Session Y31: Non-Equilibrium Open Systems

Partially observed Schrödinger flows: an application to stochastic thermodynamics

Schrödinger bridges have emerged as an enabling theory for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably interpolates such marginals. The theory plays a pivotal role in a variety of contemporary developments in machine learning, stochastic control, thermodynamics, and biology, to name a few, impacting disciplines such as single-cell genomics, meteorology, and robotics. In this talk, we generalize Schrödinger's paradigm of bridges to account for partial observations. In doing so, we propose a framework that seeks the most likely underlying stochastic dynamics that match our limited observations. At the same time, the framework enables the estimation of quantities of interest, such as entropy production, heat, or work over a finite-time transition, when we only have access to partial information. This limited information can encompass a variety of data types, ranging from knowledge of distribution moments at different time points to knowledge of the average of functions on paths (i.e. averaged currents). We illustrate the practical applicability of the framework, given only knowledge of some averaged current over the transition of an unknown Markovian thermodynamic system, by finding the most likely underlying dynamics that led to those measurements, as well as estimating the entropy production incurred by the system along that thermodynamic transition.   

Three limiting cases - one theory: Decoding quantum dynamics from continuous measurements via higher order spectra in cases of telegraph noise, Gaussian noise, and stochastic clicks

Probing the dynamics of a quantum system is always challenging as the probe itself is quantum resulting in stochastic measurement records. We discuss measurement schemes from quantum transport [1], optical spin noise spectroscopy [2], and single photon counting [3,4] that exhibit very diverse records like random telegraph noise, mainly Gaussian laser shot noise, or stochastic clicks. This raises the question for a suitable quantitative unified evaluation procedure that can relate signatures of the measurement to a theoretical treatment of the system. We solve the problem by calculating higher-order spectra up to fourth order of the measurement records [1]. System parameters follow from fitting theoretical to experimental spectra. We employ recently derived general quantum mechanical expression for higher-order spectra that depend only on the open-system Liouvillian and the measurement operator and correctly include measurement induced back-action [2]. We demonstrate that a transition from probing a system with a continuous laser beam to probing with stochastic single photons preserves all information of the higher order spectra. Our scheme thus allows for decoding quantum dynamics from measurements at ultra-low light levels [3,4] with potential applications in high-resolution spectroscopy, quantum sensing, and quantum electrodynamics.   

Approaching the classical limit of Lindblad dynamics --- emergence of limit cycles, fixed points and algebraic decay

Iconic features of classical dissipative dynamics include persistent limit-cycle oscillations and critical slowing down at the onset of such oscillations, whereby the system relaxes purely algebraically in time.  On the other hand, quantum systems subject to generic Markovian dissipation decohere exponentially in time, approaching a unique steady state. We show how coherent limit-cycle oscillations and algebraic decay can emerge in a quantum system governed by a Markovian master equation. We illustrate these mechanisms using a single-spin model motivated by Landau-Lifshitz-Gilbert dynamics.   

Spectral properties of generic local Lindbladians: Implications for open system dynamics

The advent of noisy quantum simulators has led to a lot of interest in exploring the dynamical aspects of generic open quantum systems. We study the implications of generic features in the spectrum of interacting Lindbladians for the dynamics of open quantum systems. Notably, previous work has demonstrated that in certain classes of random Lindbladians, the rate of decay of an operator is closely correlated with its "weight” (i.e. the number of sites on which it acts non-trivially). We show that the correlation between weight and decay rates is a general feature of local Lindbladian dynamics. We justify this both numerically, by studying one-dimensional spin chains evolving under a generic interacting local Lindbladian and analytically using a simple non-interacting model.  We discuss the implications of this result for the dynamics of local observables, operator spreading, and other information-theoretic quantities.   

Oral: Creating Artificial Quantum Reservoirs through Driven-Dissipative Processes in Superconducting Circuits

Energy dissipation and dephasing are commonly perceived to be detrimental to quantum information processing. However engineering driven-dissipation offers new possibilities to prepare, control and probe many-body quantum states, and can be a powerful tool to help understand the effect of environmental couplings in analog quantum simulators. In this context, we develop a superconducting circuit lattice experiment with tunable local baths, and utilize the driven-dissipative processes between superconducting qubits and their readout resonators to prepare and stabilize single- and multi- qubit states. These quantum states can serve as artificial quantum reservoirs with controllable chemical potential or temperature. We discuss plans to apply these controlled artificial reservoirs to study the dynamics of many-body systems in our open-system quantum simulator, and for quantum thermodynamics and implementing quantum heat engines.   

Signature of Liouvillian exceptional point in stationary current noise

Open quantum systems coupled to thermal reservoirs naturally exhibit non-Hermitian physics; their time evolution can be described by quantum master equations characterized by Liouvillian superoperators, accounting for both free Hamiltonian evolution and dissipation due to coupling to the reservoirs, the latter being inherently non-Hermitian. An interesting feature of non-Hermitian physics is the presence of exceptional points (EPs), which can also be found in dissipative open quantum systems as Liouvillian EPs. At an EP, the operator exhibits a singularity where eigenvalues and corresponding eigenvectors coincide, rendering the operator non-diagonalizable and only transformable into the Jordan block form. In the present study, we consider a quantum thermal machine, consisting of two interacting quantum dots attached to two electrodes, whose Liouvillian has an EP. By focusing on the steady state electronic current noise between the electrodes, we show that the Jordan block structure at the Liouvillian EP leads to a super-Lorentzian line shape of the current noise spectrum.   

