Fault-tolerant quantum computation with few qubits

Abstract

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. Here, we study the 15-qubit Hamming code, which protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 in total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 in total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance. A new approach provides a way to realise fault-tolerant quantum operations with smaller qubit overhead as opposed to existing protocols. In order to protect quantum computers from errors, quantum information is stored in logical qubits—ensembles of physical qubits where eventual errors can be detected and corrected. However, performing quantum operations on logical qubits in a fault-tolerant way is difficult, and normally requires large qubit overheads. Rui Chao and Ben W. Reichardt from the University of Southern California have now demonstrated that carefully designed circuits where gates are replaced with “gadgets”—gates involving extra qubits to catch error propagation—ensure useful fault-tolerant operations on logical qubits. This protocol may make it possible to run fault-tolerant operations on near-term, small quantum computers.