Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits

Meenambika Gowrishankar; Jerimiah Wright; Daniel Claudino; Thien Nguyen; Alexander McCaskey; Travis S. Humble

doi:10.1109/QCE52317.2021.00032

Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits

Meenambika Gowrishankar, Jerimiah Wright, Daniel Claudino, Thien Nguyen, Alexander McCaskey, Travis S. Humble

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.

Original language	English
Title of host publication	Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021
Editors	Hausi A. Muller, Greg Byrd, Candace Culhane, Travis Humble
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	155-159
Number of pages	5
ISBN (Electronic)	9781665416917
DOIs	https://doi.org/10.1109/QCE52317.2021.00032
State	Published - 2021
Event	2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021 - Virtual, Online, United States Duration: Oct 17 2021 → Oct 22 2021

Publication series

Name	Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021

Conference

Conference	2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021
Country/Territory	United States
City	Virtual, Online
Period	10/17/21 → 10/22/21

Funding

The research is supported by the Department of Energy Office of Science, Basic Energy Sciences. This work used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. (http://energy.gov/downloads/doe-public-access-plan).

Keywords

quantum algorithms
quantum chemistry
variational quantum eigensolver

Access to Document

10.1109/QCE52317.2021.00032

Cite this

Gowrishankar, M., Wright, J., Claudino, D., Nguyen, T., McCaskey, A., & Humble, T. S. (2021). Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits. In H. A. Muller, G. Byrd, C. Culhane, & T. Humble (Eds.), Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021 (pp. 155-159). (Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/QCE52317.2021.00032

Gowrishankar, Meenambika ; Wright, Jerimiah ; Claudino, Daniel et al. / Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits. Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021. editor / Hausi A. Muller ; Greg Byrd ; Candace Culhane ; Travis Humble. Institute of Electrical and Electronics Engineers Inc., 2021. pp. 155-159 (Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021).

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title = "Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits",

abstract = "This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.",

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author = "Meenambika Gowrishankar and Jerimiah Wright and Daniel Claudino and Thien Nguyen and Alexander McCaskey and Humble, {Travis S.}",

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Gowrishankar, M, Wright, J, Claudino, D, Nguyen, T, McCaskey, A & Humble, TS 2021, Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits. in HA Muller, G Byrd, C Culhane & T Humble (eds), Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021. Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021, Institute of Electrical and Electronics Engineers Inc., pp. 155-159, 2nd IEEE International Conference on Quantum Computing and Engineering, QCE 2021, Virtual, Online, United States, 10/17/21. https://doi.org/10.1109/QCE52317.2021.00032

Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits. / Gowrishankar, Meenambika; Wright, Jerimiah; Claudino, Daniel et al.
Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021. ed. / Hausi A. Muller; Greg Byrd; Candace Culhane; Travis Humble. Institute of Electrical and Electronics Engineers Inc., 2021. p. 155-159 (Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Claudino, Daniel

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AU - McCaskey, Alexander

AU - Humble, Travis S.

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N2 - This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.

AB - This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.

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Gowrishankar M, Wright J, Claudino D, Nguyen T, McCaskey A, Humble TS. Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits. In Muller HA, Byrd G, Culhane C, Humble T, editors, Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021. Institute of Electrical and Electronics Engineers Inc. 2021. p. 155-159. (Proceedings - 2021 IEEE International Conference on Quantum Computing and Engineering, QCE 2021). doi: 10.1109/QCE52317.2021.00032

Numerical Simulations of Noisy Variational Quantum Eigensolver Ansatz Circuits

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