Dual unitary circuits in random geometries

Abstract

Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. Here we show that regularity of the circuit lattice is not crucial for exact solvability. We consider a circuit where random 2-qubit dual unitary gates sit at intersections of random arrangements of straight lines in two dimensions (mikado) and analytically compute the variance of the spatio-temporal correlation function of local operators. Note that the average correlator vanishes due to local Haar randomness of the gates. The result can be physically motivated for two random mikado settings. The first corresponds to the thermal state of free particles carrying internal qubit degrees of freedom which experience interaction at kinematic crossings, while the second represents rotationally symmetric (random euclidean) space-time.

arXiv comment12 pages, 3 figures

References in corpus (15)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Exact dynamics in dual-unitary quantum circuits
• Matrix Product States for dynamical simulation of infinite chains
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Maximum velocity quantum circuits
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Hybrid semiclassical theory of quantum quenches in one dimensional systems
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Tri-unitary quantum circuits

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• Entanglement Entropy of Free Fermions in Timelike Slices
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Exactly solvable many-body dynamics from space-time duality
• Tensor network decompositions for absolutely maximally entangled states
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Exact results on the dynamics of the stochastic Floquet-East model
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Logarithmic growth of operator entanglement in a clean non-integrable circuit