Probabilistic Unitary Formulation of Open Quantum System Dynamics

We show explicitly that for any continuously evolving open quantum system, be it finite (d-dimensional) or countably infinite dimensional,  its dynamics can be described by a time-dependent Hamiltonian and probabilistic combinations of up to d-1 (d → ∞ for infinite dimensional case), instead of d²-1, time-dependent unitary operators, resulting in a quadratic improvement in simulation resources. Importantly, both types of operations must be initial state-dependent in general, and thus the simulation is tailored to that initial state. Such description is exact under all cases, and does not rely on any assumptions other than the continuity and differentiability of the density matrix. It turns out that upon generalizations, the formalism can also be used to describe general quantum channels, which may not be complete positive or even positive, and results in a Kraus-like representation. Experimentally, the formalism provides a scheme to control a quantum state to evolve along designed quantum trajectories, and can be particularly useful in quantum computing and quantum simulation scenes since only unitary resources are needed for implementation. Philosophically,  it provides us with a new perspective to understand the dynamics of open quantum systems and related problems such as decoherence and quantum measurement, i.e. the non-unitary evolution of quantum states can thereby be regarded as the combined effect of state-dependent deterministic evolutions and probabilistic applications of unitary operators.   

Exact speed limit for measurement of quantum systems

We present a fundamental lower limit on the time required for a measurement apparatus to extract the information of a quantum system. The "measurement speed limit" is exact, i.e., derived without any approximations. In particular, the bound is valid for any strength of coupling between system and device, and thus can account for arbitrarily strong non-Markovian correlation effects. The limit depends on the details of the coupling between the system and measurement device, and the correlation functions of the measurement device. In the context of quantum information processing, the result provides a fundamental lower limit (“best case scenario”) for the readout time of qubits for a given device, providing a possible benchmark and guiding principles for optimizing protocols and architectures. We compare the limit with actual readout times in circuit-based qubit architectures.

The bound also provides an upper limit ("worst case scenario") for the rate of uncontrolled information loss in quantum systems due to noise and fluctuations from the environment.   

Real-time Quantum Monte Carlo Algorithm for Open Quantum Systems

We present a real-time stochastic approach based on density matrix quantum Monte Carlo (QMC) to simulate the dynamics of open quantum systems coupled to infinite-dimensional quantum baths. This approach stochastically samples the time-dependent density matrix of a many-body system evolving under a Markovian or non-Markovian master equation, enabling a comprehensive investigation of the dynamics of open quantum systems within the field of Hamiltonian quantum computing, including both gate-model quantum computing and quantum annealing. Through comparative analysis with exact solutions of quantum master equations, we demonstrate that QMC exhibits excellent agreement and showcases significant improvements in computational time and memory overhead. Additionally, the method's inherent ability to access the density matrix enables the efficient computation of various quantum information metrics, such as entanglement entropy and purity, during time evolution. As QMC is unconstrained by entanglement, this paves the way for larger scale simulations of various time-dependent system behaviors such as quantum quenches than is possible using alternative methods.   

Unveiling average symmetry-protected topological phases through tensor network states

Tensor network states serve as a natural framework for characterizing the topological phases of matter, and handling the decoherence of the quantum states in open quantum systems. In this talk, we will introduce the tensor network representation of average symmetry-protected topological (ASPT) phases by locally-purified density operators. In this framework, we can unambiguously define the exact and average symmetries and produce the complete classification of ASPT phases in (1+1)D and (2+1)D systems without choosing a specific basis.   

Tunable discrete time crystals

Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, where multiple interacting bodies settle into a dynamical collective steady state, breaking the discrete time translational symmetry of the Hamiltonian. Several questions regarding DTCs remain unanswered, for example, their stability mechanism against drive heating and fluctuations, possibility of realization in a classical system and existence of multiple DTC phases beyond subharmonic entrainment [1]. Here, we report observation of multiple DTC phases, including subharmonic, anharmonic, and a novel biharmonic phase, stabilized by dissipation, in a nanoelectromechanical system (NEMS) based on coupled graphene and silicon nitride membrane resonators [2]. Experimental evidence for emergence of many-body features, existence of long-range time and spatial order, and rigidity against parameter fluctuations or noise confirm the time-crystalline nature of these symmetry-broken phases. Furthermore, controlled mechanical strain drive transitions between these

phases with different symmetries, thereby mapping the emergent time-crystalline phase diagram. Analysis of a mean-field model provides crucial insights into the dynamical nature of these phases. However, failure of the mean-field model at time-crystalline phase boundary confirms many-body nature of the emergent DTC phases. These observations of the rich phase diagram with a range of distinct DTC phases rival the complexity of time crystals to that of spatial crystals.   

Maximum Caliber Principle derives Maxwell-Onsager reciprocal relations for Fundamental Observables and Forces in Nonequilibria

A powerful concept of thermodynamic equilibria is Maxwell's reciprocal relations. They can give hard-to-measure information about important driving forces from easy-to-measure observables. It would be valuable to have corresponding reciprocal relations for nonequilibrium dynamics. While some efforts have been made in this direction in the fields of large deviation theory and stochastic thermodynamics, they are often ad-hoc and/or limited by idealized-reservoir assumptions. Here we derive general and foundational relations based on the nonequilibrium principle of Maximum Caliber. We define a set of non-degenerate observables of distribution and fluxes that parametrizes the full degrees of freedom of nonequilibria and show how their conjugated path entropic forces can be connected to those defined in stochastic thermodynamics. We illustrate the reciprocal relationships on toy models of molecular motors.