Evaluating the noise resilience of variational quantum algorithms

Fontana, Enrico and Fitzpatrick, Nathan and Ramo, David Muñoz and Duncan, Ross and Rungger, Ivan (2021) Evaluating the noise resilience of variational quantum algorithms. Physical Review A, 104 (2). 022403. ISSN 2469-9926 (https://doi.org/10.1103/PhysRevA.104.022403)

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Abstract

We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in the presence of noise and adopt two quality measures in addition to the energy, namely, fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimized parameters. We find that the inclusion of redundant parameterized gates makes the quantum circuits more resilient to noise. For such overparameterized circuits, different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region, the deviation is well described by a stochastic model. Above the threshold, the optimization can converge to states with largely different physical properties from the true target state, so for practical applications it is critical to ensure that noise levels are below this threshold.

ORCID iDs

Fontana, Enrico, Fitzpatrick, Nathan, Ramo, David Muñoz, Duncan, Ross ORCID logoORCID: https://orcid.org/0000-0001-6758-1573 and Rungger, Ivan;
  • Item type:Article
    ID code:81769
    Dates:
    Date
    Event
    4 August 2021
    Published
    15 June 2021
    Accepted
    Notes:Funding Information: E.F. and I.R. acknowledge the support of the UK government department for Business, Energy and Industrial Strategy through the UK national quantum technologies program. E.F. acknowledges the support of an industrial CASE (iCASE) studentship, funded by the UK Engineering and Physical Sciences Research Council (Grant No. EP/T517665/1), in collaboration with the University of Strathclyde, the National Physical Laboratory, and Cambridge Quantum Computing Ltd. We thank Marco Cerezo, Lingling Lao, Dan Browne, Andrew Patterson, and Prakash Murali for useful discussions. In part of our simulations, we used the software quantumsim . Funding Information: Department for Business, Energy and Industrial Strategy Engineering and Physical Sciences Research Council University of Strathclyde Publisher Copyright: ©2021 American Physical Society
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:09 Aug 2022 09:20
    Last modified:11 Nov 2024 13:35
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/81769
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