Comparing Experiments to the Fault-Tolerance Threshold
arXiv:1510.05653 · doi:10.1103/PhysRevLett.117.170502
Abstract
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.
5 pages, 2 figures, 13 page appendix
References in corpus (19)
- Randomized Benchmarking of Quantum Gates
- High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
- Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Characterization of addressability by simultaneous randomized benchmarking
- Randomized benchmarking and process tomography for gate errors in a solid-state qubit
- Randomized benchmarking of single qubit gates in a 2D array of neutral atom qubits
- Process verification of two-qubit quantum gates by randomized benchmarking
- Subsystem fault tolerance with the Bacon-Shor code
- Estimating the Coherence of Noise
- Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking
- Randomized Benchmarking of Multi-Qubit Gates
- Bounding quantum gate error rate based on reported average fidelity
- Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
- The effect of noise correlations on randomized benchmarking
- Non-exponential Fidelity Decay in Randomized Benchmarking with Low-Frequency Noise
- Accelerated Randomized Benchmarking
- Robust Characterization of Loss Rates
- Bounding experimental quantum error rates relative to fault-tolerant thresholds
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