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arXiv:1905.06878 · Physical Review Letters

Probing Qubit Memory Errors at the Part-per-Million Level

M. A. Sepiol, A. C. Hughes, J. E. Tarlton, D. P. Nadlinger, T. G. Ballance, Christopher J. Ballance, T. P. Harty, Andrew M. Steane, Joseph F. Goodwin, D. M. Lucas

Published Sep 13, 2019• 31 citations
arXivHTMLPDF

Abstract

Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error ${\ensuremath{\epsilon}}_{m}$ for a $^{43}{\mathrm{Ca}}^{+}$ trapped-ion qubit in the small-error regime and find ${\ensuremath{\epsilon}}_{m}<{10}^{\ensuremath{-}4}$ for storage times $t\ensuremath{\lesssim}50\text{ }\text{ }\mathrm{ms}$. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at $t=1\text{ }\text{ }\mathrm{ms}$ we measure ${\ensuremath{\epsilon}}_{m}=1.2(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, around ten times smaller than that extrapolated from the ${T}_{2}^{*}$ time, and limited by instability of the atomic clock reference used to benchmark the qubit.

DOI
10.1103/physrevlett.123.110503

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Robust qubit memory is essential for quantum computing, both for near-term devices operating without error correction, and for the long-term goal of a fault-tolerant processor. We directly measure the memory error \ensuremathϵm{\ensuremath{\epsilon}}_{m}\ensuremathϵm​ for a 43Ca+^{43}{\mathrm{Ca}}^{+}43Ca+ trapped-ion qubit in the small-error regime and find \ensuremathϵm<10\ensuremath−4{\ensuremath{\epsilon}}_{m}<{10}^{\ensuremath{-}4}\ensuremathϵm​<10\ensuremath−4 for storage times t\ensuremath≲50  mst\ensuremath{\lesssim}50\text{ }\text{ }\mathrm{ms}t\ensuremath≲50  ms. This exceeds gate or measurement times by three orders of magnitude. Using randomized benchmarking, at t=1  mst=1\text{ }\text{ }\mathrm{ms}t=1  ms we measure \ensuremathϵm=1.2(7)\ifmmode×\else\texttimes\fi10\ensuremath−6{\ensuremath{\epsilon}}_{m}=1.2(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\ensuremathϵm​=1.2(7)\ifmmode×\else\texttimes\fi10\ensuremath−6, around ten times smaller than that extrapolated from the T2∗{T}_{2}^{*}T2∗​ time, and limited by instability of the atomic clock reference used to benchmark the qubit.
Trapped atomic ions are a promising candidate system for developing a quantum computer. All elementary operations for quantum information processing have al- ready been achieved in trapped-ion systems with errors below the “fault-tolerant threshold”, meaning that these errors are sufficiently small to be removed with quan- tum error correction. However, the preservation of quantum information over the short timescales that are relevant for quantum computing has not, to our knowledge, been measured before in trapped-ion qubits. Previous investigations have measured decoherence over long times and extrapolated an exponential decay model to short times. We directly measure the qubit memory error rate over short timescales, which is made possible by the high-fidelity single-qubit gates and state preparation and mea- surement in our system. Our qubit is a hyperfine “atomic clock” transition in 43Ca+, and gates are applied with near-field microwaves. We find that the assumption of exponential decay of qubit state coherence does not apply in our system. The data is fit well by a model of 1/f frequency noise with a low-frequency cutoff. The small- est memory error that we measure is 3(1)×10−6 over 2ms. The time at which our qubit memory error is 1×10−3, an important threshold for viable quantum error correction, is ≈400ms. We also present a design study into a new ion trap electrode geometry for applying near-field microwave two-qubit gates. This design features an ‘S’-shaped meander electrode to passively null the microwave field at the ions’ locations. It has improved isolation between the meander and other electrodes compared to previous work on this, which should reduce the sensitivity of the microwave field distribution to the boundary conditions of these electrodes. We show that the trap would allow for ion chains to be trapped, transported and split with feasible DC and RF voltages.
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 (quantum charge-coupled device) trapped-ion quantum computer to encode a single logical qubit using the color code. 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(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, which are tracked software or applied physically.
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]][[7,1,3]][[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)×10−31.7(6) \times 10^{-3}1.7(6)×10−3, compared to the average physical SPAM error 2.4(8)×10−32.4(8) \times 10^{-3}2.4(8)×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.
Logical qubits can be protected from decoherence by performing quantum error-correction (QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit-based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multiatom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support midcircuit measurements. Published by the American Physical Society 2024
We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion ^{43}Ca^{+} hyperfine clock qubit. We explore the speed and fidelity trade-off for gate times 4.4≤t_{g}≤35 μs, and benchmark a minimum error per Clifford gate of 1.5(4)×10^{-7}. Calibration errors are suppressed to <10^{-8}, leaving qubit decoherence (T_{2}≈70 s), leakage, and measurement as the dominant error contributions. The ion is held above a microfabricated surface-electrode trap that incorporates a chip-integrated microwave resonator for electronic qubit control; the trap is operated at room temperature without magnetic shielding.
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.