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  • Open Access

Unified architecture for quantum lookup tables

Shuchen Zhu*

Aarthi Sundaram and Guang Hao Low

  • Microsoft Quantum, Redmond, Washington 98052, USA

  • *Contact author: sz424@georgetown.edu
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Phys. Rev. Research 7, 043230 – Published 1 December, 2025

DOI: https://doi.org/10.1103/d896-mktn

Abstract

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the boolean circuit for a classical lookup table. We present a general parametrized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal trade-offs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results, with the appropriate parameters, polylogarithmic error scaling. We also identify regimes, such as simultaneous sublinear scaling, in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

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References (46)

  1. D. W. Berry and A. M. Childs, Black-box hamiltonian simulation and unitary implementation, Quantum Inf. Comput. 12, 29 (2012).
  2. D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, Simulating Hamiltonian dynamics with a truncated taylor series, Phys. Rev. Lett. 114, 090502 (2015).
  3. D. W. Berry, A. M. Childs, and R. Kothari, Hamiltonian simulation with nearly optimal dependence on all parameters, in 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (ACM's, New York, 2015), pp. 792–809.
  4. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear T complexity, Phys. Rev. X 8, 041015 (2018).
  5. G. H. Low and I. L. Chuang, Hamiltonian simulation by qubitization, Quantum 3, 163 (2019).
  6. B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quantum materials science, Chem. Rev. 120, 12685 (2020).
  7. S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum algorithms for supervised and unsupervised machine learning, arXiv:1307.0411.
  8. P. Wittek, Quantum Machine Learning: What Quantum Computing Means to Data Mining (Academic Press, Cambridge, 2014).
  9. J. Adcock, E. Allen, M. Day, S. Frick, J. Hinchliff, M. Johnson, S. Morley-Short, S. Pallister, A. Price, and S. Stanisic, Advances in quantum machine learning, arXiv:1512.02900.
  10. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature (London) 549, 195 (2017).
  11. C. Ciliberto, M. Herbster, A. D. Ialongo, M. Pontil, A. Rocchetto, S. Severini, and L. Wossnig, Quantum machine learning: A classical perspective, Proc. R. Soc. A. 474, 20170551 (2018).
  12. H.-Y. Huang, R. Kueng, G. Torlai, V. V. Albert, and J. Preskill, Provably efficient machine learning for quantum many-body problems, Science 377, eabk3333 (2022).
  13. R. Babbush, J. R. McClean, M. Newman, C. Gidney, S. Boixo, and H. Neven, Focus beyond quadratic speedups for error-corrected quantum advantage, PRX Quantum 2, 010103 (2021).
  14. T. Hoefler, T. Häner, and M. Troyer, Disentangling hype from practicality: On realistically achieving quantum advantage, Commun. ACM 66, 82 (2023).
  15. D. Liu, S. Zhu, G. H. Low, L. Lin, and C. Yang, Block encoding with low gate count for second-quantized hamiltonians, arXiv:2510.08644.
  16. V. von Burg, G. H. Low, T. Häner, D. S. Steiger, M. Reiher, M. Roetteler, and M. Troyer, Quantum computing enhanced computational catalysis, Phys. Rev. Res. 3, 033055 (2021).
  17. V. Giovannetti, S. Lloyd, and L. Maccone, Architectures for a quantum random access memory, Phys. Rev. A 78, 052310 (2008).
  18. D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum 3, 128 (2019).
  19. M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sundaram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage, arXiv:2211.07629.
  20. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum random access memory, Phys. Rev. Lett. 100, 160501 (2008).
  21. S. Arunachalam, V. Gheorghiu, T. Jochym-O’Connor, M. Mosca, and P. V. Srinivasan, On the robustness of bucket brigade quantum ram, New J. Phys. 17, 123010 (2015).
  22. D. W. Berry, C. Gidney, M. Motta, J. R. McClean, and R. Babbush, Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization, Quantum 3, 208 (2019).
  23. O. D. Matteo, V. Gheorghiu, and M. Mosca, Fault-tolerant resource estimation of quantum random-access memories, IEEE Trans. Quantum Eng. 1, 1 (2020).
  24. G. H. Low, V. Kliuchnikov, and L. Schaeffer, Trading T gates for dirty qubits in state preparation and unitary synthesis, Quantum 8, 1375 (2024).
  25. C. T. Hann, G. Lee, S. Girvin, and L. Jiang, Resilience of quantum random access memory to generic noise, PRX Quantum 2, 020311 (2021).
  26. S. Xu, C. T. Hann, B. Foxman, S. M. Girvin, and Y. Ding, Systems architecture for quantum random access memory, in Proceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture (ACM, 2023), pp. 526–538.
  27. C. Gidney and A. G. Fowler, Flexible layout of surface code computations using AutoCCZ states, arXiv:1905.08916.
  28. J. Allcock, J. Bao, J. F. Doriguello, A. Luongo, and M. Santha, Constant-depth circuits for uniformly controlled gates and boolean functions with application to quantum memory circuits, Quantum 8, 1530 (2024).
  29. S. Jaques and A. G. Rattew, QRAM: A survey and critique, arXiv:2305.10310.
  30. A. M. Dalzell, S. McArdle, M. Berta et al., Quantum Algorithms: A Survey of Applications and End-to-End Complexities (Cambridge University Press, Cambridge, 2025).
  31. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  32. J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. Allman, C. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer et al., Demonstration of the trapped-ion quantum ccd computer architecture, Nature (London) 592, 209 (2021).
  33. E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature (London) 549, 172 (2017).
  34. S. Bravyi and D. Gosset, Improved classical simulation of quantum circuits dominated by clifford gates, Phys. Rev. Lett. 116, 250501 (2016).
  35. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
  36. B. B. Mandelbrot and B. B. Mandelbrot, The Fractal Geometry of Nature (WH freeman, New York, 1982), Vol. 1.
  37. M. Beverland, V. Kliuchnikov, and E. Schoute, Surface code compilation via edge-disjoint paths, PRX Quantum 3, 020342 (2022).
  38. J. van de Wetering, ZX-calculus for the working quantum computer scientist, arXiv:2012.13966.
  39. M. M. Wilde, H. Krovi, and T. A. Brun, Convolutional entanglement distillation, in 2010 IEEE International Symposium on Information Theory (IEEE, New York, 2010), pp. 2657–2661.
  40. Z.-Y. Chen, C. Xue, Y.-J. Wang, T.-P. Sun, H.-Y. Liu, X.-N. Zhuang, M.-H. Dou, T.-R. Zou, Y. Fang, Y.-C. Wu et al., Efficient and error-resilient data access protocols for a limited-sized quantum random access memory, arXiv:2303.05207.
  41. C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, Realization of real-time fault-tolerant quantum error correction, Phys. Rev. X 11, 041058 (2021).
  42. R. Acharya, I. Aleiner, R. M. Allen, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, R. Babbush et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  43. A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel et al., Entangling logical qubits with lattice surgery, Nature (London) 589, 220 (2021).
  44. L. Postler, S. Heußen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. D. Marciniak, R. Stricker, M. Ringbauer, R. Blatt et al., Demonstration of fault-tolerant universal quantum gate operations, Nature (London) 605, 675 (2022).
  45. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  46. D. Litinski and N. Nickerson, Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections, arXiv:2211.15465.

Outline

Information

Phys. Rev. Research 7, 043230– Published 1 December, 2025
  • Received 26 August 2024
  • Revised 27 February 2025
  • Accepted 6 November 2025
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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.

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