Effective Fault-Tolerant Quantum Computation with Slow Measurements

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.

Figure 1

Fragment of an error-correction circuit in which a “cat state” ancilla [9] is prepared, verified, coupled to the data, and then measured. The first three controlled-NOT (cnot) gates prepare the four-qubit ancilla state $|0000⟩+|1111⟩$. The next two cnots and the measurement of $Z\equiv {\sigma }_z$ comprise the verification of this ancilla. In this protocol, this measurement outcome must be known before the verified ancilla is coupled to the data block: If the measurement outcome is $-1$, the cat state is to be discarded and ancilla preparation is to be attempted again.

Figure 2

The modified circuit from Fig. 1: Ancilla verification is removed and is replaced by a decoding and measurement of the ancilla.

Figure 3

Simulation of the gate $T$ using the ancilla $|a_{\pi /8}⟩\equiv T{\sigma }_x|0⟩$, Clifford-group operations, and measurement. The gate $S$ is performed only if the measurement outcome is $-1$.

Figure 4

Creation of the logical ancilla $|\overline{a_{\pi /8}}⟩$ by teleportation.