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Physics

Real-Time Error Correction for Quantum Computing

Philip Ball

Published Dec 23, 2021• 4 citations
Publisher

Abstract

An experiment shows that errors in quantum computation can be repeatedly corrected on the fly.
DOI
10.1103/physics.14.184

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As quantum computers advance toward the regime of MegaQuOp machines executing millions of gates, a decoding system capable of real-time error correction in such a device will be crucial. Recent efforts have been focused on decoding an error-corrected memory or a small number of logical operations. Here we demonstrate an end-to-end real-time decoding stack for a universal fault-tolerant trapped-ion quantum computer architecture capable of decoding real workloads with millions of logical gates over hundreds of logical qubits. The complete pipeline, including on the fly detector error model generation, decoding of all logical qubits, logical operations, and magic-state factories, runs on a single CPU. We benchmark the decoder on practically relevant quantum applications spanning up to 408 logical qubits, and up to one million TTT gates. Assuming a trapped-ion architecture with 1 to 5 ms cycle time, the decoding delay stretches the computation by less than 0.3%0.3\%0.3% at pCNOT=10−4p_{\mathrm{CNOT}}=10^{-4}pCNOT​=10−4 and less than 12%12\%12% at pCNOT=5×10−4p_{\mathrm{CNOT}}=5\times 10^{-4}pCNOT​=5×10−4 for all workloads studied. These results demonstrate real-time decoding at MegaQuOp scale on a single conventional CPU.
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels inversely proportional to the size of the computation. As a step towards this ambitious goal, we present experiments on a trapped-ion QCCD processor where, through the use of fault-tolerant encoding and error correction, we are able to suppress logical error rates to levels below the physical error rates. In particular, we entangled logical qubits encoded in the [[7,1,3]] code with error rates 9.8 times to 500 times lower than at the physical level, and entangled logical qubits encoded in a [[12,2,4]] code based on Knill's C4/C6 scheme with error rates 4.7 times to 800 times lower than at the physical level, depending on the judicious use of post-selection. Moreover, we demonstrate repeated error correction with the [[12,2,4]] code, with logical error rates below physical circuit baselines corresponding to repeated CNOTs, and show evidence that the error rate per error correction cycle, which consists of over 100 physical CNOTs, approaches the error rate of two physical CNOTs. These results signify a transition from noisy intermediate scale quantum computing to reliable quantum computing, and demonstrate advanced capabilities toward large-scale fault-tolerant quantum computing.