QuantumAlgorithms.aiA citable library

Library

References

Every citation on the site points at one of these records. The record is a pointer to the paper, plus a note on what this library uses it for.

Quantum algorithms is the guide. The complexity table is the row-by-row comparison.

  1. Suzuki, M. (1991). General theory of fractal path integrals with applications to many-body theories and statistical physics. Journal of Mathematical Physics, 32(2), 400–407.
  2. Deutsch, D., & Jozsa, R. (1992). Rapid solution of problems by quantum computation. Proceedings of the Royal Society A, 439, 553–558.
  3. Shor, P. W. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science (pp. 124–134). IEEE.
  4. Goemans, M. X., & Williamson, D. P. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM, 42(6), 1115–1145.
  5. Kitaev, A. Yu. (1995). Quantum measurements and the Abelian stabilizer problem. arXiv:quant-ph/9511026.
  6. Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52(4), R2493–R2496.
  7. Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing (pp. 212–219). ACM.
  8. Lloyd, S. (1996). Universal quantum simulators. Science, 273(5278), 1073–1078.
  9. Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997). Strengths and weaknesses of quantum computing. SIAM Journal on Computing, 26(5), 1510–1523.
  10. Bernstein, E., & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on Computing, 26(5), 1411–1473.
  11. Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 79(2), 325–328.
  12. Shor, P. W. (1997). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5), 1484–1509.
  13. Simon, D. R. (1997). On the power of quantum computation. SIAM Journal on Computing, 26(5), 1474–1483.
  14. Boyer, M., Brassard, G., Høyer, P., & Tapp, A. (1998). Tight bounds on quantum searching. Fortschritte der Physik, 46(4–5), 493–505.
  15. Brassard, G., Høyer, P., & Tapp, A. (1998). Quantum counting. In Automata, Languages and Programming (ICALP 1998), Lecture Notes in Computer Science (Vol. 1443, pp. 820–831).
  16. Cleve, R., Ekert, A., Macchiavello, C., & Mosca, M. (1998). Quantum algorithms revisited. Proceedings of the Royal Society A, 454, 339–354.
  17. Kadowaki, T., & Nishimori, H. (1998). Quantum annealing in the transverse Ising model. Physical Review E, 58, 5355.
  18. Abrams, D. S., & Lloyd, S. (1999). A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Physical Review Letters, 83, 5162–5165.
  19. Brassard, G., Høyer, P., Mosca, M., & Tapp, A. (2002). Quantum amplitude amplification and estimation. In Quantum Computation and Information, Contemporary Mathematics (Vol. 305, pp. 53–74). American Mathematical Society.
  20. Proos, J., & Zalka, C. (2003). Shor's discrete logarithm quantum algorithm for elliptic curves. Quantum Information and Computation, 3(4), 317–344.
  21. Shenvi, N., Kempe, J., & Whaley, K. B. (2003). Quantum random-walk search algorithm. Physical Review A, 67, 052307.
  22. Aspuru-Guzik, A., Dutoi, A. D., Love, P. J., & Head-Gordon, M. (2005). Simulated quantum computation of molecular energies. Science, 309(5741), 1704–1707.
  23. Harrow, A. W., Hassidim, A., & Lloyd, S. (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15), 150502.
  24. Nielsen, M. A., & Chuang, I. L. (2010). Quantum computation and quantum information (10th anniversary ed.). Cambridge University Press.
  25. Belovs, A. (2013). Quantum algorithms for learning symmetric juntas via the adversary bound. arXiv:1311.6777.
  26. Farhi, E., Goldstone, J., & Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv:1411.4028.
  27. Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O'Brien, J. L. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5, 4213.
  28. Aaronson, S. (2015). Read the fine print. Nature Physics, 11(4), 291–293.
  29. Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015). Simulating Hamiltonian dynamics with a truncated Taylor series. Physical Review Letters, 114, 090502.
  30. McClean, J. R., Romero, J., Babbush, R., & Aspuru-Guzik, A. (2016). The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, 18, 023023.
  31. Childs, A. M., Kothari, R., & Somma, R. D. (2017). Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM Journal on Computing, 46(6), 1920–1950.
  32. Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M. (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549, 242–246.
  33. Low, G. H., & Chuang, I. L. (2017). Optimal Hamiltonian simulation by quantum signal processing. Physical Review Letters, 118, 010501.
  34. Gilyén, A., Lloyd, S., & Tang, E. (2018). Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension. arXiv:1811.04909.
  35. McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications, 9, 4812.
  36. Preskill, J. (2018). Quantum computing in the NISQ era and beyond. Quantum, 2, 79.
  37. Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019). 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 (pp. 193–204).
  38. Hadfield, S., Wang, Z., O'Gorman, B., Rieffel, E. G., Venturelli, D., & Biswas, R. (2019). From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms, 12(2), 34.
  39. Low, G. H., & Chuang, I. L. (2019). Hamiltonian simulation by qubitization. Quantum, 3, 163.
  40. Childs, A. M., Su, Y., Tran, M. C., Wiebe, N., & Zhu, S. (2021). Theory of Trotter error with commutator scaling. Physical Review X, 11, 011020.
  41. Gidney, C., & Ekerå, M. (2021). How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum, 5, 433.
  42. Berry, D. W., Wan, K., Baczewski, A. D., Eklund, E. C., Tikku, A., & Babbush, R. (2025). Quantum simulation of electronic structure via quantum fast multipole method. arXiv:2510.07380.
  43. Gidney, C. (2025). How to factor 2048 bit RSA integers with less than a million noisy qubits. arXiv:2505.15917.
  44. Cai, J.-Y., & Young, B. (2026). A sharp noise threshold for Shor's quantum factoring and discrete log algorithms. arXiv:2609.24316.
  45. Günther, J., & Harrow, A. W. (2026). Sublinear-depth quantum simulation of electrons with atomic orbitals. arXiv:2610.00950.
  46. Krivcenko, A., Nguyen, T., & de Wolf, R. (2026). Fast quantum algorithms for learning linear threshold functions. arXiv:2609.40331.