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. arXiv: 2505.20265 [download pdf]
[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 [download pdf] 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. arXiv: 2002.08070 [download pdf]
[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 [download pdf]
[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 [download pdf]
[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. arXiv: 1611.08571 [download pdf]
[13]
gilyén, a. Testing quantum state engineering protocols via LIQUi|⟩ simulations. Tech. rep., 2nd 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