- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Quantum circuits for partial differential equations in Fourier space

Michael Lubasch1,*, Yuta Kikuchi2,3, Lewis Wright1, and Conor Mc Keever1

  • 1Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom
  • 2Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan
  • 3RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan

  • *Contact author: michael.lubasch@quantinuum.com
PDF

Phys. Rev. Research 7, 043326 – Published 22 December, 2025

DOI: https://doi.org/10.1103/tbzc-w9x8

Abstract

For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements. This is shown by explicit circuit constructions for the incompressible advection, heat, isotropic acoustic wave, and Poisson's equations as canonical examples. We utilize quantum singular value transformation to develop circuits that are expected to be of optimal computational complexity. Additionally, we consider approximations suited for smooth initial conditions and describe circuits that make lower demands on hardware. The simple QFT-based circuits are efficient with respect to dimensionality and pave the way for current quantum computers to solve high-dimensional PDEs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (123)

  1. D. W. Berry, High-order quantum algorithm for solving linear differential equations, J. Phys. A: Math. Theor. 47, 105301 (2014).
  2. D. W. Berry, A. M. Childs, A. Ostrander, and G. Wang, Quantum algorithm for linear differential equations with exponentially improved dependence on precision, Commun. Math. Phys. 356, 1057 (2017).
  3. S. Lloyd, G. De Palma, C. Gokler, B. Kiani, Z.-W. Liu, M. Marvian, F. Tennie, and T. Palmer, Quantum algorithm for nonlinear differential equations, arXiv:2011.06571.
  4. J.-P. Liu, H. Ø. Kolden, H. K. Krovi, N. F. Loureiro, K. Trivisa, and A. M. Childs, Efficient quantum algorithm for dissipative nonlinear differential equations, Proc. Natl. Acad. Sci. USA 118, e2026805118 (2021).
  5. A. M. Childs, J.-P. Liu, and A. Ostrander, High-precision quantum algorithms for partial differential equations, Quantum 5, 574 (2021).
  6. J. F. Wendt, Computational Fluid Dynamics: An Introduction (Springer, Berlin, Heidelberg, 2009).
  7. O. C. Zienkiewicz, R. L. Taylor, and D. D. Fox, The Finite Element Method for Solid and Structural Mechanics (Elsevier, Kidlington, 2014).
  8. D. J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (John Wiley & Sons, Chichester, 2006).
  9. S. J. Jang, Quantum Mechanics for Chemistry (Springer, Cham, 2023).
  10. Y. Cao, A. Papageorgiou, I. Petras, J. Traub, and S. Kais, Quantum algorithm and circuit design solving the Poisson equation, New J. Phys. 15, 013021 (2013).
  11. A. Montanaro and S. Pallister, Quantum algorithms and the finite element method, Phys. Rev. A 93, 032324 (2016).
  12. G. Xu, A. J. Daley, P. Givi, and R. D. Somma, Turbulent mixing simulation via a quantum algorithm, AIAA J. 56, 687 (2018).
  13. P. C. S. Costa, S. Jordan, and A. Ostrander, Quantum algorithm for simulating the wave equation, Phys. Rev. A 99, 012323 (2019).
  14. G. Xu, A. J. Daley, P. Givi, and R. D. Somma, Quantum algorithm for the computation of the reactant conversion rate in homogeneous turbulence, Combust. Theory Model. 23, 1090 (2019).
  15. J. M. Arrazola, T. Kalajdzievski, C. Weedbrook, and S. Lloyd, Quantum algorithm for nonhomogeneous linear partial differential equations, Phys. Rev. A 100, 032306 (2019).
  16. A. M. Childs and J.-P. Liu, Quantum spectral methods for differential equations, Commun. Math. Phys. 375, 1427 (2020).
  17. P. Givi, A. J. Daley, D. Mavriplis, and M. Malik, Quantum speedup for aeroscience and engineering, AIAA J. 58, 3715 (2020).
  18. F. Gaitan, Finding flows of a Navier–Stokes fluid through quantum computing, npj Quantum Inf. 6, 61 (2020).
  19. L. Budinski, Quantum algorithm for the advection–diffusion equation simulated with the lattice Boltzmann method, Quantum Inf. Process. 20, 57 (2021).
