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Demonstration of Fault-Tolerant Steane Quantum Error Correction

Lukas Postler1,*, Friederike Butt2,3, Ivan Pogorelov1, Christian D. Marciniak1, Sascha Heußen2,3, Rainer Blatt1,4,5, Philipp Schindler1, Manuel Rispler2,3,†, Markus Müller2,3 et al.

Thomas Monz1,4

  • *Contact author: lukas.postler@uibk.ac.at
  • †Contact author: rispler@physik.rwth-aachen.de
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PRX Quantum 5, 030326 – Published 7 August, 2024

DOI: https://doi.org/10.1103/PRXQuantum.5.030326

Abstract

Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves preparing an auxiliary logical qubit of the same QEC code as used for the data register. The data and auxiliary registers are then coupled with a logical controlled-not (cnot) gate, enabling a measurement of the auxiliary register to reveal the error syndrome. This study presents the implementation of multiple rounds of fault-tolerant (FT) Steane QEC on a trapped-ion quantum computer. Various QEC codes are employed and the results are compared to a previous experimental approach utilizing flag qubits. Our experimental findings show improved logical fidelities for Steane QEC and accompanying numerical simulations indicate an even larger performance advantage for quantum processors limited by entangling-gate errors. This establishes experimental Steane QEC as a competitive paradigm for FT quantum computing.

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Popular Summary

To harness the full advantage that quantum computation is promising to deliver, large-scale systems with high-quality gate operations are required. Given the inherent sensitivity to the noise that quantum information processors possess, currently, there is no platform that can provide such high-performance gate operations natively, presumably rendering error correction indispensable for advantageous quantum computation. We show the first experimental implementation of a scheme proposed by Steane that minimizes the overhead for fault-tolerant quantum error correction. Therefore, this scheme promises to increase error-correction performance on noisy quantum processors.

Here we show the implementation of multiple cycles of Steane error correction on various quantum error-correction codes. To be more specific, we demonstrate the operation of the bit-flip and phase-flip repetition codes below their respective break-even thresholds utilizing the scheme proposed by Steane. Furthermore, we present the practical advantage of Steane error correction over an alternative state-of-the-art protocol for the widely used seven-qubit color code. The experimental results are underpinned by circuit-level numerical simulations that suggest a performance advantage of up to a factor of 2 of Steane error correction over competing protocols.

The emergence of growing register sizes and operational capabilities in various quantum computing architectures facilitates exploiting the high degree of modularity and parallelism that Steane error correction offers. Leveraging the benefits Steane error correction provides, the implementation of quantum error correction can be sped up while improving its performance, as we show in this work.

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PRX Quantum 5, 030326– Published 7 August, 2024
  • Received 8 February 2024
  • Accepted 13 June 2024
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