Planar algebras, quantum information theory and subfactors

Kodiyalam, Vijay; Sruthymurali,; Sunder, V. S.

doi:10.48550/arxiv.1912.07228

Cited by 1 publication

(2 citation statements)

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“…These diagonal compositions can be seen as special cases of the constructions treated in the papers [35,36], which deal with a more general notion of bi-unitarity. The specific formulas we gave appear to be new.…”

Section: Diagonal Compositionsmentioning

confidence: 99%

“…The notion of dual unitarity (called bi-unitarity in the mathematical literature) appears in this theory. Implications for quantum information theory were studied in [35] and more recently in [36]. The general concept of bi-unitarity treated in these works accommodates not only the actual DU gates, but also complex Hadamard matrices, quantum error correcting codes, and quantum Latin squares.…”

Section: Introductionmentioning

confidence: 99%

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Construction and the ergodicity properties of dual unitary quantum circuits

Borsi,

Pozsgay

2022

Preprint

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We consider one dimensional quantum circuits of the brickwork type, where the fundamental quantum gate is dual unitary. Such models are solvable: the dynamical correlation functions of the infinite temperature ensemble can be computed exactly. We review various existing constructions for dual unitary gates and we supplement them with new ideas in a number of cases. We discuss connections with various topics in physics and mathematics, including quantum information theory, tensor networks for the AdS/CFT correspondence (holographic error correcting codes), classical combinatorial designs (orthogonal Latin squares), planar algebras, and Yang-Baxter maps. Afterwards we consider the ergodicity properties of a special class of dual unitary models, where the local gate is a permutation matrix. We find an unexpected phenomenon: non-ergodic behaviour can manifest itself in multi-site correlations, even in those cases when the one-site correlation functions are fully chaotic (completely thermalizing). We also discuss the circuits built out of perfect tensors. They appear locally as the most chaotic and most scrambling circuits, nevertheless they can show global signs of non-ergodicity: if the perfect tensor is constructed from a linear map over finite fields, then the resulting circuit can show exact quantum revivals at unexpectedly short times. A brief mathematical treatment of the recurrence time in such models is presented in the Appendix by Roland Bacher and Denis Serre.

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Section: Diagonal Compositionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%