Holonomic quantum computation in subsystems

TL;DR

This paper presents a generalized approach to holonomic quantum computation using subsystem encoding, enabling fault-tolerant gates with noisy ancillas and 2-local Hamiltonians, without requiring subspace initialization.

Contribution

It introduces a novel subsystem-based HQC method and demonstrates fault-tolerance with noisy ancillas and perturbative gadgets, expanding practical quantum computing techniques.

Findings

Holonomic gates can be applied to unencoded qubits using noisy ancillas.

Fault-tolerant HQC can be achieved with 2-local Hamiltonians.

The method does not require initialization in a subspace.

Abstract

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.