[Paper Review] Measurement Error Mitigation for Variational Quantum Algorithms

George S. Barron, Christopher J. Wood|arXiv (Cornell University)|Oct 16, 2020

Quantum Computing Algorithms and Architecture39 references44 citations

TL;DR

This paper applies Continuous-Time Markov Process Error Mitigation (CTMP-EM) to variational quantum algorithms, showing improved VQE cost-function estimates and revealing long-range readout-error correlations on IBM devices up to 20 qubits.

ABSTRACT

Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the near-term potential of VQAs as well as understanding the correlations in measurement errors on large, near-term devices.

Motivation & Objective

• Motivate the need to mitigate errors in variational quantum algorithms (VQAs) on near-term devices.
• Adapt and apply CTMP-EM to mitigate measurement errors in VQAs.
• Demonstrate that CTMP-EM shapes and improves the objective function used in VQE.
• Characterize correlated readout errors and their dependence on device connectivity using CTMP-EM.

Proposed method

• Review VQA framework and how measurement noise affects expectation values and gradients.
• Describe CTMP-EM model where readout A is treated as A = e^G with G = sum_i r_i G_i.
• Use a minimal circuit calibration with n+2 circuits to determine CTMP-EM generator rates r_i for 1- and 2-qubit generators.
• Apply CTMP-EM post-processing to measurement data to estimate mitigated expectation values of observables.
• Demonstrate that CTMP-EM can modify the objective-function landscape beyond the minimum, improving global sampling of f(θ).
• Quantify overhead: ~8192 n shots to compensate for mitigation overhead; remaining error due to undersampling.

Experimental results

Research questions

• RQ1 Can CTMP-EM improve the accuracy of expectation-value estimates and gradients used in VQAs such as VQE and QAOA?
• RQ2 How does CTMP-EM affect the shape of the VQA objective function across parameter space?
• RQ3 What can CTMP-EM reveal about correlated, particularly long-range, readout errors on multi-qubit superconducting devices?
• RQ4 To what extent can CTMP-EM calibration data quantify and characterize multi-qubit readout correlations in real devices?

Key findings

• CTMP-EM significantly improves ground-state energy estimates and surrounding objective-function values in VQE for the Fermi-Hubbard model.
• Mitigated objective-function samples show reduced deviation from noiseless results across 1–8 qubits, compared to unmitigated cases.
• The standard deviation of the error distribution is reduced by factors of ~7.46, ~7.64, ~5.18, and ~3.40 for 2, 4, 6, and 8 qubits respectively (without providing exact counts).
• CTMP-EM reveals long-range correlations in readout errors that can be as strong between distant qubits as neighboring ones, and these correlations persist across device connectivity scales up to 20 qubits.
• CTMP-EM provides a scalable characterization method using O(n^2) generator rates r_i, enabling analysis of correlated errors without full A-matrix tomography.