enabling a wide range of applications in quantum communication, quantum metrology, and quantum information processing.
Abstract: We propose a level-resolved protocol in a hybrid architecture for connecting a superconducting qubit and a magnon mode contained within a microwave cavity (resonator) to generate the local and global entangled states, enabling a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Exploiting the high-degree of controllability in such a hybrid qubit-photon-magnon system, we derive effective Hamiltonians at the second- or the third-order resonant points by virtue of the strong counter-rotating interactions between the resonator and the qubit and between the resonator and the magnon. Consequently, we can efficiently generate the Bell states of the photon-magnon and the qubit-magnon subsystems and the Greenberger-Horne-Zeilinger state of the whole hybrid system. We also check the robustness of our protocol against the environmental noise by the Lindblad master equation. Our work makes this hybrid platform of high-degree of controllability a high-fidelity candidate for the realization of the maximally-entangled multiple states.
13 citations
TL;DR: The QNODE as mentioned in this paper is a latent neural ordinary differential equation (ODE) trained on expectation values of closed and open quantum systems dynamics, which can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations in an unsupervised way.
Abstract: The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counterintuitive nature of quantum mechanics. Here we present the QNODE, a latent neural ordinary differential equation (ODE) trained on expectation values of closed and open-quantum-systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems, respectively, in an unsupervised means. Furthermore, the QNODE rediscovers quantum-mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.
13 citations
TL;DR: In this article , the dynamics of entanglement in the quantum Ising chain with dephasing dissipation in a Lindblad master equation form were studied, and two unravelings which preserve the Gaussian form of the state were considered.
Abstract: We study the dynamics of entanglement in the quantum Ising chain with dephasing dissipation in a Lindblad master equation form. We consider two unravelings which preserve the Gaussian form of the state, allowing us to address large system sizes. The first unraveling gives rise to a quantum-state-diffusion dynamics, while the second one describes a specific form of quantum-jump evolution, suitably constructed to preserve Gaussianity. In the first case we find a crossover from area-law to logarithm-law entanglement scaling and draw the related phase diagram. In the second case we only find logarithm-law scaling, remarking on the different entanglement behavior for different unravelings of the same Lindblad equation. Finally, we compare these outcomes with the predictions of a non-Hermitian Hamiltonian evolution, finding conflicting results.
10 citations
TL;DR: In this article , a four-stroke Otto engine whose working fluid is a quantum Ising chain is modeled in a thermodynamically consistent way by means of a nonlocal Lindblad master equation.
Abstract: We study a four-stroke Otto engine whose working fluid is a quantum Ising chain. The thermodynamic cycle consists in sweeps of the transverse magnetic field occurring in thermal isolation, alternated by thermalisation strokes with reservoirs at different temperatures. The system–environment coupling is modelled in a thermodynamically consistent way by means of a nonlocal Lindblad master equation. We show that the engine may operate in four different operation modes, depending on the various parameters, in particular it can act as a heat engine and as a refrigerator. We detect an enhancement of the thermodynamic performance as the critical point is crossed, and investigate it in detail.
10 citations
TL;DR: In this paper , the authors present a short review of two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonians to a GKSL master equation for the full density matrix.
Abstract: A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.
10 citations
TL;DR: In this article , the authors consider the Schwinger model, a 1+1 dimensional U(1) gauge theory coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory.
Abstract: We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the non-equilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology.
9 citations
TL;DR: In this article , a general-purpose framework for formulating the dynamics of any subset of electronic reduced density matrix elements in terms of a formally exact generalized quantum master equation (GQME) is described.
Abstract: We describe a general-purpose framework for formulating the dynamics of any subset of electronic reduced density matrix elements in terms of a formally exact generalized quantum master equation (GQME). Within this framework, the effect of coupling to the nuclear degrees of freedom, as well as to any projected-out electronic reduced density matrix elements, is captured by a memory kernel and an inhomogeneous term, whose dimensionalities are dictated by the number of electronic reduced density matrix elements included in the subset of interest. We show that the memory kernel and inhomogeneous term within such GQMEs can be calculated from projection-free inputs of the same dimensionality, which can be cast in terms of the corresponding subsets of overall system two-time correlation functions. The applicability and feasibility of such reduced-dimensionality GQMEs is demonstrated on the two-state spin-boson benchmark model. To this end, we compare and contrast the following four types of GQMEs: (1) a full density matrix GQME, (2) a single-population scalar GQME, (3) a populations-only GQME, and (4) a subset GQME for any combination of populations and coherences. Using a method based on the mapping Hamiltonian approach and linearized semiclassical approximation to calculate the projection-free inputs, we find that while single-population GQMEs and subset GQMEs containing only one population are less accurate, they can still produce reasonable results and that the accuracy of the results obtained via the populations-only GQME and a subset GQME containing both populations is comparable to that obtained via the full density matrix GQMEs.
