Direct measurement of Bacon-Shor stabilizers

The Bacon-Shor code is a fascinating quantum error correction code that has a simple description in terms of two redundancy codes, can be derived from a compass model of interacting spins, and is a subsystem code, whose extra degrees of freedom allows for syndrome extraction from measuring gauge operators and fault-tolerant computation procedures that include two-qubit unitaries in a block. In arXiv:1804.01127, we show that Bacon-Shor stabilizers of any size can be measured fault tolerantly with a bare ancilla.  This has practical implications for the implementation of a small distance-3 code, where we find that the Bacon-Shor code requires less qubits, takes less time, and has a lower error than the surface code for a simple circuit of prepare, error correct, and measure.