  20. F. Oz, R. K. S. S. Vuppala, K. Kara, and F. Gaitan, Solving Burgers’ equation, with quantum computing, Quantum Inf. Process. 21, 30 (2022).
  21. S. Jin and N. Liu, Quantum algorithms for nonlinear partial differential equations, Bull. Sci. Math. 194, 103457 (2024).
  22. N. Linden, A. Montanaro, and C. Shao, Quantum vs. classical algorithms for solving the heat equation, Commun. Math. Phys. 395, 601 (2022).
  23. S. Jin, N. Liu, and Y. Yu, Quantum simulation of partial differential equations via Schrödingerisation, Phys. Rev. Lett. 133, 230602 (2024).
  24. H. Krovi, Improved quantum algorithms for linear and nonlinear differential equations, Quantum 7, 913 (2023).
  25. S. Jin, N. Liu, and Y. Yu, Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations, J. Comput. Phys. 487, 112149 (2023).
  26. S. Jin, N. Liu, and Y. Yu, Quantum simulation of partial differential equations: Applications and detailed analysis, Phys. Rev. A 108, 032603 (2023).
  27. D. An, J.-P. Liu, and L. Lin, Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost, Phys. Rev. Lett. 131, 150603 (2023).
  28. S. Succi, W. Itani, K. Sreenivasan, and R. Steijl, Quantum computing for fluids: Where do we stand? Europhys. Lett. 144, 10001 (2023).
  29. S. S. Bharadwaj and K. R. Sreenivasan, Hybrid quantum algorithms for flow problems, Proc. Natl. Acad. Sci. USA 120, e2311014120 (2023).
  30. W. Itani, K. R. Sreenivasan, and S. Succi, Quantum algorithm for lattice Boltzmann (QALB) simulation of incompressible fluids with a nonlinear collision term, Phys. Fluids 36, 017112 (2024).
  31. F. Tennie and L. Magri, Solving nonlinear differential equations on quantum computers: A Fokker-Planck approach, arXiv:2401.13500.
  32. S. Jin, N. Liu, and Y. Yu, Quantum simulation of the Fokker-Planck equation via Schrödingerization, arXiv:2404.13585.
  33. Y. Sato, H. Tezuka, R. Kondo, and N. Yamamoto, Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters, Phys. Rev. Appl. 23, 014063 (2025).
  34. P. Brearley and S. Laizet, Quantum algorithm for solving the advection equation using Hamiltonian simulation, Phys. Rev. A 110, 012430 (2024).
  35. J. Ingelmann, S. S. Bharadwaj, P. Pfeffer, K. R. Sreenivasan, and J. Schumacher, Two quantum algorithms for solving the one-dimensional advection–diffusion equation, Comput. Fluids 281, 106369 (2024).
  36. J. Gonzalez-Conde, D. Lewis, S. S. Bharadwaj, and M. Sanz, Quantum Carleman linearisation efficiency in nonlinear fluid dynamics, Phys. Rev. Res. 7, 023254 (2025).
  37. S. S. Bharadwaj and K. R. Sreenivasan, Towards simulating fluid flows with quantum computing, Sādhanā 50, 57 (2025).
  38. H.-Y. Wu, A. E. Paine, E. Philip, A. A. Gentile, and O. Kyriienko, Quantum algorithm for solving nonlinear differential equations based on physics-informed effective Hamiltonians, arXiv:2504.13174.
  39. E. Devereux and A. Datta, Quantum algorithms for solving a drift-diffusion equation, Phys. Rev. A 112, 042419 (2025).
  40. M. Lubasch, J. Joo, P. Moinier, M. Kiffner, and D. Jaksch, Variational quantum algorithms for nonlinear problems, Phys. Rev. A 101, 010301(R) (2020).
  41. O. Kyriienko, A. E. Paine, and V. E. Elfving, Solving nonlinear differential equations with differentiable quantum circuits, Phys. Rev. A 103, 052416 (2021).
  42. H.-L. Liu, Y.-S. Wu, L.-C. Wan, S.-J. Pan, S.-J. Qin, F. Gao, and Q.-Y. Wen, Variational quantum algorithm for the Poisson equation, Phys. Rev. A 104, 022418 (2021).
  43. Y. Sato, R. Kondo, S. Koide, H. Takamatsu, and N. Imoto, Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation, Phys. Rev. A 104, 052409 (2021).
  44. H. Alghassi, A. Deshmukh, N. Ibrahim, N. Robles, S. Woerner, and C. Zoufal, A variational quantum algorithm for the Feynman-Kac formula, Quantum 6, 730 (2022).
  45. P. Pfeffer, F. Heyder, and J. Schumacher, Hybrid quantum-classical reservoir computing of thermal convection flow, Phys. Rev. Res. 4, 033176 (2022).