TL;DR: In this article , a detailed investigation of the energy transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses is presented.
Abstract: This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N2 and NO have dominant contributions to the NO formation and the corresponding extinction of N2 through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N2 and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.
TL;DR: In this article , two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation is studied, and the results not only demonstrate the interplay of PT symmetry and interaction on the exact few-body level, but also serve as a minimal illustration on how key features of non-hermitian many-body physics can be probed in a single-particle system.
Abstract: We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation. Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation, we show that the non-Hermitian effective Hamiltonian of the master equation gives rise to two-body scattering states with state- and interaction-dependent parity-time transition. The resulting two-body exceptional points can be extracted from the trace-preserving density-matrix dynamics of the same dissipative system with three atoms. Our results not only demonstrate the interplay of PT symmetry and interaction on the exact few-body level, but also serve as a minimal illustration on how key features of non-Hermitian few-body physics can be probed in an open dissipative many-body system.
TL;DR: In this paper , the authors considered the equilibration dynamics of a two-level quantum system in contact with multiple structured reservoirs that carry quantum information and developed a micromaser-like quantum master equation based on repeated interactions.
Abstract: We consider the equilibration dynamics of a two-level quantum system in contact with multiple structured reservoirs that carry quantum information. We develop a micromaser-like quantum master equation based on repeated interactions and show that some information is transferred from the quantum reservoir into the quantum system in the steady-state. In the results we obtained from the analytical methods we used, we have developed a clear expression of the information transferred to the two-level system in terms of information reservoir parameters and interaction coefficients of the probe qubit with the reservoirs. We propose an open quantum classifier model by developing a binary classification rule by use of these results. We also develop the analytical description of the classification process by quantum parameter estimation.
TL;DR: In this paper , the speed limit of the state transformation in open quantum systems described by the Lindblad type quantum master equation was investigated and the authors obtained universal bounds of the total entropy produced by the trace distance between the initial and final states in the interaction picture.
Abstract: We investigate the speed limit of the state transformation in open quantum systems described by the Lindblad type quantum master equation. We obtain universal bounds of the total entropy production described by the trace distance between the initial and final states in the interaction picture. Our bounds can be tighter than the bound of Vu and Hasegawa (2021 Phys. Rev. Lett. 126 010601) which measures the distance by the eigenvalues of the initial and final states: this distance is less than or equal to the trace distance. For this reason, our results can significantly improve Vu–Hasegawa’s bound. The trace distance in the Schrödinger picture is bounded by a sum of the trace distance in the interaction picture and the trace distance for unitary dynamics described by only the Hamiltonian in the quantum master equation.
TL;DR: In this article , a numerical method to determine the Hamiltonian of mean force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir was introduced, and the method adapts the time evolving matrix product operator (TEMPO) algorithm to imaginary-time propagation.
Abstract: We introduce a numerical method to determine the Hamiltonian of mean force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the time evolving matrix product operator (TEMPO) algorithm to imaginary-time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.
TL;DR: Cirio et al. as discussed by the authors proposed a method for quantum computing based on the Quantum Quantum Computing (QCOC) project at the University of Michigan, Ann Arbor, Michigan 48109-1040, USA
Abstract: Mauro Cirio ,1,* Po-Chen Kuo ,2,3 Yueh-Nan Chen ,2,3 Franco Nori ,4,5,6 and Neill Lambert 4,† 1Graduate School of China Academy of Engineering Physics, Haidian District, Beijing 100193, China 2Department of Physics, National Cheng Kung University, 701 Tainan, Taiwan 3Center for Quantum Frontiers of Research & Technology, NCKU, 70101 Tainan, Taiwan 4Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wakoshi, Saitama 351-0198, Japan 5RIKEN Center for Quantum Computing (RQC), Wakoshi, Saitama 351-0198, Japan 6Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
TL;DR: In this article , the Lyapunov equation is considered as a fundamental formalism for non-Hermitian quantum systems, and three different forms of the LME are derived via an equation of motion approach, by making increasing levels of controlled approximations.
