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Finding eigenvectors with a quantum variational algorithm

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Juan Carlos Garcia-Escartin

Quantum Physics · Submitted 22 Nov 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit.

how it is stated · asserted 1.00 read the record →

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arXiv ID2311.13543 (version 2)
Pith IDPAA5MOIF, Pith's permanent record of this paper and its review
CitationJuan Carlos Garcia-Escartin. "Finding eigenvectors with a quantum variational algorithm." arXiv:2311.13543 (2023). https://pith.science/paper/PAA5MOIF
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,905 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.84 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis (QPCA) on unknown input mixed states. These algorithms can all be run with low depth quantum circuits, suitable for an efficient implementation on noisy intermediate state quantum computers (NISQC) and, with some restrictions, on linear optical systems. Limitations and potential applications are discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. contribution 1.00 0.91 0.53 asserted 1.00
s1 The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. method 1.00 0.75 0.06 asserted 1.00
s2 The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. result 0.43 0.81 0.17 asserted 1.00
s3 This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis (QPCA) on unknown input mixed states. contribution 0.90 0.73 0.16 asserted 0.57
s4 These algorithms can all be run with low depth quantum circuits, suitable for an efficient implementation on noisy intermediate state quantum computers (NISQC) and, with some restrictions, on linear optical systems. interpretation 0.49 0.55 0.11 asserted 0.67
s5 Limitations and potential applications are discussed. limitation 0.75 0.37 0.04 asserted 0.67

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from argument 0.59.

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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis (QPCA) on unknown input mixed states. These algorithms can all be run with low depth quantum circuits, suitable for an efficient implementation on noisy intermediate state quantum computers (NISQC) and, with some restrictions, on linear optical systems. Limitations and potential applications are discussed.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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