  46. R. Demirdjian, D. Gunlycke, C. A. Reynolds, J. D. Doyle, and S. Tafur, Variational quantum solutions to the advection–diffusion equation for applications in fluid dynamics, Quantum Inf. Process. 21, 322 (2022).
  47. Y. Y. Liu, Z. Chen, C. Shu, S.-C. Chew, B. C. Khoo, X. Zhao, and Y. D. Cui, Application of a variational hybrid quantum-classical algorithm to heat conduction equation and analysis of time complexity, Phys. Fluids 34, 117121 (2022).
  48. A. J. Pool, A. D. Somoza, M. Lubasch, and B. Horstmann, Solving partial differential equations using a quantum computer, in Proceedings of the 2022 IEEE International Conference on Quantum Computing and Engineering (IEEE, New York City, 2022), pp. 864–866.
  49. D. Jaksch, P. Givi, A. J. Daley, and T. Rung, Variational quantum algorithms for computational fluid dynamics, AIAA J. 61, 1885 (2023).
  50. N. M. Guseynov, A. A. Zhukov, W. V. Pogosov, and A. V. Lebedev, Depth analysis of variational quantum algorithms for the heat equation, Phys. Rev. A 107, 052422 (2023).
  51. M. Ali and M. Kabel, Performance study of variational quantum algorithms for solving the Poisson equation on a quantum computer, Phys. Rev. Appl. 20, 014054 (2023).
  52. H.-M. Li, Z.-X. Wang, and S.-M. Fei, Variational quantum algorithms for Poisson equations based on the decomposition of sparse Hamiltonians, Phys. Rev. A 108, 032418 (2023).
  53. P. Pfeffer, F. Heyder, and J. Schumacher, Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing, Phys. Rev. Res. 5, 043242 (2023).
  54. Y. Y. Liu, Z. Chen, C. Shu, P. Rebentrost, Y. G. Liu, S. C. Chew, B. C. Khoo, and Y. D. Cui, A variational quantum algorithm-based numerical method for solving potential and Stokes flows, Ocean Eng. 292, 116494 (2024).
  55. N. Köcher, H. Rose, S. S. Bharadwaj, J. Schumacher, and S. Schumacher, Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm, Sci. Rep. 15, 23478 (2025).
  56. A. J. Pool, A. D. Somoza, C. Mc Keever, M. Lubasch, and B. Horstmann, Nonlinear dynamics as a ground-state solution on quantum computers, Phys. Rev. Res. 6, 033257 (2024).
  57. A. Sarma, T. W. Watts, M. Moosa, Y. Liu, and P. L. McMahon, Quantum variational solving of nonlinear and multidimensional partial differential equations, Phys. Rev. A 109, 062616 (2024).
  58. C. Sanavio, F. Mascherpa, A. Marruzzo, A. Amendola, and S. Succi, Variational-adiabatic quantum solver for systems of linear equations with warm starts, arXiv:2505.24285.
  59. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nat. Commun. 9, 4812 (2018).
  60. M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost function dependent barren plateaus in shallow parametrized quantum circuits, Nat. Commun. 12, 1791 (2021).
  61. A. V. Uvarov and J. D. Biamonte, On barren plateaus and cost function locality in variational quantum algorithms, J. Phys. A: Math. Theor. 54, 245301 (2021).
  62. C. Zhao and X.-S. Gao, Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus, Quantum 5, 466 (2021).
  63. T. L. Patti, K. Najafi, X. Gao, and S. F. Yelin, Entanglement devised barren plateau mitigation, Phys. Rev. Res. 3, 033090 (2021).
  64. C. Ortiz Marrero, M. Kieferová, and N. Wiebe, Entanglement-induced barren plateaus, PRX Quantum 2, 040316 (2021).
  65. S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-induced barren plateaus in variational quantum algorithms, Nat. Commun. 12, 6961 (2021).
  66. Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022).
  67. M. Larocca, P. Czarnik, K. Sharma, G. Muraleedharan, P. J. Coles, and M. Cerezo, Diagnosing barren plateaus with tools from quantum optimal control, Quantum 6, 824 (2022).
  68. E. Cervero Martín, K. Plekhanov, and M. Lubasch, Barren plateaus in quantum tensor network optimization, Quantum 7, 974 (2023).
  69. D. Coppersmith, An approximate Fourier transform useful in quantum factoring, arXiv:quant-ph/0201067.
  70. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, 2010).
  71. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 (Association for Computing Machinery, New York, NY, 2019), pp. 193–204.