Abstract: The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems, typically from quantum master equations. Despite this, the Lyapunov equation is seldom considered a fundamental formalism for linear open quantum systems. In this work we aim to change that. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems that can go beyond the limitations of various standard quantum master equation descriptions, while remaining of much less complexity than general exact formalisms. This also provides valuable insights for non-Hermitian quantum physics. In particular, we derive the Lyapunov equation for the most general number conserving linear system in a lattice of arbitrary dimension and geometry, connected to an arbitrary number of baths at different temperatures and chemical potentials. Three slightly different forms of the Lyapunov equation are derived via an equation of motion approach, by making increasing levels of controlled approximations, without reference to any quantum master equation. Then we discuss their relation with quantum master equations, positivity, accuracy and additivity issues, the possibility of describing dark states, general perturbative solutions in terms of single-particle eigenvectors and eigenvalues of the system, and quantum regression formulas. Our derivation gives a clear understanding of the origin of the non-Hermitian Hamiltonian describing the dynamics and separates it from the effects of quantum and thermal fluctuations. Many of these results would have been hard to obtain via standard quantum master equation approaches.
TL;DR: In this article , a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators is presented, and the transition to chaos is characterized by spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.
Abstract: The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators. Making use of this new region of integrability, we study the transition to chaos in terms of a two-parameter Liouvillian. The transition is characterized by the spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.
TL;DR: In this article , the authors discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes, and demonstrate how phases and phase transitions pertaining to the non-Hermitian quasICrystals fundamentally change the long-time, steady-state-approaching dynamics under the Lindblad master equation.
Abstract: We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While the resulting short-time dynamics is governed by non-Hermitian variants of the Aubry-Andr\'e-Harper model, we demonstrate how phases and phase transitions pertaining to the non-Hermitian quasicrystals fundamentally change the long-time, steady-state-approaching dynamics under the Lindblad master equation. Our schemes are based on an exact mapping between the eigenspectrum of the Liouvillian superoperator with that of the non-Hermitian Hamiltonian, under the condition of quadratic fermionic systems subject to linear dissipation. Our work suggests a systematic route toward engineering exotic quantum dynamics in open systems, based on insights of non-Hermitian physics.
TL;DR: In this article , the authors show how to use repeated interaction models, highlighting their strengths and some technical subtleties often overlooked in the literature, and compare the standard collisional derivation with the standard microscopic one.
Abstract: In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model.
TL;DR: In this article , a dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation, where the Lindblad jump operators constitute the eigenoperators of the free dynamics.
Abstract: A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator form. The kinetic coefficients are generally time-dependent and incorporate information on the kinematics and memory effects, while the operators manifest the dynamical symmetry. Specifically, we focus on time-translation symmetric dynamics, where the Lindblad jump operators constitute the eigenoperators of the free dynamics. This symmetry is motivated by thermodynamic microscopic considerations, where strict energy conservation between system and environment imposes the time-translation symmetry. The construction is generalized to other symmetries, and to driven quantum systems. The formalism is illustrated by three exactly solvable non-Markovian models, where the exact reduced description exhibits a dynamical symmetric structure. The formal structure of the master equation leads to a first principle calculation of the exact kinetic coefficients. This opens the possibility to simulate in a modular fashion non-Markovian dynamics.
TL;DR: An analysis of single-cell and single-nucleus RNA sequencing data using models of transcriptional dynamics reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.
Abstract: The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a bursty or switching promoter to a fairly general set of Markovian or deterministically delayed monomolecular RNA interconversion reactions with no feedback. We provide numerical solutions for the RNA copy number distributions the models induce, and solve several systems with splicing and degradation. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.
TL;DR: In this paper , a quantum algorithm for the prediction of population dynamics via the unraveled Lindblad equation is presented. But the quantum algorithm is not suitable for the simulation of quantum systems.
Abstract: Accurate simulation of the time evolution of a quantum system under the influence of an environment is critical to making accurate predictions in chemistry, condensed-matter physics, and materials sciences. Whereas there has been a recent surge in interest in quantum algorithms for the prediction of nonunitary time evolution in quantum systems, few studies offer a direct quantum analog to the Lindblad equation. Here, we present a quantum algorithm---utilizing a decomposition of nonunitary operators approach---that models dynamic processes via the unraveled Lindblad equation. This algorithm is employed to probe both a two-level system in an amplitude damping channel as well as the transverse field Ising model in a variety of parameter regimes; the resulting population dynamics demonstrate excellent agreement with classical simulation, showing the promise of predicting population dynamics utilizing quantum devices for a variety of important systems in molecular energy transport, quantum optics, and other open quantum systems.
TL;DR: In this paper , the authors generalize the previous concept of thermomajorization by introducing the concept of continuous thermOMajorization, and show that this partial order of energy distributions provides necessary and sufficient conditions for the existence of a thermalization process generated by a Markovian master equation.
