Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States

A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.

Figure 1

Qubit-level logical error rate induced by GKP error correction with CV cluster states. The indicated level of squeezing is assumed to apply both to the initial momentum-squeezed states used to create the cluster state and in the Gaussian spikes that comprise the encoded GKP states. Also shown: maximum single-mode squeezing achieved to date (12.7 dB) [48, 49] and squeezing achieved in a large CV cluster state (5 dB) [9].