[Paper Review] Error mitigated quantum circuit cutting

Ritajit Majumdar, Christopher J. Wood|arXiv (Cornell University)|Nov 24, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes error mitigation techniques—readout error mitigation and dominant eigenvalue truncation (DEVT)—for quantum circuit cutting under gate and measurement noise. DEVT significantly improves reconstruction fidelity for depolarizing and Pauli noise, outperforming standard circuit cutting, while linear inversion tomography with DEVT enables efficient partial-data reconstruction.

ABSTRACT

We investigate an error mitigated tomographic approach to the quantum circuit cutting problem in the presence of gate and measurement noise. We explore two tomography specific error mitigation techniques; readout error mitigated conditional fragment tomography, which uses knowledge of readout errors on all cut and conditional qubit measurements in the tomography reconstruction procedure; and dominant eigenvalue truncation (DEVT), which aims to improve the performance of circuit cutting by performing truncation of the individual conditional tomography fragments used in the reconstruction. We find that the performance of both readout error mitigated tomography and DEVT tomography are comparable for circuit cutting in the presence of symmetric measurement errors. For gate errors our numerical results show that probability estimates for the original circuit obtained using DEVT outperforms general circuit cutting for measurement, depolarization and weakly biased Pauli noise models, but does not improve performance for amplitude damping and coherent errors, and can greatly decrease performance for highly biased Pauli noise. In cases where DEVT was effective, it as also found to improve performance of partial tomographic reconstruction using at least 50% of the full tomographic data with a conditional least-squares tomographic fitter, while linear inversion tomography with or without DEVT mitigation was found to perform poorly with with partial data.

Motivation & Objective

• Address the challenge of inaccurate expectation value reconstruction in quantum circuit cutting due to gate and measurement noise on near-term devices.
• Investigate whether tomography-specific error mitigation techniques can improve the fidelity of circuit cutting beyond standard methods.
• Evaluate the effectiveness of readout error mitigation and dominant eigenvalue truncation (DEVT) in mitigating noise during tomographic reconstruction of circuit fragments.
• Determine the conditions under which DEVT improves performance, especially under partial tomographic data and various noise models.
• Compare the performance of linear inversion and constrained least-squares tomography fitters when combined with DEVT and error mitigation.

Proposed method

• Apply readout error mitigated conditional fragment tomography by incorporating knowledge of readout errors into the tomographic reconstruction process.
• Implement dominant eigenvalue truncation (DEVT) to truncate negative or unphysical eigenvalues in the density matrices of individual circuit fragments during tomography.
• Use conditional least-squares (CLS) and linear inversion (LIN) tomography fitters to reconstruct the full circuit expectation values from fragment data.
• Simulate a random Trotterized circuit under various noise models: symmetric and asymmetric readout errors, depolarizing, Pauli, amplitude damping, and coherent rotation errors.
• Evaluate performance using fidelity metrics between reconstructed and ideal probability distributions, comparing with unmitigated circuit cutting.
• Apply Pauli twirling to symmetrize asymmetric readout errors before post-processing correction.

Experimental results

Research questions

• RQ1 Can readout error mitigation improve the accuracy of tomographic circuit cutting under measurement noise?
• RQ2 Does dominant eigenvalue truncation (DEVT) enhance the fidelity of circuit cutting under gate noise, and for which noise models is it most effective?
• RQ3 How does DEVT perform when only partial tomographic data is available, and does it enable better reconstruction than standard methods?
• RQ4 Can linear inversion tomography with DEVT achieve performance comparable to constrained least-squares fitters, especially with incomplete data?
• RQ5 What is the impact of highly biased Pauli noise on DEVT performance, and can it be mitigated through preprocessing?

Key findings

• DEVT significantly improves reconstruction fidelity over standard circuit cutting for depolarizing and Pauli noise models, with performance gains observed even at 50% of full tomographic data.
• For amplitude damping and coherent errors, DEVT provides marginal improvement over unmitigated circuit cutting but does not substantially reduce error.
• DEVT fails dramatically under highly biased Pauli noise, increasing reconstruction error, highlighting a critical limitation of the method.
• Linear inversion tomography with DEVT performs comparably to constrained least-squares fitter when full data is available, enabling faster post-processing.
• Constrained least-squares fitter outperforms linear inversion with partial data, both with and without DEVT, due to compressed sensing-like properties.
• Classical shadow tomography is not beneficial for circuit cutting, as it is equivalent to linear inversion and incompatible with DEVT mitigation.