Abstract: The authors generalize the previous concept of thermomajorization by introducing the concept of continuous thermomajorization, and show that this partial order of energy distributions provides necessary and sufficient conditions for the existence of a thermalization process generated by a Markovian master equation. The results may pave the way to an algorithmic approach to the development of quantum thermodynamic protocols.
TL;DR: In this paper , a generalized cumulant expansion is used to derive a time-local master equation for Rabi-driven quantum systems subject to non-Markovian noise.
Abstract: Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. We present a systematic method based on generalized cumulant expansions for deriving a time-local master equation for such systems. This master equation has an intuitive form that directly parallels a standard Lindblad equation, but contains several surprising features: the combination of driving and non-Markovianity results in effective time-dependent dephasing rates that can be negative, and the noise can generate Hamiltonian renormalizations even though it is classical. We analyze in detail the highly relevant case of a Rabi-driven qubit subject to various kinds of non-Markovian noise including 1/f fluctuations, finding an excellent agreement between our master equation and numerically-exact simulations over relevant timescales. The approach outlined here is more accurate than commonly employed phenomenological master equations which ignore the interplay between driving and noise.
TL;DR: In this paper , a simple phenomenological dynamical model known as the post-Markovian master equation (PMME) accurately captures and predicts non-markovian noise in a superconducting qubit system.
Abstract: Non-Markovian noise presents a particularly relevant challenge in understanding and combating decoherence in quantum computers, yet is challenging to capture in terms of simple models. Here we show that a simple phenomenological dynamical model known as the post-Markovian master equation (PMME) accurately captures and predicts non-Markovian noise in a superconducting qubit system. The PMME is constructed using experimentally measured state dynamics of an IBM Quantum Experience cloud-based quantum processor, and the model thus constructed successfully predicts the non-Markovian dynamics observed in later experiments. The model also allows the extraction of information about crosstalk and measures of non-Markovianity. We demonstrate definitively that the PMME model predicts subsequent dynamics of the processor better than the standard Markovian master equation.
TL;DR: In this article , the authors investigate the validity of local quantum master equations by analyzing a paradigmatic system made of two harmonic oscillators each in contact with a heat bath and find that local master equations generally fail to reproduce the results of an exact quantum-Langevin-equation description.
Abstract: Local quantum master equations provide a simple description of interacting subsystems coupled to different reservoirs. They have been widely used to study nonequilibrium critical phenomena in open quantum systems. We here investigate the validity of such a local approach by analyzing a paradigmatic system made of two harmonic oscillators each in contact with a heat bath. We evaluate the steady-state mean occupation number for varying temperature differences and find that local master equations generally fail to reproduce the results of an exact quantum-Langevin-equation description. We relate this property to the inability of the local scheme to properly characterize intersystem correlations, which we quantify with the help of the quantum mutual information.
TL;DR: In this paper , a low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection is proposed, which alleviates this problem and restores consistency with the weak-coupling master equation with a minimal hierarchy.
Abstract: The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling strength. However, in its standard form, this method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here, we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection, which alleviates this problem and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna-Matthews-Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.
TL;DR: In this paper , the authors measured the statistical vibrational autodetachment (VAD) and radiative cooling rates of isolated para-benzoquinone (pBQ, C6H4O2) radical anions using the cryogenic electrostatic ion storage ring facility DESIREE.
Abstract: We report measurements of the statistical vibrational autodetachment (VAD, also called thermionic emission) and radiative cooling rates of isolated para-benzoquinone (pBQ, C6H4O2) radical anions using the cryogenic electrostatic ion storage ring facility DESIREE. The results are interpreted using master equation simulations with rate coefficients calculated using statistical detailed balance theory. The VAD rate is determined by measuring the time-dependent yield of neutral pBQ due to spontaneous electron emission from a highly-excited ensemble of anions formed in an electron-attachment ion source. Competition with radiative cooling quenches the VAD rate after a critical time of τc = 11.00(5) ms. Master equation simulations which reproduce the VAD yield provide an estimate of the initial effective vibrational temperature of the ions of 1100(20) K, and provide insight into the anion formation scenario. A second measurement of the radiative cooling rate of pBQ- stored for up to 0.5 s was achieved using time-dependent photodetachment action spectroscopy across the 2Au ← 2B2g and 2B2u ← 2B2g transitions. The rate at which hot-band contributions fade from the action spectrum is quantified by non-negative matrix factorisation. This is found to be commensurate with the average vibrational energy extracted from the simulations, with 1/e lifetimes of 0.16(3) s and 0.1602(7) s, respectively. Implications for astrochemistry are discussed.