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Error-Mitigated Quantum Gates Exceeding Physical Fidelities in a Trapped-Ion System
Shuaining Zhang, Yao Lu, Kuan Zhang, Wentao Chen, Ying Li, Jing-Ning Zhang, Kihwan Kim
TL;DR
Near-term quantum devices require error reduction without the costly overhead of quantum error correction. This paper combines probabilistic error cancellation with gate set tomography in a trapped-ion system, reducing effective error rates to (1.44±5.28)×10^-5 for single-qubit gates and (0.96±0.10)×10^-3 for two-qubit gates.
Problem
Experimental error mitigation must reduce operational errors on near-term quantum devices without relying on unaffordable quantum-error-correction overheads.
Source: Characterization of the two-qubit gate… · p. 7Method
The experiment combines probabilistic error cancellation with gate set tomography to characterize gate noise and mitigate its effects.
Source: SUPPLEMENTARY MATERIALS · p. 6, Characterization of the two-qubit gate… · p. 7Results
Effective error rates reach (1.44±5.28)×10^-5 for single-qubit gates and (0.96±0.10)×10^-3 for two-qubit gates after mitigation.
Source: Characterization of the two-qubit gate… · p. 7Takeaways & Limitations
The experiment shows that probabilistic error cancellation can substantially suppress residual gate errors in a trapped-ion system.
Source: Characterization of the two-qubit gate… · p. 7Residual errors arise from the Pauli-error assumption, time-correlated systematic drift, and crosstalk between qubits.
Source: Characterization of the two-qubit gate… · p. 7
Abstract
from arXiv · showhide
Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here, we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e. we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from $(1.10\pm 0.12)\times10^{-3}$ to $(1.44\pm 5.28)\times10^{-5}$ and from $(0.99\pm 0.06)\times10^{-2}$ to $(0.96\pm 0.10)\times10^{-3}$ for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device.
SUPPLEMENTARY MATERIALS
The supplement describes gate-set-tomography characterization of single-qubit operations under a Pauli-error model and derives experimentally implementable decompositions for error cancellation.
Characterization
- Gate-set tomography models each single-qubit operation as an ideal 4 × 4 Pauli-transfer matrix followed by Pauli noise with normalized error rates.The noise operation is written as N_s = p_s,0R_I + p_s,1R_X + p_s,2R_Y + p_s,3R_Z, with Σ_j p_s,j = 1.Source: SUPPLEMENTARY MATERIALS · p. 6
- 36 parameters are estimated from 3 × 11 × 4 experimental settings, each repeated 10,000 times, by numerically maximizing a likelihood function.The parameters include 11 × 3 gate parameters and 3 initial-state parameters; the resulting PTMs appear in Fig. 2b and Fig. S1a.Source: SUPPLEMENTARY MATERIALS · p. 6
Error decomposition
- The inverse noise PTM is decomposed into experimental Pauli operations, enabling each ideal operation to be expressed as a linear combination of noisy experimental operations.Specifically, N_s^-1 = q_s,0R_I + q_s,1R_X + q_s,2R_Y + q_s,3R_Z, which yields the corresponding decomposition of G_s.Source: SUPPLEMENTARY MATERIALS · p. 6
Characterization of the two-qubit gate set
The two-qubit gate set is characterized by combining single-qubit gate-set tomography with Pauli-error modeling of the native MSYY gate and PTM composition for MSZZ. Residual errors after mitigation are attributed mainly to non-Pauli effects, crosstalk, and systematic drift.
Characterization of the two-qubit gate set
- Single-qubit operations are characterized by gate-set tomography, and their two-qubit PTMs are constructed as direct products for operations in G1⊗2.This also determines the PTMs of the fiducial operations.Source: Characterization of the two-qubit gate… · pp. 6–7
- The native MSYY PTM is decomposed into a 15-parameter trace-preserving two-qubit Pauli-error channel, determined from 15 independent equations selected from 16 × 9 settings.The selected equations minimize projection error because many measured probabilities are close to 0 or 1.Source: Characterization of the two-qubit gate… · p. 7
- The MSZZ PTM is obtained by multiplying the experimentally characterized PTMs of an MSYY gate sandwiched between appropriate single-qubit X rotations.Thus, MSZZ inherits the implementation-dependent effects of its constituent single-qubit operations.Source: Characterization of the two-qubit gate… · p. 7
Analysis on residual errors in the error-mitigated quantum
- The Pauli-error assumption is supported because simulated and experimental error rates agree within fitting errors for both single- and two-qubit random sequences.The reported pairs are (1.09 ± 0.06) × 10^-3 versus (1.10 ± 0.12) × 10^-3, and (0.97 ± 0.05) × 10^-2 versus (0.99 ± 0.06) × 10^-2.Source: Figure S2 · p. 8
- 0.68 × 10^-3 of residual error comes from crosstalk, 0.08 × 10^-3 from time-correlated drift, and 0.20 × 10^-3 from non-Pauli errors in two-qubit gates.MSZZ fidelity degrades with crosstalk strength, whereas MSYY is insensitive; the total mitigated two-qubit residual error is (0.96±0.10)×10^-3.Source: Characterization of the two-qubit gate… · pp. 7–8, Figure S4 · p. 10