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Quantum computation with universal error mitigation on superconducting quantum processor
Chao Song, Jing Cui, H. Wang, J. Hao, H. Feng, Ying Li
TL;DR
Near-future quantum devices may lack the resources for fault tolerance, motivating methods that reduce device and control errors without encoding. This paper combines gate set tomography with quasiprobability decomposition and tests the protocol on one- and two-qubit superconducting circuits, where computation accuracy improves, including a reduction from 0.1690 to 0.0102 at φ = π/2. The method's scope depends on assumptions such as manageable error correlations and has variance-related circuit-depth limits.
Problem
Near-future quantum devices may lack fault-tolerant resources, creating a need to minimize computation errors without encoding.
Source: INTRODUCTION · p. 1Method
The protocol uses gate set tomography to characterize experimental operations and quasiprobability decomposition to sample error-mitigated circuits.
Source: INTRODUCTION · p. 1, MITIGATING READOUT AND ENTANGLING GATE… · p. 3Results
At φ = π/2, QEM reduced the difference from the ideal computation result from 0.1690 to 0.0102.
Source: MITIGATING READOUT AND ENTANGLING GATE… · p. 4Takeaways & Limitations
The demonstrated protocol significantly reduces computation error on a noisy superconducting device without sub-threshold error rates or tremendous additional physical-qubit resources.
Source: DISCUSSIONS · p. 5Scaling relies on treating errors as uncorrelated, while neglecting correlations sacrifices QEM accuracy and computation variance limits circuit depth.
Source: DISCUSSIONS · p. 5
Abstract
from arXiv · showhide
Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, such devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge of exploring the advantage of quantum computation is to minimize the impact of device and control imperfections without encoding. Quantum error mitigation is a solution satisfying the requirement. Here, we demonstrate an error mitigation protocol based on gate set tomography and quasiprobability decomposition. One- and two-qubit circuits are tested on a superconducting device, and computation errors are successfully suppressed. Because this protocol is universal for digital quantum computers and algorithms computing expected values, our results suggest that error mitigation can be an essential component of near-future quantum computation.
INTRODUCTION
The paper demonstrates universal quantum error mitigation by combining gate set tomography with quasiprobability decomposition on one- and two-qubit superconducting circuits. Experiments show improved computation accuracy while addressing readout and entangling-gate errors, with scope limited by variance and assumptions about error correlations.
INTRODUCTION
- Gate set tomography reconstructs preparation, measurement, and gate operations in the Pauli-transfer-matrix representation for estimating experimental errors.GST uses selected initial states and Pauli observables, then obtains Gram and operation matrices from sequential experiments.Source: INTRODUCTION · pp. 1–2
MITIGATING READOUT ERROR IN ONE-QUBIT COMPUTATION
- For one-qubit computation, QEM reduced the measured result to ⟨Z⟩QEM = 0.003 ± 0.022 and improved accuracy over computation without QEM.The protocol decomposes the readout into experimentally accessible measurements sampled according to quasiprobabilities.Source: MITIGATING READOUT ERROR IN ONE-QUBIT… · p. 2
MITIGATING READOUT AND ENTANGLING GATE ERRORS IN TWO-QUBIT COMPUTATION
- The experiment decomposes an ideal controlled-phase gate using 257 linearly independent operations and selects minimum quasiprobability norm solutions to reduce variance.The decomposition includes 256 tensor-product single-qubit operations and a Pauli-twirled controlled-phase operation.Source: MITIGATING READOUT AND ENTANGLING GATE… · pp. 3–4
- For the two-qubit computation at φ = π/2, QEM reduced the difference from the ideal value from 0.1690 to 0.0102.The experiment mitigated both the controlled-phase gate and measurement by sampling decomposed operations.Source: MITIGATING READOUT AND ENTANGLING GATE… · p. 4
DISCUSSIONS
- The approach can scale through one- and two-qubit GST when errors are uncorrelated, but neglecting correlations sacrifices QEM accuracy and circuit-depth performance is limited by variance.The experiment did not observe a significant correlation effect, while higher gate fidelity could extend the circuit depth.Source: DISCUSSIONS · p. 5
- The protocol significantly reduces computation error on a noisy superconducting device without requiring fault-tolerant encoding or large additional qubit resources.It combines gate set tomography with quasiprobability decomposition and is intended for expected-value algorithms.Source: INTRODUCTION · p. 1, DISCUSSIONS · p. 5
Supplementary Information for ”Quantum computation with universal
The supplementary experiments characterize single-qubit gates, heating and readout errors, and the measurement-reset operations used in quantum error mitigation. They also demonstrate one-qubit QEM with experimentally obtained quasiprobabilities.
