Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction

TL;DR

This paper presents a model for universal quantum computation using a fixed ancilla-register interaction, avoiding measurements and requiring only unitary control, with specific interaction forms and fault-tolerant gate sets.

Contribution

It characterizes the form of the fixed interaction needed for universal computation and provides concrete examples and a fault-tolerant gate set within this model.

Findings

Interaction is locally equivalent to SWAP plus an entangling gate

Two Hamiltonians (XY and XXZ) can generate the required interaction

A simple, finite, fault-tolerant gate set is demonstrated

Abstract

We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.