Holonomic quantum computation in subsystems

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.

Improved presentation, references added

References in corpus (7)

• Subsystem fault tolerance with the Bacon-Shor code
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• The structure of preserved information in quantum processes
• Fault-tolerant holonomic quantum computation
• Operator quantum error correction for continuous dynamics
• Robustness of operator quantum error correction with respect to initialization errors
• A general treatment of geometric phases and dynamical invariants