- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Automated design of photonic two-qubit quantum gates and circuits via optimization and pruning

Javier Osca*

Jiri Vala†

  • *Contact author: javier.osca@uib.cat
  • †Contact author: jiri.vala@mu.ie
PDF

APS Open Sci. 1, 000115 – Published 31 August, 2026

DOI: https://doi.org/10.1103/xjrz-csmx

Abstract

We develop an algorithm to automatically design photonic gates and circuits that is based on a combination of optimization and pruning methods. It starts with a general ansatz for optical circuits with tunable parameters that are then subjected to optimization. The algorithm simplifies the final circuit by pruning its unnecessary elements following predefined criteria. We demonstrate the algorithm by producing both approximate and numerically exact implementations of the cnot gate and Deutsch-Jozsa, Grover, and Fourier transform two-qubit quantum circuits. All implementations of the different gates and circuits can be integrated into larger quantum information protocols.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2010).
  2. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum computers, Nature (London) 464, 45 (2010).
  3. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  4. E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature (London) 409, 46 (2001).
  5. C. R. Myers and R. Laflamme, Linear optics quantum computation: An overview, in Proceedings of the International School of Physics “Enrico Fermi”, edited by G. Casati, D. L. Shepelyansky, P. Zoller, and G. Benenti, Volume 162: Quantum Computers, Algorithms and Chaos (IOS Press / Sage Publishing, Amsterdam, The Netherlands, 2006), pp. 45–93.
  6. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
  7. J. L. O’Brien, A. Furusawa, and J. Vučković, Photonic quantum technologies, Nat. Photon. 3, 687 (2009).
  8. T. C. Ralph and G. J. Pryde, Optical quantum computation, in Progress in Optics (Elsevier, 2010), Vol. 54, Chap. 4, pp. 209–269.
  9. J. L. O’Brien, Optical quantum computing, Science 318, 1567 (2007).
  10. Q. Zhang, M. Li, Y. Chen, X. Ren, R. Osellame, Q. Gong, and Y. Li, Femtosecond laser direct writing of an integrated path-encoded cnot quantum gate, Opt. Mater. Express 9, 2318 (2019).
  11. J. Wang, D. Bonneau, M. Villa, J. W. Silverstone, R. Santagati, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, Chip-to-chip quantum photonic interconnect by path-polarization interconversion, Optica 3, 407 (2016).
  12. G. J. Milburn, Quantum optical Fredkin gate, Phys. Rev. Lett. 62, 2124 (1989).
  13. W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walmsley, Optimal design for universal multiport interferometers, Optica 3, 1460 (2016).
  14. S. A. Fldzhyan, M. Y. Saygin, and S. P. Kulik, Optimal design of error-tolerant reprogrammable multiport interferometers, Opt. Lett. 45, 2632 (2020).
  15. J. Eisert, Optimizing linear optics quantum gates, Phys. Rev. Lett. 95, 040502 (2005).
  16. M. Krenn, J. S. Kottmann, N. Tischler, and A. Aspuru-Guzik, Conceptual understanding through efficient automated design of quantum optical experiments, Phys. Rev. X 11, 031044 (2021).
  17. M. Krenn, M. Malik, R. Fickler, R. Lapkiewicz, and A. Zeilinger, Automated search for new quantum experiments, Phys. Rev. Lett. 116, 090405 (2016).
  18. Stochastic optical quantum circuit simulator (SOQCS), GitHub, 2023, https://github.com/SOQCSAdmin/SOQCS, accessed: 15 August 2013.
  19. J. Osca and J. Vala, SOQCS: A stochastic optical quantum circuit simulator, SoftwareX 25, 101603 (2024).
  20. S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborge, and P. J. Coles, Quantum-assisted quantum compiling, Quantum 3, 140 (2019).
  21. L. Madden and A. Simonetto, Best approximate quantum compiling problems, ACM Trans. Quantum Comput. 3, 1 (2022).
  22. X. Qiang, X. Zhou, J. Wang, C. M. Wilkes, T. Loke, S. O’Gara, L. Kling, G. D. Marshall, R. Santagati, T. C. Ralph, J. B. Wang, J. L. O’Brien, M. G. Thompson, and J. C. F. Matthews, Large-scale silicon quantum photonics implementing arbitrary two-qubit processing, Nat. Photon. 12, 534 (2018).
  23. X. Gao, M. Erhard, A. Zeilinger, and M. Krenn, Computer-inspired concept for high-dimensional multipartite quantum gates, Phys. Rev. Lett. 125, 050501 (2020).
  24. T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Linear optical controlled-NOT gate in the coincidence basis, Phys. Rev. A 65, 062324 (2002).
  25. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Demonstration of an all-optical quantum controlled-NOT gate, Nature (London) 426, 264 (2003).
  26. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Software 23, 550 (1997).
  27. E. Knill, Approximation by quantum circuits, arXiv:quant-ph/9508006.
  28. P. Lundow and K. Markström, Efficient computation of permanents, with applications to boson sampling and random matrices, J. Comput. Phys. 455, 110990 (2022).
  29. E. Knill, Quantum gates using linear optics and postselection, Phys. Rev. A 66, 052306 (2002).
  30. D. David and J. Richard, Rapid solution of problems by quantum computation, Proc. R. Soc. London A 439, 553 (1992).
  31. L. K. Grover, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC ’96 (Association for Computing Machinery, New York, 1996), pp. 212–219.
  32. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26, 1484 (1997).
  33. M. Treinish, J. Lishman, L. Bello, J. Gambetta, D. M. Rodríguez, M. Marques, J. Gacon, P. Nation, C. J. Wood, Ewinston, et al., Qiskit/qiskit: Qiskit 2.3.0, https://www.ibm.com/quantum/qiskit, accessed: 1 December 2025.

Outline

Information

APS Open Sci. 1, 000115– Published 31 August, 2026
Vol. 1
  • Received 16 December 2025
  • Accepted 19 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation