Invitation to Hadamard matrices

Banica, Teodor

doi:10.48550/arxiv.1910.06911

Cited by 1 publication

(1 citation statement)

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“…This property -known as space-time duality -has been exploited in various contexts in recent years, as described in the introduction. For introductions to complex Hadamard matrices, we refer the reader to [26,27].…”

Section: Modelmentioning

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: Modelmentioning

confidence: 99%