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 to the local coherent dynamics or by removing the dephasing. In particular, even circuits built from convex combinations of local free-fermion unitaries are nonintegrable. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.
We show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the $\check{R}$-matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of integrable nonunitary quantum circuits.
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptio…
Open-boundary integrable quantum circuits with different geometries
Instituto Galego de Física de Altas Enerxías (IGFAE), and Departamento de Física de Partículas, Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥德孔波斯特拉大学粒子物理系）；Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院物理系）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
Effective Noise Mitigation via Quantum Circuit Learning in Quantum Simulation of Integrable Spin Chains
School of Physical Science and Technology, Soochow University（苏州大学物理科学与技术学院）；Institute for Advanced Study, Soochow University（苏州大学前沿科学研究院）；Jiangsu Key Laboratory of Frontier Material Physics and Devices, Soochow University（苏州大学江苏省前沿材料物理与器件重点实验室）
We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly velocity $v_{B} = 1$. Using a transfer matrix approach, we present analytic results for the long-time value of the OTOC on and inside the light cone. First, we consider `dual-unitary' circuits with various levels of ergodicity, including the integrable and non-integrable kicked Ising model, where we show exponential decay away from the light cone and relate both the decay rate and the long-time val…
A family of reversible deterministic cellular automata, including the rules 54 and 201 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] as well as their kinetically constrained quantum (unitary) or stochastic deformations, is shown to correspond to integrable Floquet circuit models with local interactions round-a-face. Using inhomogeneous solutions of the star-triangle relation with a one or two dimensional spectral parameter, changing their functional form depending on the orientation, we provide an explicit construction of the transfer matrix and establish its conservation law and in…
Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In p…
Infinite-Level Hierarchy of Solvable Quantum Circuits
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Freie Universität Berlin（柏林自由大学）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；School of Physics, Trinity College Dublin（都柏林三一学院物理学院）
The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able to discriminate between quantum systems with integrable and chaotic dynamics. For chaotic systems the local-operator entanglement is expected to grow linearly in time, while it is expected to grow at most logarithmically in the integrable case. Here we study local-operator entanglement in dual-unitary quantum circuits, a class of "statistically solvable" quan…
Quantum integrability has proven to be a useful tool to study quantum many-body systems out of equilibrium. In this paper we construct a generic framework for integrable quantum circuits through the procedure of Floquet Baxterisation. The integrability is guaranteed by establishing a connection between Floquet evolution operators and inhomogeneous transfer matrices obtained from the Yang-Baxter relations. This allows us to construct integrable Floquet evolution operators with arbitrary depths and various boundary conditions. Furthermore, we focus on the example related to the staggered 6-verte…
We demonstrate ballistic spin transport of an integrable unitary quantum circuit, which can be understood either as a paradigm of an integrable periodically driven (Floquet) spin chain, or as a Trotterized anisotropic ($XXZ$) Heisenberg spin-1/2 model. We construct an analytic family of quasi-local conservation laws that break the spin-reversal symmetry and compute a lower bound on the spin Drude weight which is found to be a fractal function of the anisotropy parameter. Extensive numerical simulations of spin transport suggest that this fractal lower bound is in fact tight.
We study integrable spin chains and quantum and classical cellular automata with interaction range $\ell\ge 3$. This is a family of integrable models for which there was no general theory so far. We develop an algebraic framework for such models, generalizing known methods from nearest neighbor interacting chains. This leads to a new integrability condition for medium range Hamiltonians, which can be used to classify such models. A partial classification is performed in specific cases, including $U(1)$-symmetric three site interacting models, and Hamiltonians that are relevant for interaction-…
Kardar-Parisi-Zhang superdiffusion in chaotic quantum circuits
University of Ljubljana（卢布尔雅那大学）；King’s College London（伦敦国王学院）；Laboratoire de Physique de l’École Normale Superieure, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Cité（法国国家科学研究中心、巴黎高等师范学院、巴黎文理研究大学、索邦大学、巴黎西岱大学联合物理实验室）
We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front which never fades. We argue that these effects are valid for generic systems whose correlations propagate inside a light-con…
Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems
Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家研究委员会理论物理研究所）；Institute of Fundamental Physics IFF-CSIC（西班牙国家研究委员会基础物理研究所）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Max-Planck-Institut fur Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
We consider a class of quantum lattice models in $1+1$ dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in space" are given in terms of unitary transfer matrices. We show that for this class of circuits, generically non-integrable, one can compute explicitly all dynamical correlations of local observables. Our result is exact, non-pertubative, and holds for any dimension $d$ of the local Hilbert space. In the minimal case of qubits ($d = 2$) we also present a classif…
We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Rényi entropies. We argue that the latter generically grow \emph{sub-ballistically}, as $\propto\sqrt{t}$, in systems with diffusive transport. We provide strong evidence for this in both a U$(1)$ symmetric random circuit model and in a paradigmatic non-integrable spin chain, where energy is the sole conserved quantity. We interpret our results as a consequence of local quantum fluctuations in conserved densities, whose behavi…
We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mech…
We study 2-local Hamiltonian quantum systems, consisting of qubits interacting on the star graph of N vertices. We numerically demonstrate that these models are generically non-integrable at infinite temperature, and find evidence for a finite temperature phase transition to a glassy phase in generic models. Operators can become complicated in constant time: we explicitly find that there is no bound on out-of-time-ordered correlators, even at finite temperature. Operator growth is not correctly modeled by stochastic quantum dynamics, including Brownian Hamiltonian dynamics or random unitary ci…