  72. J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang, Grand unification of quantum algorithms, PRX Quantum 2, 040203 (2021).
  73. J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19, 297 (1965).
  74. M. Frigo and S. G. Johnson, The design and implementation of FFTW3, Proc. IEEE 93, 216 (2005).
  75. M. Plesch and Č. Brukner, Quantum-state preparation with universal gate decompositions, Phys. Rev. A 83, 032302 (2011).
  76. X.-M. Zhang, T. Li, and X. Yuan, Quantum state preparation with optimal circuit depth: Implementations and applications, Phys. Rev. Lett. 129, 230504 (2022).
  77. X. Sun, G. Tian, S. Yang, P. Yuan, and S. Zhang, Asymptotically optimal circuit depth for quantum state preparation and general unitary synthesis, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 42, 3301 (2023).
  78. K. Plekhanov, M. Rosenkranz, M. Fiorentini, and M. Lubasch, Variational quantum amplitude estimation, Quantum 6, 670 (2022).
  79. S. Ramos-Calderer, Efficient quantum interpolation of natural data, Phys. Rev. A 106, 062427 (2022).
  80. I. Y. Akhalwaya, A. Connolly, R. Guichard, S. Herbert, C. Kargi, A. Krajenbrink, M. Lubasch, C. Mc Keever, J. Sorci, M. Spranger, and I. Williams, A modular engine for quantum Monte Carlo integration, arXiv:2308.06081.
  81. G. Marin-Sanchez, J. Gonzalez-Conde, and M. Sanz, Quantum algorithms for approximate function loading, Phys. Rev. Res. 5, 033114 (2023).
  82. M. Moosa, T. W. Watts, Y. Chen, A. Sarma, and P. L. McMahon, Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions, Quantum Sci. Technol. 9, 015002 (2024).
  83. M. Rosenkranz, E. Brunner, G. Marin-Sanchez, N. Fitzpatrick, S. Dilkes, Y. Tang, Y. Kikuchi, and M. Benedetti, Quantum state preparation for multivariate functions, Quantum 9, 1703 (2025).
  84. Y. Sato, R. Kondo, I. Hamamura, T. Onodera, and N. Yamamoto, Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits, Phys. Rev. Res. 6, 033246 (2024).
  85. L. Wright, C. Mc Keever, J. T. First, R. Johnston, J. Tillay, S. Chaney, M. Rosenkranz, and M. Lubasch, Noisy intermediate-scale quantum simulation of the one-dimensional wave equation, Phys. Rev. Res. 6, 043169 (2024).
  86. J. Hu, S. Jin, N. Liu, and L. Zhang, Quantum circuits for partial differential equations via Schrödingerisation, Quantum 8, 1563 (2024).
  87. S. S. Bharadwaj and K. R. Sreenivasan, Compact quantum algorithms for time-dependent differential equations, Phys. Rev. Res. 7, 023262 (2025).
  88. N. Guseynov, X. Huang, and N. Liu, Explicit gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations, Phys. Rev. Res. 7, 033100 (2025).
  89. S. Jin, N. Liu, and Y. Yu, Quantum circuits for the heat equation with physical boundary conditions via Schrödingerisation, arXiv:2407.15895.
  90. T. Kharazi, A. M. Alkadri, J.-P. Liu, K. K. Mandadapu, and K. B. Whaley, Explicit block encodings of boundary value problems for many-body elliptic operators, Quantum 9, 1764 (2025).
  91. K. Lively, V. Pagni, and G. Camacho, A quantum-inspired algorithm for wave simulation using tensor networks, arXiv:2504.11181.
  92. P. Pfeffer, P. Brearley, S. Laizet, and J. Schumacher, Spectral quantum algorithm for passive scalar transport in shear flows, Sci. Rep. 15, 41172 (2025).
  93. A. Suau, G. Staffelbach, and H. Calandra, Practical quantum computing: Solving the wave equation using a quantum approach, ACM TQC 2, 1 (2021).
  94. A. M. Childs, R. Kothari, and R. D. Somma, Quantum algorithm for systems of linear equations with exponentially improved dependence on precision, SIAM J. Comput. 46, 1920 (2017).
  95. A. Barenco, A. Ekert, K.-A. Suominen, and P. Törmä, Approximate quantum Fourier transform and decoherence, Phys. Rev. A 54, 139 (1996).
  96. J. A. Hogan and J. D. Lakey, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications (Birkhäuser, Boston, MA, 2012).
  97. G. H. Low, T. J. Yoder, and I. L. Chuang, Methodology of resonant equiangular composite quantum gates, Phys. Rev. X 6, 041067 (2016).
