Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension

Abstract

Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.

arXiv comment7 pages, 3 figures

References in corpus (31)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Discrete time crystals: rigidity, criticality, and realizations
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Solution of a minimal model for many-body quantum chaos
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Prethermalization and thermalization in models with weak integrability breaking
• Exact dynamics in dual-unitary quantum circuits
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Unitary circuits of finite depth and infinite width from quantum channels
• Spectral statistics and many-body quantum chaos with conserved charge
• Sub-ballistic growth of Rényi entropies due to diffusion
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Scrambling in Random Unitary Circuits: Exact Results
• Maximum velocity quantum circuits
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula

Cited by in corpus (89)

• Random Quantum Circuits
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Influence matrix approach to many-body Floquet dynamics
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Temporal entanglement, quasiparticles and the role of interactions
• Many-body delocalisation as symmetry breaking
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Measuring nonstabilizerness via multifractal flatness
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
• Entanglement Barriers in Dual-Unitary Circuits
• Holographic dynamics simulations with a trapped ion quantum computer
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Dynamics of charge fluctuations from asymmetric initial states
• Construction and the ergodicity properties of dual unitary quantum circuits
• Correlations and commuting transfer matrices in integrable unitary circuits
• Temporal Entanglement in Chaotic Quantum Circuits
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Transport and entanglement growth in long-range random Clifford circuits
• Growth of entanglement of generic states under dual-unitary dynamics
• Non-equilibrium dynamics of charged dual-unitary circuits
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• From Dual Unitarity to Generic Quantum Operator Spreading
• Dynamical quantum ergodicity from energy level statistics
• Hierarchical generalization of dual unitarity
• Scrambling and quantum chaos indicators from long-time properties of operator distributions
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Circuits of space and time quantum channels
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Dual unitary circuits in random geometries
• Exact Spectral Statistics in Strongly Localised Circuits
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Hilbert space delocalization under random unitary circuits
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
• Real-time correlators in chaotic quantum many-body systems
• The entanglement membrane in exactly solvable lattice models
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Exact universal bounds on quantum dynamics and fast scrambling
• Integrable nonunitary quantum circuits
• Topological Defects in Floquet Circuits
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Boundary Chaos
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Exactly solvable many-body dynamics from space-time duality
• Boundary Chaos: Exact Entanglement Dynamics
• Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators
• Quantum simulation using noisy unitary circuits and measurements
• Absence of localization in two-dimensional Clifford circuits
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Classical route to ergodicity and scarring in collective quantum systems
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Dual unitaries as maximizers of the distance to local product gates
• Fundamental charges for dual-unitary circuits
• Localization and integrability breaking in weakly interacting Floquet circuits
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Construction of perfect tensors using biunimodular vectors
• Quantum complexity phase transitions in monitored random circuits
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Exact results on the dynamics of the stochastic Floquet-East model
• Hopf algebras and solvable unitary circuits
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Ergodic theory of diagonal orthogonal covariant quantum channels
• Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
• Entanglement in dual unitary quantum circuits with impurities
• Solvable Quantum Circuits in Tree+1 Dimensions
• Dual-unitary shadow tomography
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Boundary Chaos: Spectral Form Factor
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Tri-unitary quantum circuits
• Entanglement structure for finite system under dual-unitary dynamics
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• More global randomness from less-random local gates
• Quantum transitions, ergodicity, and quantum scars in the coupled top model