Correlations and commuting transfer matrices in integrable unitary  circuits

Claeys, Pieter W.; Herzog-Arbeitman, Jonah; Lamacraft, Austen

doi:10.21468/scipostphys.12.1.007

Cited by 30 publications

(19 citation statements)

References 60 publications

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“…Explicit computation of time correlation functions can be challenging since the gates are no longer unitary. It would be interesting to see if the Bethe ansatz approach can yield useful information about the complex spectrum of the circuits [45] and, moreover, how dominant complex eigenvalues controls the long-time dynamics [61]. We may draw some inspirations from solutions to integrable systems with boundary drives [48].…”

Section: Discussionmentioning

confidence: 99%

Integrable nonunitary quantum circuits

Su¹,

Martin²

2022

Preprint

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We show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the Ř-matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of integrable nonunitary quantum circuits.

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Section: Discussionmentioning

confidence: 99%

Integrable nonunitary quantum circuits

Su¹,

Martin²

2022

Preprint

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“…where we have used that the quasi-momentum of the one magnon solutions must be real, implying that s 2 is a phase. Substituting into (20) and completing the matrix, we obtain the two-qubit quantum gates…”

Section: B One-magnon Solutionmentioning

confidence: 99%

“…1. We note that quantum circuits based on unitary R matrices were explored to compute infinite temperature correlation functions in [20].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe Circuits

Sopena,

Gordon,

García-Martín

et al. 2022

Preprint

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“…1. We note that quantum circuits based on unitary R matrices were explored to compute infinite temperature correlation functions in [24].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe Circuits

Sopena

Gordon

Sierra

et al. 2022

Quantum

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The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-12 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

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Correlations and commuting transfer matrices in integrable unitary circuits

Cited by 30 publications

References 60 publications

Integrable nonunitary quantum circuits

Integrable nonunitary quantum circuits

Algebraic Bethe Circuits

Algebraic Bethe Circuits

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