Symmetry Aspects in Quantum Computing

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Chemistry: Symmetry/Asymmetry".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 887

Special Issue Editor


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Guest Editor
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, TX 79409, USA
Interests: quantum computing for quantum chemistry

Special Issue Information

Dear Colleague,

Symmetry is a unifying concept in science and technology, its influence now extending to the flourishing field of quantum computing (QC). In fact, symmetry pervades all possible aspects of QC: formalisms, algorithms, circuits, calculations, and quantum computers. As a fast-evolving endeavor, QC challenges scientists to develop new concepts, formalisms, algorithms, and applications of symmetry theory. In this context, this Special Issue of Symmetry calls for theoretical and applied manuscripts on novel aspects of symmetry theory for QC. While manuscripts from all backgrounds are welcome, this issue highlights symmetry/QC developments relevant to general symmetry theory, quantum chemistry, quantum chemical dynamics, molecular physics, solid state physics, computer science, and computer engineering. Possible topics for this issue include (but are not limited to) the following:

  1. Lie algebras and Lie groups in QC formalisms;
  2. Point groups in QC formalisms;
  3. Symmetry in QC encodings, mappings, and circuits (e.g., for qubit reduction);
  4. Unitary group approaches for QC calculations in quantum chemistry and molecular physics;
  5. Spin-adapted and spin-free QC calculations in quantum chemistry;
  6. Symmetry conservation and symmetry breaking in QC calculations;
  7. Symmetry-protected topological states for quantum computers;
  8. Symmetry aspects of the quantum walk, Lie–Trotter–Suzuki approximation, Magnus expansion, and other propagation schemes in QC.

Dr. Jorge A. Morales
Guest Editor

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Keywords

  • quantum computing (QC)
  • symmetry theory
  • Lie algebras and Lie groups
  • quantum encoding & mapping
  • quantum circuits
  • quantum chemistry
  • molecular physics
  • spin-adapted calculations
  • symmetry conservation
  • symmetry breaking
  • quantum walk
  •  quantum formalisms
  • quantum algorithms
  • quantum computer engineering
  • symmetry in quantum simulations
  • quantum information theory

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Published Papers (1 paper)

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Research

34 pages, 5593 KiB  
Article
Toward a Quantum Computing Formulation of the Electron Nuclear Dynamics Method via Fukutome Unitary Representation
by Juan C. Dominguez, Ismael de Farias and Jorge A. Morales
Symmetry 2025, 17(2), 303; https://doi.org/10.3390/sym17020303 - 17 Feb 2025
Cited by 1 | Viewed by 627
Abstract
We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with [...] Read more.
We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H2+ We discuss the present results and future END/QC/QVS extensions. Full article
(This article belongs to the Special Issue Symmetry Aspects in Quantum Computing)
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