Abstract
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, midcircuit 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 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the [[7,1,3]] color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of 1.7(2)×10−3, compared to the average physical SPAM error 2.4(4)×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 T¯|+⟩L 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 pseudothreshold.15 MoreReceived 10 August 2021Revised 24 November 2021Accepted 7 December 2021Corrected 11 January 2022DOI:https://doi.org/10.1103/PhysRevX.11.041058Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtom & ion coolingAtom & ion trapping & guidingQuantum computationQuantum error correctionPhysical SystemsTrapped ionsQuantum InformationAtomic, Molecular & Optical
Highlights
Large-scale quantum computers promise to solve classically intractable problems in areas such as quantum simulation, prime factorization, and others [1,2,3,4,5,6,7]
Quantum error correction (QEC) codes are identified by three parameters 1⁄21⁄2n; k; d, where n is the number of physical qubits, k is the number of logical qubits the code admits, and d is the code distance, which is related to the minimum number of arbitrary singlequbit errors the code will correct, t 1⁄4 bd − 1=2c
While the error budget is useful in studying the current impact different physical error sources have on the QEC protocol, we investigate a simulation tool better suited to predicting the protocol performance assuming improved physical error rates
Summary
Large-scale quantum computers promise to solve classically intractable problems in areas such as quantum simulation, prime factorization, and others [1,2,3,4,5,6,7]. The error syndrome measurements are sent to a classical computer where real-time decoding and tracking of errors and corrections occur Since all of this can be done with high fidelity and quickly compared to the dephasing rate of the physical qubits, the logical qubit can be repeatedly error corrected, a crucial feature of scalable quantum computing. We perform these operations with the six eigenstates of the logical Pauli operators and initialize a magic state for non-Clifford operations. These results demonstrate a universal set for quantum computation, with the notable exception of an entangling gate between two logical qubits, which requires more qubits than our system currently supports
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
