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Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily studies of quantum memory[1, 2], an important first step towards quantum computation, where the objective is to increase the lifetime of the encoded quantum information. Additionally, several works have explored the implementation of logical gates[3-5]. In this<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.02079v1">arXiv:2108.02079v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjuceffeebg57a537d57fqspti">fatcat:qjuceffeebg57a537d57fqspti</a> </span>
more »... k we study a next step - fault-tolerantly implementing quantum circuits. We choose the [[4, 1, 2]] Bacon-Shor subsystem code, which has a particularly simple error-detection circuit. Through both numerics and site-counting arguments, we compute pseudo-thresholds for the Pauli error rate p in a depolarizing noise model, below which the encoded circuits outperform the unencoded circuits. These pseudo-threshold values are shown to be as high as p=3% for short circuits, and p=0.6% for circuits of moderate depth. Additionally, we see that multiple rounds of stabilizer measurements give an improvement over performing a single round at the end. This provides a concrete suggestion for a small-scale fault-tolerant demonstration of a quantum algorithm that could be accessible with existing hardware.
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