Implementation of holonomic quantum gates by an isospectral deformation of an Ising dimer chain

TL;DR

This paper presents a method to implement precise one- and two-qubit holonomic quantum gates using isospectral deformations of an Ising dimer chain, enabling dense coverage of the unitary group for quantum computation.

Contribution

The authors introduce an exact construction of holonomic quantum gates via isospectral deformations of an Ising model, providing a new approach for quantum gate implementation.

Findings

Holonomic gates are discrete yet dense in the unitary group.

Single logical qubits are formed from two spin-1/2 particles.

Arbitrary accuracy in gate approximation is achievable.

Abstract

We exactly construct one- and two-qubit holonomic quantum gates in terms of isospectral deformations of an Ising model Hamiltonian. A single logical qubit is constructed out of two spin-1/2 particles; the qubit is a dimer. We find that the holonomic gates obtained are discrete but dense in the unitary group. Therefore an approximate gate for a desired one can be constructed with arbitrary accuracy.