Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits

Abstract

We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time direction, but also when propagating in the space direction. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over $\mathrm{SU}(d)$, e.g. one concentrated around the identity, after each layer of the circuit. We identify the spectral form factor at time $t$ in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of $t$ sites. For general dual unitary circuits of qubits $(d=2)$ and a family of their extensions to higher $d>2$, we provide explicit construction of the commutant and prove that spectral form factor exactly matches the prediction of circular unitary ensemble for all $t$, if only the local 2-qubit gates are different from a SWAP (non-interacting gate). We discuss and partly prove possible extensions of our results to a weaker (more singular) forms of disorder averaging, as well as to quantum circuits with time-reversal symmetry, and to computing higher moments of the spectral form factor.

30 pages; v2 rigorous results for spatially inhomogeneous interactions added; v3 extended version, it contains some unproven conjectures not published in CMP

References in corpus (3)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Semiclassical Foundation of Universality in Quantum Chaos
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently

Cited by in corpus (62)

• Random Quantum Circuits
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Temporal entanglement, quasiparticles and the role of interactions
• Scrambling is Necessary but Not Sufficient for Chaos
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Maximal entanglement velocity implies dual unitarity
• Dynamics of charge fluctuations from asymmetric initial states
• Correlations and commuting transfer matrices in integrable unitary circuits
• Many-body quantum chaos and emergence of Ginibre ensemble
• Temporal Entanglement in Chaotic Quantum Circuits
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Many-body quantum chaos in stroboscopically-driven cold atoms
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Many-Body Quantum Chaos and Space-time Translational Invariance
• Growth of entanglement of generic states under dual-unitary dynamics
• From Dual Unitarity to Generic Quantum Operator Spreading
• Crystalline Quantum Circuits
• Hierarchical generalization of dual unitarity
• 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
• Dual unitary circuits in random geometries
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Circuits of space and time quantum channels
• Magic Resources of the Heisenberg Picture
• Exact Spectral Statistics in Strongly Localised Circuits
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Quantum information spreading in generalised dual-unitary circuits
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• Universal Dephasing Mechanism of Many-Body Quantum Chaos
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Zero-temperature entanglement membranes in quantum circuits
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Exactly solvable many-body dynamics from space-time duality
• Operator dynamics in Floquet many-body systems
• Boundary Chaos
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Fundamental charges for dual-unitary circuits
• Localization and integrability breaking in weakly interacting Floquet circuits
• Many-body quantum chaos in mixtures of multiple species
• Exact results on the dynamics of the stochastic Floquet-East model
• Effective field theory of random quantum circuits
• Entangling power, gate typicality, and measurement-induced phase transitions
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Spectral form factors and dynamical localization
• No-resonance conditions, random matrices, and quantum chaotic models
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Boundary Chaos: Spectral Form Factor
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Tri-unitary quantum circuits
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• Rationally independent free fermions with local hopping
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes