Realization of Real-Time Fault-Tolerant Quantum Error Correction

By C. Ryan-Anderson, J. Bohnet, K. Lee, D. Gresh, A. Hankin, J. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown and 7 more. Physical Review X, 2021

367 citations recorded by the source corpus.

Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, mid-circuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a ten qubit QCCD trapped-ion quantum computer to encode a single logical qubit using the $[[7,1,3]]$ color code, first proposed by Steane~\cite{steane1996error}. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical SPAM error of $1.7(6) \times 10^{-3}$, compared to the average physical SPAM error $2.4(8) \times 10^{-3}$ of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a logical magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudo-threshold.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c938b8abc50711ba2a2b1ad09ad228c1c4ec02c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

Citations in the corpus

Suppressing quantum errors by scaling a surface code logical qubit (2022, positive): “Several works have reported quantum error correction on small codes able to correct a single error [20–26] and in continuous variable codes [27–30].”
Quantum error correction below the surface code threshold (2024, neutral): “We note there are other accurate decoders that would be interesting to test on this data, including beliefmatch-ing [13], BP+OSD [14], and tensor network decoding [1].”
Demonstration of fault-tolerant universal quantum gate operations (2021, methodology): “4a: we begin with a non-FT preparation of the magic state |H〉L,nf, as recently demonstrated also in [30] (shown in subbox ”Non-FT encoding”).”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, background): “It is, therefore, desirable to develop a scheme that can realize these LRE systems efficiently, and this endeavor is timely as mid-circuit measurements are now a capability in several experimental platforms [10, 11].”