High-Threshold Low-Overhead Fault-Tolerant Classical Computation and the Replacement of Measurements with Unitary Quantum Gates

• Published in: Physical review letters 2017-07, Vol.119 (3), p.030503-030503, Article 030503
• Main Authors: Cruikshank, Benjamin, Jacobs, Kurt
• Format: Article
• Language: English
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.119.030503

von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: (i) the extremely complex circuits required by randomized connections, (ii) the difficulty of calculating its performance in practical regimes of both code size and logical error rate, and (iii) the (perceived) need for large code sizes. Here we present numerical results indicating that the third assertion is false, and introduce a novel scheme that eliminates the two remaining problems while retaining a threshold very close to von Neumann's ideal of 1/6. We present a simple, highly ordered wiring structure that vastly reduces the circuit complexity, demonstrates that randomization is unnecessary, and provides a feasible method to calculate the performance. This in turn allows us to show that the scheme requires only moderate code sizes, vastly outperforms concatenation schemes, and under a standard error model a unitary implementation realizes universal FTCC with an accuracy threshold of p