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

• URL: http://arxiv.org/abs/2108.02079v1
• Date: Wed, 4 Aug 2021 14:24:14 GMT
• Title: Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes
• Authors: Ariel Shlosberg, Anthony M. Polloreno, and Graeme Smith
• Abstract summary: We study a next step - fault-tolerantly implementing quantum circuits. We compute pseudo-thresholds for the Pauli error rate $p$ in a depolarizing noise model. We see that multiple rounds of stabilizer measurements give an improvement over performing a single round at the end.
• Score: 5.352699766206807
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 work 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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