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Variable ansatz applied to spectral operator decomposition in a physical superconducting quantum device

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Abstract

Several techniques for extracting excited states from the Hamiltonian operator have been studied in recent years. This analysis is essential in areas such as Molecular Chemistry and other branches of Quantum Physics, especially those related to optical spectra and chemical reaction processes. Moreover, the knowledge of the operators’ spectrum is required in other fields outside the Physics domains, since there are problems related to graph connectivity and principal component analysis which require a knowledge of, if not all, some important values of the operator spectrum. For those cases, part of the results clarifies that the eigenstate deflation can be used as a tool to extract the excited states. In consonance with these properties, we present a framework to perform the spectral decomposition for any dimension operator in a procedure based on the Householder reflections and unconstrained optimization using a meta-heuristic technique named Differential Evolution. The technique is discussed through examples and implemented in the superconducting real quantum device from IBM Quantum, whose results (without neglecting the system decoherence) follows the pattern expected for the respective models. We conclude our analysis, showing that the proposed framework presents encouraging results to exploit other scenarios in this field.

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Acknowledgements

We thank to IBM for access to superconducting quantum devices through the both Quantum Researchers Program and Qiskit SDK. Finally, we thank the Quantum Computing and Optimization group of the UNILA for the suggestions and discussions.

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Author notes

  1. Anton Simen Albino, Rodrigo Bloot, and Raphael F. I. Gomes have contributed equally to this work.

Authors and Affiliations

  1. Kipu Quantum, Roonstraße 23a, 76137, Karlsruhe, Germany

    Anton Simen Albino

  2. Federal University for Latin American Integration, Foz do Iguaçu, Brazil

    Anton Simen Albino, Rodrigo Bloot & Raphael F. I. Gomes

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  1. Anton Simen Albino
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  2. Rodrigo Bloot
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  3. Raphael F. I. Gomes
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All authors worked equally on the paper.

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Correspondence to Rodrigo Bloot.

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Albino, A.S., Bloot, R. & Gomes, R.F.I. Variable ansatz applied to spectral operator decomposition in a physical superconducting quantum device. Quantum Inf Process 22, 233 (2023). https://doi.org/10.1007/s11128-023-04001-5

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