Books

[38]

Dalzell, A. M., McArdle, S., Berta, M., Bienias, P., Chen, C.-F., Gilyén, A., Hann, C. T., Kastoryano, M. J., Khabiboulline, E. T., Kubica, A., Salton, G., Wang, S., and Brandão, F. G. S. L. Quantum algorithms: A survey of applications and end-to-end complexities. Cambridge University Press, 2025. arXiv:2310.03011

Publications

[37]

Dalzell, A. M., Gilyén, A., Hann, C. T., McArdle, S., Salton, G., Nguyen, Q. T., Kubica, A., and Brandão, F. G. A distillation-teleportation protocol for fault-tolerant QRAM. In Proceedings of the 66th IEEE Symposium on Foundations of Computer Science (FOCS), 2025, pp. 38–74. [download pdf] arXiv:2505.20265

[36]

Chen, C.-F., Kastoryano, M. J., Brandão, F. G., and Gilyén, A. Efficient quantum thermal simulation. Nature 646(8085):561–566, 2025

[35]

Kastoryano, M. J., Kristensen, L. B., Chen, C.-F., and Gilyén, A. A little bit of self-correction. Quantum 9:1820, 2025. arXiv:2408.14970

[34]

Chen, Y., Gilyén, A., and de Wolf, R. A quantum speed-up for approximating the top eigenvectors of a matrix. In Proceedings of the 36th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2025, pp. 994–1036. arXiv:2405.14765

[33]

Ben-David, S., Childs, A. M., Gilyén, A., Kretschmer, W., Podder, S., and Wang, D. Symmetries, graph properties, and quantum speedups. SIAM Journal on Computing 53(6):FOCS20–368–FOCS20–415, 2024. Earlier version in FOCS’20. arXiv:2006.12760

[32]

Ding, J., Gheorghiu, V., Gilyén, A., Hallgren, S., and Li, J. Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems. Quantum 7:1069, 2023. arXiv:2111.00405

[31]

van Apeldoorn, J., Cornelissen, A., Gilyén, A., and Nannicini, G. Quantum tomography using state-preparation unitaries. In Proceedings of the 34th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2023, pp. 1265–1318. arXiv:2207.08800

[30]

Gilyén, A., Song, Z., and Tang, E. An improved quantum-inspired algorithm for linear regression. Quantum 6:754, 2022. arXiv:2009.07268

[29]

Gilyén, A., Lloyd, S., Marvian, I., Quek, Y., and Wilde, M. M. Quantum algorithm for Petz recovery channels and pretty good measurements. Physical Review Letters 128(22):220502, 2022. arXiv:2006.16924

[28]

Gilyén, A., Hastings, M. B., and Vazirani, U. (Sub)Exponential advantage of adiabatic quantum computation with no sign problem. In Proceedings of the 53rd ACM Symposium on the Theory of Computing (STOC), 2021, pp. 1357–1369. Earlier version available on arXiv:2011.09495.

[27]

Apers, S., Gilyén, A., and Jeffery, S. A unified framework of quantum walk search. In Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS), 2021, pp. 6:1–6:13. arXiv:1912.04233

[26]

Chia, N.-H., Gilyén, A., Lin, H.-H., Lloyd, S., Tang, E., and Wang, C. Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension. In Proceedings of the 31st International Symposium on Algorithms and Computation (ISAAC), 2020, pp. 47:1–47:17. Earlier version available on arXiv:1811.04909

[25]

Kollár, B., Gilyén, A., Tkáčová, I., Kiss, T., Jex, I., and Štefaňák, M. Complete classification of trapping coins for quantum walks on the two-dimensional square lattice. Physical Review A 102(1):012207, 2020. [download pdf] arXiv:2002.08070

[24]

Chia, N.-H., Gilyén, A. P., Li, T., Lin, H.-H., Tang, E., and Wang, C. Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning. Journal of the ACM 69(5), 2022. Earlier version in STOC’20, arXiv:1910.06151

[23]

Bannink, T., Buhrman, H., Gilyén, A., and Szegedy, M. The interaction light cone of the Discrete Bak-Sneppen, Contact and other local processes. Journal of Statistical Physics 176(6):1500–1525, 2019. arXiv:1903.12607

[22]

Ambainis, A., Gilyén, A., Jeffery, S., and Kokainis, M. Quadratic speedup for finding marked vertices by quantum walks. In Proceedings of the 52nd ACM Symposium on the Theory of Computing (STOC), 2020, p. 412–424. arXiv:1903.07493

[21]

