Error mitigation, optimization, and extrapolation on a trapped ion testbed

TL;DR

This paper investigates error mitigation via zero noise extrapolation in a trapped-ion quantum device, testing different scaling methods to improve ground state energy calculations of HeH+ with variational algorithms.

Contribution

The study compares three noise scaling techniques for ZNE in a trapped-ion quantum computer, highlighting the importance of choosing suitable methods for specific hardware architectures.

Findings

Time-stretching and sideband amplitude scaling did not effectively scale noise for extrapolation.

Global gate identity insertions enabled better noise scaling and improved energy estimates.

Error mitigation reduced the energy estimate error from 0.127 to within -0.004 +- 0.04 Hartree.

Abstract

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here, we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom in the presence of realistic noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time-stretching the two-qubit gates, scaling the sideband amplitude parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find time-stretching and sideband amplitude scaling fail to scale the noise on our particular hardware in a way that can be directly extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve an estimate of the ground state energy within -0.004 +- 0.04 Hartree; outside chemical accuracy, but greatly improved over our non-error-mitigated estimate with error 0.127 +- 0.008 Hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.