Quantum Information & Computation
Volume 26
RESEARCH ARTICLE Open access

Quantum Circuit Optimization Techniques: A Literature Survey

Mariia Makarova, Davide Pastorello, Valter Cavecchia, Enrico Blanzieri, Kamil Khadiev, Alexander Rumyantsev

Author affiliations
  • Mariia Makarova1
  • Davide Pastorello2
  • Valter Cavecchia3
  • Enrico Blanzieri4
  • Kamil Khadiev5
  • Alexander Rumyantsev6
  1. Institute of Applied Mathematical Research, Karelian Research Centre of RAS, Pushkinskaya Str. 11, Petrozavodsk, Russia; Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenina Pr. 33, Petrozavodsk, Russia; Department of Information Engineering and Computer Science, University of Trento, Via Sommarive 9, Povo Trento, Italy
  2. Department of Information Engineering and Computer Science, University of Trento, Via Sommarive 9, Povo Trento, Italy; Trento Institute of Fundamental Physics and Applications, Via Sommarive 14, Povo Trento, Italy; Department of Mathematics, Universit‘a di Bologna, Piazza di Porta San Donato 5, Bologna, Italy
  3. Institute of Materials for Electronics and Magnetism (CNR), Via Alla Cascata 56/c, Povo Trento, Italy
  4. Department of Information Engineering and Computer Science, University of Trento, Via Sommarive 9, Povo Trento, Italy; Trento Institute of Fundamental Physics and Applications, Via Sommarive 14, Povo Trento, Italy; Institute of Materials for Electronics and Magnetism (CNR), Via Alla Cascata 56/c, Povo Trento, Italy
  5. Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kremlyovskaya Str. 18, Kazan, Russia; Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Sibirsky Tract, 10/7, Kazan, Russia
  6. Institute of Applied Mathematical Research, Karelian Research Centre of RAS, Pushkinskaya Str. 11, Petrozavodsk, Russia; Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, Lenina Pr. 33, Petrozavodsk, Russia

pp. 154-179 · 10.2478/qic-2026-0008

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Abstract

We present a literature survey of the mathematical aspects of optimization and optimal synthesis of quantum circuits. The optimization techniques we consider perform the synthesis of quantum circuit by minimizing a given cost function. A total of 179 papers were filtered by inclusion/exclusion criteria and reviewed according to representation models adopted, the techniques used or developed, the kind of benchmarks adopted and the comparison against competitors performed. The survey shows that a very diverse literature has been accumulating in the recent years and although it resists a common formalization, some trends can be individuated. In particular, there is a lack of shared benchmarks with some exceptions. Moreover, many approaches change the representation of the problem to a formulation other than the simple sequence of gates. Final conclusions are drawn and possible lines of future research are suggested.
Open accessCC BY-NC-ND 4.0

Keywords

  • quantum computing
  • circuit synthesis
  • quantum circuit optimization

Suggested citation

Mariia Makarova, Davide Pastorello, Valter Cavecchia, Enrico Blanzieri, Kamil Khadiev, Alexander Rumyantsev (2026). Quantum Circuit Optimization Techniques: A Literature Survey. Quantum Information & Computation, 26(1), 154-179. https://doi.org/10.2478/qic-2026-0008

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