A generalized circuit for the Hamiltonian dynamics through the truncated series

Kitaev, A.: Quantum measurements and the Abelian stabilizer problem. Electron. Colloq. Comput. Complex. (ECCC) 3, 5 (1996)

Somma, R., Ortiz, G., Gubernatis, J.E., Knill, E., Laflamme, R.: Simulating physical phenomena by quantum networks. Phys. Rev. A 65, 042323 (2002)

Brown, K.L., Munro, W.J., Kendon, V.M.: Using quantum computers for quantum simulation. Entropy 12, 2268–2307 (2010)

Kassal, I., Whitfield, J.D., Perdomo-Ortiz, A., Yung, M.-H., Aspuru-Guzik, A.: Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185–207 (2011)

Wecker, D., Bauer, B., Clark, B.K., Hastings, M.B., Troyer, M.: Gate-count estimates for performing quantum chemistry on small quantum computers. Phys. Rev. A 90, 022305 (2014)

Montanaro, A.: Quantum algorithms: an overview. NPJ Quant. Inf. 2, 15023 (2016)

Nielsen, M.A., Chuang, I.: Quantum computation and quantum information (2002)

Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303–332 (1999)

Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009)

Trotter, H.F.: On the product of semi-groups of operators. Proc. Am. Math. Soc. 10, 545–551 (1959)

Suzuki, M.: Generalized trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Commun. Math. Phys. 51, 183–190 (1976)

Poulin, D., Hastings, M.B., Wecker, D., Wiebe, N., Doberty, A.C., Troyer, M.: The trotter step size required for accurate quantum simulation of quantum chemistry. Quant. Inf. Comput. 15, 361–384 (2015)

Berry, D.W., Childs, A.M., Cleve, R., Kothari, R., Somma, R.D.: Simulating hamiltonian dynamics with a truncated taylor series. Phys. Rev. Lett. 114, 090502 (2015)

Daskin, A., Kais, S.: An Ancilla-based quantum simulation framework for non-unitary matrices. Quant. Inf. Process. 16, 33 (2017)

Low, G.H., Chuang, I.L.: Optimal hamiltonian simulation by quantum signal processing. Phys. Rev. Lett. 118, 010501 (2017)

Poulin, D., Kitaev, A., Steiger, D.S., Hastings, M.B., Troyer, M.: Fast quantum algorithm for spectral properties. arXiv preprint arXiv:1711.11025 (2017)

Daskin, A., Kais, S.: Direct application of the phase estimation algorithm to find the eigenvalues of the hamiltonians. arXiv preprint arXiv:1703.03597 (2017)

Babbush, R., Berry, D.W., Sanders, Y.R., Kivlichan, I.D., Scherer, A., Wei, A.Y., Love, P.J., Aspuru-Guzik, A.: Exponentially more precise quantum simulation of fermions in the configuration interaction representation. Quant. Sci. Technol. 3, 015006 (2018)

Daskin, A., Grama, A., Kollias, G., Kais, S.: Universal programmable quantum circuit schemes to emulate an operator. J. Chem. Phys. 137, 234112 (2012)

Babbush, R., Berry, D., Kieferová, M., Low, H.G., Sanders, Y., Scherer, A., Wiebe, N.: Improved techniques for preparing eigenstates of fermionic hamiltonians. arXiv preprint arXiv:1711.10460 (2017)

Low, H.G., Chuang, I.L.: Hamiltonian simulation by uniform spectral amplification. arXiv preprint arXiv:1707.05391 (2017)

Low, H.G., Chuang, I.L.: Hamiltonian simulation by qubitization. arXiv preprint arXiv:1610.06546 (2016)

Pei, W.: Additive Combinations of Special Operators, pp. 337–361. Banach Center Publications, Warszawa (1994)

Möttönen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93, 130502 (2004)

Bullock, S.S., OLeary, D.P., Brennen, G.K.: Asymptotically optimal quantum circuits for d-level systems. Phys. Rev. Lett. 94, 230502 (2005)

Urías, J.: Householder factorizations of unitary matrices. J. Math. Phys. 51, 072204 (2010)

Novo, L., Berry, D.W.: Improved Hamiltonian simulation via a truncated Taylor series and corrections. arXiv preprint arXiv:1611.10033 (2016)

Babbush, R., Berry, D.W., Kivlichan, I.D., Wei, A.Y., Love, P.J., Aspuru-Guzik, A.: Exponentially more precise quantum simulation of fermions in second quantization. N. J. Phys. 18, 033032 (2016)

Berry, D.W., Ahokas, G., Cleve, R., Sanders, B.C.: Efficient quantum algorithms for simulating sparse Hamiltonians. Commun. Math. Phys. 270, 359–371 (2007)

Childs, A.M., Kothari, R.: Simulating sparse Hamiltonians with star decompositions. In: Conference on Quantum Computation, Communication, and Cryptography pp. 94–103, Springer, Berlin (2010)

Lanyon, B.P., Whitfield, J.D., Gillett, G.G., Goggin, M.E., Almeida, M.P., Kassal, I., Biamonte, J.D., Mohseni, M., Powell, B.J., Barbieri, M., et al.: Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010)

Whitfield, J.D., Biamonte, J., Aspuru-Guzik, A.: Simulation of electronic structure hamiltonians using quantum computers. Mol. Phys. 109, 735–750 (2011)

Seeley, J.T., Richard, M.J., Love, P.J.: The Bravyi–Kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 137, 224109 (2012)

Jordan, P., Wigner, E.: Über das paulische äquivalenzverbot. Zeitschrift für Physik 47, 631–651 (1928)

Bravyi, S.B., Kitaev, A.Y.: Fermionic quantum computation. Ann. Phys. 298, 210–226 (2002)

Fassbender, H., Kressner, D.: Structured eigenvalue problems. GAMM Mitt. 29, 297–318 (2006)

Guhr, T., Müller-Groeling, A., Weidenmüller, H.A.: Random-matrix theories in quantum physics: common concepts. Phys. Rep. 299, 189–425 (1998)

Escher, B.M., de Matos Filho, R.L., Davidovich, L.: General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys. 7, 406–411 (2011)

Romero, J., Olson, J.P., Aspuru-Guzik, A.: Quantum autoencoders for efficient compression of quantum data. Quant. Sci. Technol. 2, 045001 (2017)

Widrow, B., McCool, J.M., Larimore, M.G., Richard Johnson, C.: Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proc. IEEE 64, 1151–1162 (1976)