  98. G. H. Low and I. L. Chuang, Optimal Hamiltonian simulation by quantum signal processing, Phys. Rev. Lett. 118, 010501 (2017).
  99. G. H. Low and I. L. Chuang, Hamiltonian simulation by qubitization, Quantum 3, 163 (2019).
  100. A. Pérez-Salinas, D. López-Núñez, A. García-Sáez, P. Forn-Díaz, and J. I. Latorre, One qubit as a universal approximant, Phys. Rev. A 104, 012405 (2021).
  101. T. de Lima Silva, L. Borges, and L. Aolita, Fourier-based quantum signal processing, arXiv:2206.02826.
  102. J. M. Martyn, Y. Liu, Z. E. Chin, and I. L. Chuang, Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation, J. Chem. Phys. 158, 024106 (2023).
  103. T. L. Silva, M. M. Taddei, S. Carrazza, and L. Aolita, Fragmented imaginary-time evolution for early-stage quantum signal processors, Sci. Rep. 13, 18258 (2023).
  104. D. Motlagh and N. Wiebe, Generalized quantum signal processing, PRX Quantum 5, 020368 (2024).
  105. Y. Dong, K. B. Whaley, and L. Lin, A quantum Hamiltonian simulation benchmark, npj Quantum Inf. 8, 131 (2022).
  106. Y. Kikuchi, C. Mc Keever, L. Coopmans, M. Lubasch, and M. Benedetti, Realization of quantum signal processing on a noisy quantum computer, npj Quantum Inf. 9, 93 (2023).
  107. K. DeBry, J. Sinanan-Singh, C. D. Bruzewicz, D. Reens, M. E. Kim, M. P. Roychowdhury, R. McConnell, I. L. Chuang, and J. Chiaverini, Experimental quantum channel discrimination using metastable states of a trapped ion, Phys. Rev. Lett. 131, 170602 (2023).
  108. E. Karacan, C. Mc Keever, M. Foss-Feig, D. Hayes, and M. Lubasch, Filter-enhanced adiabatic quantum computing on a digital quantum processor, Phys. Rev. Res. 7, 033153 (2025).
  109. A. M. Childs and N. Wiebe, Hamiltonian simulation using linear combinations of unitary operations, Quant. Inf. Comput. 12, 901 (2012).
  110. Therefore, strictly speaking, we work with a special case of QSVT referred to as quantum eigenvalue transformation [72].
  111. J. Haah, Product decomposition of periodic functions in quantum signal processing, Quantum 3, 190 (2019).
  112. R. Chao, D. Ding, A. Gilyen, C. Huang, and M. Szegedy, Finding angles for quantum signal processing with machine precision, arXiv:2003.02831.
  113. Y. Dong, X. Meng, K. B. Whaley, and L. Lin, Efficient phase-factor evaluation in quantum signal processing, Phys. Rev. A 103, 042419 (2021).
  114. N. Hatano and M. Suzuki, Finding exponential product formulas of higher orders, in Quantum Annealing and Other Optimization Methods, edited by A. Das and B. K. Chakrabarti (Springer, Berlin, Heidelberg, 2005), pp. 37–68.
  115. A. N. Chowdhury and R. D. Somma, Quantum algorithms for Gibbs sampling and hitting-time estimation, Quantum Inf. Comput. 17, 41 (2017).
  116. Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning, Quantum 4, 276 (2020).
  117. R. Babbush, D. W. Berry, R. Kothari, R. D. Somma, and N. Wiebe, Exponential quantum speedup in simulating coupled classical oscillators, Phys. Rev. X 13, 041041 (2023).
  118. M. E. S. Morales, L. Pira, P. Schleich, K. Koor, P. C. S. Costa, D. An, A. Aspuru-Guzik, L. Lin, P. Rebentrost, and D. W. Berry, Quantum linear system solvers: A survey of algorithms and applications, arXiv:2411.02522.
  119. L. Clinton, J. Bausch, and T. Cubitt, Hamiltonian simulation algorithms for near-term quantum hardware, Nat. Commun. 12, 4989 (2021).
  120. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52, 3457 (1995).
  121. B. Zindorf and S. Bose, Efficient implementation of multi-controlled quantum gates, arXiv:2404.02279.
  122. E. C. R. Rosa, E. I. Duzzioni, and R. de Santiago, Optimizing gate decomposition for high-level quantum programming, Quantum 9, 1659 (2025).
  123. A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of Trotter error with commutator scaling, Phys. Rev. X 11, 011020 (2021).

Outline

Information

Phys. Rev. Research 7, 043326– Published 22 December, 2025
  • Received 6 June 2025
  • Accepted 18 November 2025
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