Quantum Master Equation Research Articles

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems.

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

Computation of biological conductance with Liouville quantum master equation

Recent experiments have revealed that single proteins can display high conductivity, which stays finite for low temperatures, decays slowly with distance, and exhibits a rich spatial structure featuring highly conducting and strongly insulating domains. Here, we intruduce a new formula by combining the density matrix of the Liouville-Master Equation simulating quantum transport in nanoscale devices, and the phenomenological model of electronic conductance through molecules, that can account for the observed distance- and temperature dependence of conductance in proteins. We demonstrate its efficacy on experimentally highly conductive extracellular cytochrome nanowires, which are good candidates to illustrate our new approach by calculating and visualizing their electronic wiring, given the interest in the arrangement of their conducting and insulating parts. As proteins and protein nanowires exhibit significant potential for diverse applications, including energy production and sensing, our computational technique can accelerate the design of nano-bioelectronic devices.

Coherent Acoustic Control of Defect Orbital States in the Strong-Driving Limit

We use a bulk acoustic wave resonator to demonstrate coherent control of the excited orbital states in a diamond nitrogen-vacancy (NV) center at cryogenic temperature. Coherent quantum control is an essential tool for understanding and mitigating decoherence. Moreover, characterizing and controlling orbital states is a central challenge for quantum networking, where optical coherence is tied to orbital coherence. We study resonant multiphonon orbital Rabi oscillations in both the frequency and time domain, extracting the strength of the orbital-phonon interactions and the coherence of the acoustically driven orbital states. We reach the strong-driving limit, where the physics is dominated by the coupling induced by the acoustic waves. We find agreement between our measurements, quantum master-equation simulations, and a Landau-Zener transition model in the strong-driving limit. Using perturbation theory, we derive an expression for the orbital Rabi frequency versus the acoustic drive strength that is nonperturbative in the drive strength and agrees well with our measurements for all acoustic powers. Motivated by continuous-wave spin-resonance-based decoherence protection schemes, we model the orbital decoherence and find good agreement between our model and our measured few-to-several-nanoseconds orbital decoherence times. We discuss the outlook for orbital decoherence protection. Published by the American Physical Society 2024

Efficient Microwave Photon-to-Electron Conversion in a High-Impedance Quantum Circuit.

We demonstrate an efficient and continuous microwave photon-to-electron converter with large quantum efficiency (83%) and low dark current. These unique properties are enabled by the use of a high kinetic inductance disordered superconductor, granular aluminium, to enhance light-matter interaction and the coupling of microwave photons to electron tunneling processes. As a consequence of strong coupling, we observe both linear and nonlinear photon-assisted processes where two, three, and four photons are converted into a single electron at unprecedentedly low light intensities. Theoretical predictions, which require quantization of the photonic field within a quantum master equation framework, reproduce well the experimental data. This experimental advancement brings the foundation for high-efficiency detection of individual microwave photons using charge-based detection techniques.

Coherent feedback ground state cooling of the mechanical resonator in quadratic optomechanical system assisted by an atomic ensemble.

We propose a scheme for cooling a mechanical resonator to its ground state in a quadratic optomechanical system, assisted by an atomic ensemble in the unresolved sideband regime. The system features an auxiliary cavity directly coupled to an optical cavity, with a portion of the optical cavity's output field being fed back through an asymmetric beam splitter. Utilizing quantum Langevin and master equations, we derive the optical fluctuation spectrum, the cooling rate, and the mean phonon number of the mechanical resonator. Our results demonstrate that the feedback mechanism substantially enhances the cooling rate. Furthermore, under optimal cooling conditions, the mechanical resonator achieves ground state cooling even with weaker optomechanical coupling strengths and higher auxiliary cavity dissipation rates, thereby mitigating the experimental constraints associated with these parameters. Additionally, we provide the feasible ranges for optomechanical coupling strength and atomic decay rates. Our findings suggest promising avenues for quantum manipulation in nonlinear systems and its applications in macroscopic optical devices.

Adding stubs to quantum string field theories

Generalizing recent work by Schnabl-Stettinger and Erbin-Fırat, we outline a universal algebraic procedure for ‘adding stubs’ to string field theories obeying the BV quantum master equation. We apply our results to classical and quantum closed string field theory as well as to open-closed string field theory. We also clarify several aspects of the integration-out process in the co-algebraic formulation of string field theory at the quantum level.

