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A quantum scheme of state overlap based on quantum mean estimation and support vector machine

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  • Liu, Wen
  • Yin, Han-Wen

Abstract

Given two unknown quantum states |ϕ〉 and |ψ〉, the overlap between them is defined as |〈ϕ|ψ〉|2, i.e. the inner product between their state vectors. Estimating the overlap between two states is an important task with several applications. In most applications, overlap estimation is carried out through the swap test. A new scheme for estimating the overlap between two states based on Quantum Mean Estimation (QME) algorithm and Support Vector Machine (SVM) is presented. Compared with other schemes, this new scheme offers a quadratic speedup over the swap test while it obtains a better output with relatively high accuracy. Using QME, the uncertainty in the estimated value falls as O(1q) in the number of queries q to unitaries, which are used to the create the states 〈ϕ|ψ〉. Using SVM, a more accurate estimate of the estimated value is obtained. The accuracy of new scheme has a significant improvement than using QME algorithm alone. The correctness and efficiency of the proposed scheme is verified by an experimental simulation on the IBM quantum cloud platform.

Suggested Citation

  • Liu, Wen & Yin, Han-Wen, 2022. "A quantum scheme of state overlap based on quantum mean estimation and support vector machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    • Handle: RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122006926
    DOI: 10.1016/j.physa.2022.128117
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