The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system), the steady state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems.
Exact nonequilibrium steady states of boundary driven circuit with XYZ gates
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；Institute of Mathematics, Physics and Mechanics（数学、物理和力学研究所）；Department of Physics, University of Wuppertal（伍珀塔尔大学物理系）
Electrical circuits with transient elements can be good examples of systems where non--steady irreversible processes occur, so in the same way as a steady state energy converter, we use the formal construction of the first order irreversible thermodynamic (FOIT) to describe the energetics of these circuits. In this case, we propose an isothermic model of two meshes with transient and passive elements, besides containing two voltage sources (which can be functions of time); this is a non--steady energy converter model. Through the Kirchhoff equations, we can write the circuit phenomenological e…
We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved superoperator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the local dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions t…
Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
Fuzhou University（福州大学）；College of Physics and Information Engineering, Fuzhou University（福州大学物理与信息工程学院）；Zhejiang University（浙江大学）；Tsinghua University（清华大学）；Tulane University（杜兰大学）
The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size -- from logarithmic to extensive to \emph{fractal}. We show how these outcomes in non-unitary circuits (that are "spacetime-dual" to…
Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（联合量子研究所，美国国家标准与技术研究院/马里兰大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Department of Physics, University of Basel（巴塞尔大学物理系）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
Dissipation-Induced Threshold on Integrability Footprints
Universidade de Lisboa（里斯本大学）；University of Stuttgart（斯图加特大学）；Center for Integrated Quantum Science and Technology（集成量子科学与技术中心）；Universidad Autónoma de Madrid（马德里自治大学）；OsloMet – Oslo Metropolitan University（奥斯陆城市大学）；University of Cambridge（剑桥大学）；Norwegian Quantum Software Centre (NorQSoft)（挪威量子软件中心）；Beijing Computational Science Research Center（北京计算科学研究中心）
Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp …
Symmetry and Topology of Monitored Quantum Dynamics
International Center for Quantum Materials, Peking University（北京大学量子材料国际中心）；Princeton Quantum Initiative, Princeton University（普林斯顿大学量子倡议计划）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）
We study heat current and the full statistics of heat fluctuations in a capacitively-coupled double quantum dot system. This work is motivated by recent theoretical studies and experimental works on heat currents in quantum dot circuits. As expected intuitively, within the (static) mean-field approximation, the system at steady-state decouples into two single-dot equilibrium systems with renormalized dot energies, leading to zero average heat flux and fluctuations. This reveals that dynamic correlations induced between electrons on the dots is solely responsible for the heat transport between …
We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the s…
Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate results in a steady state with an $L^{1/3}$ power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechan…
Dual-unitary circuits have emerged as a minimal model for chaotic quantum many-body dynamics in which the dynamics of correlations and entanglement remains tractable. Simultaneously, there has been intense interest in the effect of measurements on the dynamics of quantum information in many-body systems. In this work we introduce a class of models combining dual-unitary circuits with particular projective measurements that allow the exact computation of dynamical correlations of local observables, entanglement growth, and steady-state entanglement. We identify a symmetry preventing a measureme…
Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume and area-law entanglement. There is a correspondence between measurement-induced transitions in non-unitary quantum circuits in $d$ spatial dimensions and classical statistical mechanical models in $d+1$ dimensions. In certain limits these models map to percolation, but there is analytical and numerical evidenc…
We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling beh…
Charging capacitors using diodes at different temperatures. II Numerical studies
University of Arkansas（阿肯色大学）；G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Mathematics, Universidad Carlos III de Madrid（卡洛斯三世大学）
We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area law entanglement phase of the steady state. Our primary example is circuits with unitaries respecting a global Ising symmetry and two competing types of measurements. The phase diagram has an area law phase with spin glass order, which undergoes a direct transition to a paramagnetic phase with volume law entanglement, as well as a critical regime. Using mutual information diagnostics, we find that such entanglement transitions preserving a global symmetry …
Quantum trajectory simulation of two-dimensional non-equilibrium steady states with a trapped ion quantum processor
University of Nottingham（诺丁汉大学）；Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham（诺丁汉大学量子非平衡系统数学与理论物理中心）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Quantinuum；London Centre for Nanotechnology, University College London（伦敦纳米技术研究中心，伦敦大学学院）
We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two distinct dynamical phases, one characterized by a volume-law scaling of entanglement entropy, the other by an area-law. Employing stabilizer states and Clifford random unitary gates, we numerically investigate square lattices of linear dimension up to $L=48$ for two distinct measurement protocols. For both protocols, we observe a transition point where the domi…