Gilyén, A., and Li, T. Distributional property testing in a quantum world. In Proceedings of the 11th Innovations in Theoretical Computer Science Conference (ITCS), 2020, pp. 25:1–25:19. arXiv:1902.00814

[20]

van Apeldoorn, J., Gilyén, A., Gribling, S., and de Wolf, R. Convex optimization using quantum oracles. Quantum 4:220, 2020. arXiv:1809.00643

[19]

Gilyén, A., Su, Y., Low, G. H., and Wiebe, N. Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics. In Proceedings of the 51st ACM Symposium on the Theory of Computing (STOC), 2019, pp. 193–204. Full version in arXiv: 1806.01838

[18]

Chakraborty, S., Gilyén, A., and Jeffery, S. The power of block-encoded matrix powers: Improved regression techniques via faster Hamiltonian simulation. In Proceedings of the 46th International Colloquium on Automata, Languages, and Programming (ICALP), 2019, pp. 33:1–33:14. arXiv:1804.01973

[17]

van Apeldoorn, J., and Gilyén, A. Improvements in quantum SDP-solving with applications. In Proceedings of the 46th International Colloquium on Automata, Languages, and Programming (ICALP), 2019, pp. 99:1–99:15. arXiv:1804.05058

[16]

Gilyén, A., Arunachalam, S., and Wiebe, N. Optimizing quantum optimization algorithms via faster quantum gradient computation. In Proceedings of the 30th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2019, pp. 1425–1444. arXiv:1711.00465

[15]

van Apeldoorn, J., Gilyén, A., Gribling, S., and de Wolf, R. Quantum SDP-solvers: Better upper and lower bounds. Quantum 4:230, 2020. Earlier version in FOCS’17. arXiv: 1705.01843

[14]

Gilyén, A., and Sattath, O. On preparing ground states of gapped Hamiltonians: An efficient quantum Lovász local lemma. In Proceedings of the 58th IEEE Symposium on Foundations of Computer Science (FOCS), 2017, pp. 439–450. [download pdf] arXiv:1611.08571

[13]

Gilyén, A. Testing quantum state engineering protocols via LIQUi|⟩ simulations. Tech. rep., 2^nd prize winner entry at the Microsoft Quantum Challange, 2016

[12]

Gilyén, A., Kiss, T., and Jex, I. Exponential sensitivity and its cost in quantum physics. Scientific Reports 6:20076, 2016. arXiv:1508.03191

To be peer-reviewed arXiv preprints:

[11]

Vasconcelos, F., and Gilyén, A. Methods for reducing ancilla-overhead in block encodings. arXiv:2507.07900, 2025

[10]

Zimborás, Z., Koczor, B., Holmes, Z., Borrelli, E.-M., Gilyén, A., Huang, H.-Y., Cai, Z., Acín, A., Aolita, L., Banchi, L., Brandão, F. G. S. L., Cavalcanti, D., Cubitt, T., Filippov, S. N., García-Pérez, G., Goold, J., Kálmán, O., Kyoseva, E., Rossi, M. A. C., Sokolov, B., Tavernelli, I., and Maniscalco, S. Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don’t. arXiv: 2501.05694, 2025

[9]

Gilyén, A., Chen, C.-F., Doriguello, J. F., and Kastoryano, M. J. Quantum generalizations of Glauber and Metropolis dynamics. arXiv:2405.20322, 2024

[8]

Németh, B., Kövér, B., Kulcsár, B., Miklósi, R. B., and Gilyén, A. On variants of multivariate quantum signal processing and their characterizations. arXiv:2312.09072, 2023

[7]

Chen, C.-F., Kastoryano, M. J., and Gilyén, A. An efficient and exact noncommutative quantum Gibbs sampler. arXiv:2311.09207, 2023

[6]

Chen, C.-F., Kastoryano, M. J., Brandão, F. G. S. L., and Gilyén, A. Quantum thermal state preparation. arXiv:2303.18224, 2023

[5]

McArdle, S., Gilyén, A., and Berta, M. Quantum state preparation without coherent arithmetic. arXiv:2210.14892, 2022

[4]

McArdle, S., Gilyén, A., and Berta, M. A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits. arXiv:2209.12887, 2022

[3]

Cornelissen, A., Bausch, J., and Gilyén, A. Scalable benchmarks for gate-based quantum computers. arXiv:2104.10698, 2021

[2]

Chao, R., Ding, D., Gilyén, A., Huang, C., and Szegedy, M. Finding angles for quantum signal processing with machine precision. arXiv:2003.02831, 2020

[1]

van Apeldoorn, J., and Gilyén, A. Quantum algorithms for zero-sum games. arXiv: 1904.03180, 2019