Stabilisation of Quantum Computations by Symmetrisation

TL;DR

An efficient algorithm and quantum network effecting $\cal SYM$--projection and the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction are discussed.

Abstract

We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into $\cal SYM$, the symmetric subspace of the full state space of $R$ redundant copies of the computer. We describe an efficient algorithm and quantum network effecting $\cal SYM$--projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.

Figures (2)

• Figure 1: Schematic representation of a Fredkin gate. A Fredkin gate exchanges the state of the second and third qubit if and only if the first qubit is in state $|a\rangle=|1\rangle$.
• Figure 2: Quantum network for symmetrising $R=4$ qubits. Six auxiliary qubits initially in state $|0\rangle$ are needed. The auxiliary qubits are put into an entangled state and used to control the state swapping of the four computer qubits. The operations are then undone and the auxiliary qubits measured. If every auxiliary qubit is found in state $|0\rangle$ the symmetrisation has been successful.