RANDOMIZED BENCHMARKING FOR SINGLE-QUBIT GATES
- 0.9982 and 0.9976 are the measured fidelities of the Xπ and Xπ/2 single-qubit gates on Q1.Source: RANDOMIZED BENCHMARKING FOR… · p. 7
HEATING RATE MEASUREMENT
- 0.0023 is the estimated ground-state preparation error after waiting 1.6 µs for the readout resonator to settle.The estimate uses T1 = 24.7 µs and the fitted heating and decay rates.Source: READOUT ERROR FOR Q1 AND Q2 · p. 8
READOUT ERROR FOR Q1 AND Q2.
- Readout error rates are measured by repeatedly preparing |0⟩ or |1⟩ and recording the probability of an incorrect output.Source: READOUT ERROR FOR Q1 AND Q2 · p. 7, Table S1 · p. 8
ONE-QUBIT QEM EXPERIMENT
- The one-qubit QEM experiment estimates ⟨Z⟩ from 3,000 samples and repeats the experiment 100 times to obtain its distribution.The experiment uses Gram matrices and quasiprobability coefficients for Q1 and Q2.Source: ONE-QUBIT QEM EXPERIMENT · p. 8, Figure S3 · p. 8
MEASUREMENT AND RESET GATES
- 0.912 ± 0.014 is the measured fidelity of the Q1 measurement-reset gate.The reset uses an ancillary qubit and an i-swap gate to exchange states with the target qubit.Source: MEASUREMENT AND RESET GATES · p. 8
- Measurement-reset gates are characterized with GST, and their fidelities are listed for all gates used in the experiments.Source: MEASUREMENT AND RESET GATES · p. 8, Figure S3 · p. 8, Figure S4 · p. 8
DECOMPOSING Cφ GATE
The supplementary analysis decomposes the Cφ gate using GST-characterized measurement-reset operations and evaluates the resulting error model. Pauli twirling reduces the decomposition cost, while a depolarizing model estimates the fidelity needed for comparable accuracy.
DECOMPOSING Cφ GATE
- The Cφ decomposition treats the first 10 gates in Table I as ideal and characterizes the last 6 measurement-reset gates with GST.The decomposition coefficients for Cπ are shown in Fig. S5.Source: DECOMPOSING Cφ GATE · p. 8, Table S2 · p. 9, Figure S5 · p. 9
- 8.71 to 1.77 is the reduction in decomposition cost P_j| obtained by applying Pauli twirling to the Cπ gate.The two-qubit QEM experiment generates random circuits using the twirled coefficients.Source: DECOMPOSING Cφ GATE · p. 9, Figure S5 · p. 9
DEPOLARIZING ERROR CHANNELS
- For depolarizing two-qubit-gate errors, the success probability is (16F2 − 1)/15 and the failure probability is 16(1 − F2)/15.Source: DEPOLARIZING ERROR CHANNELS · p. 9
- For depolarizing measurement errors, the success probability is 2FM − 1 and the failure probability is 2(1 − FM).Source: DEPOLARIZING ERROR CHANNELS · p. 9
- 0.01 is the estimated computation error when F2 = FM = 0.993 for φ = π/2 in the depolarizing model.The estimate uses Δ⟨X⟩ ≃ ⟨X⟩ideal(3 − F2 − 2FM) with ⟨X⟩ideal = 1/2.Source: DEPOLARIZING ERROR CHANNELS · p. 9