Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes [article]

Ariel Shlosberg, Anthony M. Polloreno, Graeme Smith
<span title="2021-08-04">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... 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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