Fault-Tolerant Operation of a Quantum Error-Correction Code

Laird Egan; Dripto M. Debroy; Crystal Noel; Andrew Risinger; Daiwei Zhu; Debopriyo Biswas; Michael Newman; Muyuan Li; Kenneth R. Brown; Marko Cetina; Christopher Monroe

arXiv · 2009.11482

Fault-Tolerant Operation of a Quantum Error-Correction Code

Laird Egan·Dripto M. Debroy·Crystal Noel·Andrew Risinger·Daiwei Zhu·Debopriyo Biswas·Michael Newman·Muyuan Li·Kenneth R. Brown·Marko Cetina·Christopher Monroe

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Abstract

Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.

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Laird Egan, Dripto M. Debroy, Crystal Noel, Andrew Risinger, Daiwei Zhu, Debopriyo Biswas, Michael Newman, Muyuan Li, Kenneth R. Brown, Marko Cetina, Christopher Monroe. 2020-09-24. Fault-Tolerant Operation of a Quantum Error-Correction Code. https://arxiv.org/abs/2009.11482

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