Algebraic Bethe Circuits

Abstract

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-$\frac{1}{2}$ 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.

arXiv commentAccepted for publication in Quantum

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• The Bethe Ansatz as a Quantum Circuit
• Deterministic Bethe state preparation
• The Floquet Baxterisation
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• Large-scale simulations of Floquet physics on near-term quantum computers
• Qudit Dicke state preparation
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• Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
• Entanglement at the interplay between single- and many-bodyness
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
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