Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics

Abstract

The chaotic dynamics of quantum many-body systems are expected to quickly randomize any structured initial state, delocalizing it in Fock space. In this work, we study the spreading of an initial product state in Hilbert space under dual-unitary dynamics, captured by the inverse participation ratios and the distribution of overlaps (bit-string probabilities). We consider the self-dual kicked Ising model, a minimal model of many-body quantum chaos which can be seen as either a periodically driven Floquet model or a dual-unitary quantum circuit. Both analytically and numerically, we show that the inverse participation ratios rapidly approach their ergodic values, corresponding to those of Haar random states, and establish the emergence of the Porter-Thomas distribution for the overlap distribution. Importantly, this convergence happens exponentially fast in time, with a time scale that is independent of system size. We inspect the effect of local perturbations that break dual-unitarity and show a slowdown of the spreading in Fock space, indicating that dual-unitary circuits are maximally efficient at preparing random states.

6+2 pages

References in corpus (20)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Many body localization and thermalization in quantum statistical mechanics
• Random Quantum Circuits
• Computational advantage of quantum random sampling
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Scrambling in Random Unitary Circuits: Exact Results
• Exact emergent quantum state designs from quantum chaotic dynamics
• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Maximal entanglement velocity implies dual unitarity
• Tight bounds on the convergence of noisy random circuits to the uniform distribution
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Benchmarking Quantum Simulators using Ergodic Quantum Dynamics
• Shadow tomography from emergent state designs in analog quantum simulators
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Hilbert space delocalization under random unitary circuits
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• The entanglement membrane in exactly solvable lattice models
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Zero-temperature entanglement membranes in quantum circuits
• Operator dynamics and entanglement in space-time dual Hadamard lattices

Cited by in corpus (10)

• Exactly solvable many-body dynamics from space-time duality
• Genuine quantum scars in many-body spin systems
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Projected ensemble in a system with conserved charges with local support
• Deviations from the Porter-Thomas Distribution due to Nonstatistical $\gamma$ Decay below the ${}^{150}$Nd Neutron Separation Threshold
• Solvable Quantum Circuits in Tree+1 Dimensions
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Partial projected ensembles and spatiotemporal structure of information scrambling
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Fock space prethermalization and time-crystalline order on a quantum processor