From Dual Unitarity to Generic Quantum Operator Spreading

Rampp, Michael A.; Moessner, Roderich; Claeys, Pieter W.

doi:10.1103/physrevlett.130.130402

Cited by 15 publications

(1 citation statement)

References 48 publications

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“…Operator spreading in dual-unitary dynamics has been of special interest, where the underlying space-time duality enforces that all operators grow with maximal velocity |v| = 1 [43][44][45][46][47]. This will again be the case for all operator dynamics presented below.…”

Section: Operator Dynamics In Coupled Clifford Cat Modelsmentioning

confidence: 99%

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

Claeys

Lamacraft

2022

Quantum

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Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be generated by performing projective measurements on the remainder of the system, leading to a projected ensemble. In chaotic quantum systems it was conjectured that such projected ensembles become indistinguishable from the uniform Haar-random ensemble and lead to a quantum state design. Exact results were recently presented by Ho and Choi [Phys. Rev. Lett. 128, 060601 (2022)] for the kicked Ising model at the self-dual point. We provide an alternative construction that can be extended to general chaotic dual-unitary circuits with solvable initial states and measurements, highlighting the role of the underlying dual-unitarity and further showing how dual-unitary circuit models exhibit both exact solvability and random matrix behaviour. Building on results from biunitary connections, we show how complex Hadamard matrices and unitary error bases both lead to solvable measurement schemes.

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Section: Operator Dynamics In Coupled Clifford Cat Modelsmentioning

confidence: 99%

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

Claeys

Lamacraft

2022

Quantum

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From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics

Claeys,

Lamacraft,

Vicary

2024

J. Phys. A: Math. Theor.

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Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called dual-unitary interactions round-a-face, which we here call clockwork, based on 2-controlled 1-site unitaries composed in a non-brickwork structure, yet with many of the same attractive global properties. We present a 2-categorical framework that simultaneously generalizes these two existing models, and use it to show that brickwork and clockwork circuits can interact richly, yielding new types of generalized heterogeneous circuits. We show that these interactions are governed by quantum combinatorial data, which we precisely characterize. These generalized circuits remain exactly-solvable and we show that they retain the attractive features of the original models such as single-site correlation functions vanishing everywhere except on the causal light-cone. Our framework allows us to directly extend the notion of solvable initial states to these biunitary circuits, and we show these circuits demonstrate maximal entanglement growth and exact thermalization after finitely many time steps.

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Operator dynamics and entanglement in space-time dual Hadamard lattices

Claeys,

Lamacraft

2024

J. Phys. A: Math. Theor.

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Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys. 49 112104) and in the q → ∞ limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity 34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.

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From Dual Unitarity to Generic Quantum Operator Spreading

Cited by 15 publications

References 48 publications

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics

Operator dynamics and entanglement in space-time dual Hadamard lattices

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