Adaptive spiking, itinerancy, and quantum effects in artificial neuron circuit hardware with niobium–hafnium oxide-niobium memristor devices inserted

To improve artificial intelligence/autonomous systems and help with treating neurological conditions, there is a requirement for the discovery and design of artificial neuron hardware that mimics the advanced functionality and operation of the neural networks available in biological organisms. We examine experimental artificial neuron circuits that we designed and built in hardware with memristor devices using 4.2 nm of hafnium oxide and niobium metal inserted in the positive and negative feedback of an oscillator. At room temperature, these artificial neurons have adaptive a spiking behavior and hybrid non-chaotic/chaotic modes. When networked, they output with strong itinerancy, and we demonstrate a four-neuron learning network and modulation of signals. The superconducting state at 8.1 K results in Josephson tunneling with signs that the hafnium oxide ionic states are influenced by quantum control effects in accordance with quantum master equation calculations of the expectation values and correlation functions with a calibrated time-dependent Hamiltonian. These results are of importance to continue advancing neuromorphic hardware technologies that integrate memristors and other memory devices for many biological-inspired applications and beyond that can function with adaptive-itinerant spiking and quantum effects in their principles of operation.

Understanding multiple timescales in quantum dissipative dynamics: Insights from quantum trajectories

Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously. Published by the American Physical Society 2024

Coherent control from quantum commitment probabilities.

We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail.

Entropy variances of pure coherent states in the diffusion channel

Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system’s complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

The Quantum A∞-relations on the elliptic curve

We define and prove the existence of the Quantum A∞-relations on the Fukaya category of the elliptic curve, using the notion of the Feynman transform of a modular operad, as defined by Getzler and Kapranov. Following Barannikov, these relations may be viewed as defining a solution to the quantum master equation of Batalin-Vilkovisky geometry.

Quarkonium dynamics in the quantum Brownian regime with non-abelian quantum master equations

We present numerical solutions in a one-dimensional setting of quantum master equations that have been recently derived. We focus on the dynamics of a single heavy quark-antiquark pair in a Quark-Gluon Plasma in thermal equilibrium, in the so-called quantum Brownian regime where the temperature of the plasma is large in comparison with the spacing between the energy levels of the QQ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ Q\\overline{Q} $$\\end{document} system. The one-dimensional potential used in the calculations has been adjusted so as to produce numbers that are relevant for the phenomenology of the charmonium. The equations are solved using different initial states and medium configurations. Various temperature regimes are studied and the effects of screening and collisions thoroughly analyzed. Technical features of the equations are analyzed. The contributions of the different operators that control the evolution are discussed as a function of the temperature. Some phenomenological consequences are addressed.

Quantum kernels for classifying dynamical singularities in a multiqubit system

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

Quantum Master Equations: Tips and Tricks for Quantum Optics, Quantum Computing, and Beyond

Quantum master equations are an invaluable tool to model the dynamics of a plethora of microscopic systems, ranging from quantum optics and quantum information processing to energy and charge transport, electronic and nuclear spin resonance, photochemistry, and more. This tutorial offers a concise and pedagogical introduction to quantum master equations, accessible to a broad, cross-disciplinary audience. The reader is guided through the basics of quantum dynamics with hands-on examples that increase in complexity. The tutorial covers essential methods such as the use of the Lindblad master equation, Redfield relaxation, and Floquet theory, as well as techniques such as Suzuki-Trotter expansion and numerical approaches for sparse solvers. These methods are illustrated with code snippets implemented in and other languages, which can be used as a starting point for generalization and more sophisticated implementations. Published by the American Physical Society 2024

General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity.

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

Bexcitonics: Quasiparticle approach to open quantum dynamics.

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.

Diagrammatic representation and nonperturbative approximations of the exact time-convolutionless master equation.

The time-convolutionless master equation provides a general framework to model the non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to perturbative time-convolutionless quantum master equations. We further introduce a general iterative approach to construct nonperturbative approximations for the time-local generator as nested time-ordered exponential operators.

Limitations and improvements of the relaxation time approximation in the quantum master equation: Linear conductivity in insulating systems

Limitations and improvements of the relaxation time approximation in the quantum master equation: Linear conductivity in insulating systems