Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses

Swarnadeep Majumder1,2, Christopher G. Yale3, Titus D. Morris4, Daniel S. Lobser3, Ashlyn D. Burch3, Matthew N. H. Chow3,5,6, Melissa C. Revelle3, Susan M. Clark3, and Raphael C. Pooser4

1Duke Quantum Center, Duke University, Durham, NC 27701, USA
2Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708 USA
3Sandia National Laboratories, Albuquerque, NM 87123, USA
4Quantum Information Science Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
5Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA
6Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA

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Abstract

Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can support a sufficient number of sequential operations prior to decoherence such that near term algorithms can be performed with proximate accuracy (like chemical accuracy for quantum chemistry problems). While the results of these algorithms are imperfect, these imperfections can help bootstrap quantum computer testbed development. Demonstrations of these algorithms over the past few years, coupled with the idea that imperfect algorithm performance can be caused by several dominant noise sources in the quantum processor, which can be measured and calibrated during algorithm execution or in post-processing, has led to the use of noise mitigation to improve typical computational results. Conversely, benchmark algorithms coupled with noise mitigation can help diagnose the nature of the noise, whether systematic or purely random. Here, we outline the use of coherent noise mitigation techniques as a characterization tool in trapped-ion testbeds. We perform model-fitting of the noisy data to determine the noise source based on realistic physics focused noise models and demonstrate that systematic noise amplification coupled with error mitigation schemes provides useful data for noise model deduction. Further, in order to connect lower level noise model details with application specific performance of near term algorithms, we experimentally construct the loss landscape of a variational algorithm under various injected noise sources coupled with error mitigation techniques. This type of connection enables application-aware hardware codesign, in which the most important noise sources in specific applications, like quantum chemistry, become foci of improvement in subsequent hardware generations.

NISQ-era quantum computers, are by their very definition, noisy and imperfect, requiring methods for error mitigation in order to improve circuit performance. In this paper, we demonstrate that a technique known as hidden inverses can both act as a method for error mitigation as well as for error characterization. Hidden inverses rely on the ability to construct circuits with non-native composite gates that are self-adjoint (such as the Hadamard or controlled-NOT), meaning they can be constructed via a series of hardware-native gates or those same native gates inverted in sign and time ordering. Using a trapped-ion quantum computer, we first demonstrate an experiment in which the Hadamard and its inverse are alternated with small error rotations inserted. By fitting the results to a simple model, we are then able to characterize coherent errors in the system, and see how those errors drift over time. We then use a controlled-NOT and its inverse within a variation quantum eigensolver. Through intentional error injection, we show that circuits constructed via hidden inverse protocols outperform another error mitigation technique, randomized compiling. We further examine error mitigation in this system via fermionic density matric purification, a post-processing methodology. Through this examination, we find that using the same technique, namely hidden inverses, to both characterize error sources on hardware and then mitigate via the same approach is a powerful tool for NISQ-era quantum computers.

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[2] Zhubing Jia, Shilin Huang, Mingyu Kang, Ke Sun, Robert F. Spivey, Jungsang Kim, and Kenneth R. Brown, "Angle-robust two-qubit gates in a linear ion crystal", Physical Review A 107 3, 032617 (2023).

[3] Mingyu Kang, Ye Wang, Chao Fang, Bichen Zhang, Omid Khosravani, Jungsang Kim, and Kenneth R. Brown, "Designing Filter Functions of Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains", Physical Review Applied 19 1, 014014 (2023).

[4] Oliver G. Maupin, Ashlyn D. Burch, Brandon Ruzic, Christopher G. Yale, Antonio Russo, Daniel S. Lobser, Melissa C. Revelle, Matthew N. Chow, Susan M. Clark, Andrew J. Landahl, and Peter J. Love, "Error mitigation, optimization, and extrapolation on a trapped ion testbed", arXiv:2307.07027, (2023).

[5] Gabriele Cenedese, Giuliano Benenti, and Maria Bondani, "Correcting Coherent Errors by Random Operation on Actual Quantum Hardware", Entropy 25 2, 324 (2023).

[6] Ashlyn D. Burch, Daniel S. Lobser, Christopher G. Yale, Jay W. Van Der Wall, Oliver G. Maupin, Joshua D. Goldberg, Matthew N. H. Chow, Melissa C. Revelle, and Susan M. Clark, "Batching Circuits to Reduce Compilation in Quantum Control Hardware", arXiv:2208.00076, (2022).

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