Fault-tolerant quantum computation with few qubits

Presenting Author: Rui Chao, University of Southern California
Contributing Author(s): Ben Reichardt

Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. We give space-efficient methods for fault-tolerant error correction and computation, which are promising to realize on near-term devices: 1. For many distance-three codes, two extra qubits are enough to perform fault-tolerant error correction. 2. For various small codes encoding multiple logical qubits, two ancilla qubits are also enough to apply arbitrary logical Clifford operations, and with another two ancillas we can even achieve universal computation. For example, with 19 qubits one can protect and compute universally on seven encoded qubits, fault tolerantly. Our main technique is to use circuit gadgets to catch bad faults. For space-efficient error correction, we add a “flag” ancilla to catch those faults that spread to multi-qubit data errors. For computation within a code block, multi-qubit faults are caught using flag gadgets, and are remedied before they can spread. These procedures could enable testing more sophisticated protected circuits in small-scale quantum devices, and could be used to reduce the overhead of general fault-tolerance schemes.

Read this article online: https://arxiv.org/abs/1705.02329, https://arxiv.org/abs/1705.05365

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