Quantum Computing via The Bethe Ansatz

TL;DR

This paper proposes a novel perspective on quantum computing by modeling it as a factorisable scattering process in many-body systems, specifically using the Bethe ansatz in one-dimensional delta-function interacting systems.

Contribution

It introduces a new framework linking quantum computation to integrable many-body systems solved by the Bethe ansatz, highlighting the role of factorisable scattering matrices as quantum gates.

Findings

Quantum computation can be modeled as factorisable scattering in many-body systems.

Two-body scattering matrices act as quantum gates satisfying the Yang-Baxter equation.

Comparison made between scattering-based quantum computing and topological quantum computing.

Abstract

We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantum computation, we study quantum computing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a parametric two-body quantum gate. We conclude by comparing quantum computing via the factorisable scattering with topological quantum computing.