Efficient quantum state estimation with low-rank matrix completion

Shehbaz Tariq, Ahmad Farooq, Junaid Ur Rehman, Trung Q. Duong, Hyundong Shin*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

This paper introduces a novel and efficient technique for quantum state estimation,
coined as low-rank matrix-completion quantum state tomography for characterizing
pure quantum states, as it requires only non-entangling bases and 2n + 1 local Pauli
operators. This significantly reduces the complexity of the process and increases the
accuracy of the state estimation, as it eliminates the need for the entangling bases,
which are experimentally difficult to implement on quantum devices. The required
minimal post-processing, improved accuracy and efficacy of this
matrix-completion-based method make it an ideal benchmarking tool for
investigating the properties of quantum systems, enabling researchers to verify the
accuracy of quantum devices, characterize their performance, and explore the
underlying physics of quantum phenomena. Our numerical results demonstrate that
this method outperforms contemporary techniques in its ability to accurately
reconstruct multi-qubit quantum states on real quantum devices, making it an
invaluable contribution to the field of quantum state characterization and an
essential step toward the reliable deployment of intermediate- and large-scale
quantum devices.
Original languageEnglish
Article number50
Number of pages12
JournalEPJ Quantum Technology
Volume11
Issue number1
DOIs
Publication statusPublished - 5 Aug 2024
MoE publication typeA1 Journal article-refereed

Keywords

  • Fidelity
  • Matrix completion
  • NISQ
  • Pauli operators
  • Quantum state tomography
  • Singular value decomposition

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