Universal computation with quantum fields
Tóm tắt
We explore a way of universal quantum computation with particles which cannot occupy the same position simultaneously and are symmetric under exchange of particle labels. Therefore the associated creation and annihilation operators are neither bosonic nor fermionic. In this work we first show universality of our method and numerically address several examples. We demonstrate dynamics of a Bloch electron system from a viewpoint of adiabatic quantum computation. In addition we provide a novel Majorana fermion system and analyze phase transitions with spin-coherent states and the time average of the out-of-time-order correlator (OTOC). We report that a first-order phase transition is avoided when it evolves in a non-stoquastic manner and the time average of the OTOC diagnoses the phase transitions successfully.
Tài liệu tham khảo
Turing, A.M.: Computing machinery and intelligence. In: Epstein, R., Roberts, G., Beber, G. (eds.) Parsing the Turing Test, pp. 23–65. Springer (2009)
Feynman, R.P.: Quantum mechanical computers. Found. Phys. 16, 507 (1986)
Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci. 400, 97 (1985). https://doi.org/10.1098/rspa.1985.0070
Church, A.: An unsolvable problem of elementary number theory. Am. J. Math. 58, 345 (1936)
Turing, A.M.: On computable numbers, with an application to the entscheidungsproblem. Proc. Lond. Math. Soc. s2–42, 230 (1937)
Abrams, D.S., Lloyd, S.: Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586 (1997)
Berry, D.W., Ahokas, G., Cleve, R., Sanders, B.C.: Efficient quantum algorithms for simulating sparse hamiltonians. Commun. Math. Phys. 270, 359 (2007)
Zalka, C.: Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond. Ser. A 454, 313 (1998). arXiv:quant-ph/9603026
Jordan, S.P., Lee, K.S.M., Preskill, J.: Quantum algorithms for quantum field theories. Science 336, 1130 (2012). arXiv:1111.3633
Jordan, S.P., Krovi, H., Lee, K.S.M., Preskill, J.: BQP-completeness of scattering in scalar quantum field theory. Quantum 2, 44 (2018)
Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum Computation by Adiabatic Evolution, arXiv e-prints (2000) quant [arXiv:quant-ph/0001106]
Albash, T., Lidar, D.A.: Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018)
Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse ising model. Phys. Rev. E 58, 5355 (1998)
Johnson, M.W., Amin, M.H.S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., et al.: Quantum annealing with manufactured spins. Nature 473, 194 EP (2011)
Rønnow, T.F., Wang, Z., Job, J., Boixo, S., Isakov, S.V., Wecker, D., et al.: Defining and detecting quantum speedup. Science 345, 420 (2014)
Lucas, A.: Ising formulations of many NP problems. Front. Phys. 2, 5 (2014)
Ikeda, K., Nakamura, Y., Humble, T.S.: Application of quantum annealing to nurse scheduling problem. Sci. Rep. 9, 12837 (2019)
Feynman, R.P.: Quantum mechanical computers. Opt. News 11, 11 (1985)
Biamonte, J.D., Love, P.J.: Realizable hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008)
Jozsa, R., Miyake, A.: Matchgates and classical simulation of quantum circuits. Proc. R. Soc. Lond. Ser. A 464, 3089 (2008). arXiv:0804.4050
Jordan, P., Wigner, E.: Über das paulische äquivalenzverbot. Zeitschrift für Physik 47, 631 (1928)
Ikeda, K.: Hofstadter’s butterfly and langlands duality. J. Math. Phys. 59, 061704 (2018). https://doi.org/10.1063/1.4998635
Ikeda, K.: Quantum hall effect and langlands program. Ann. Phys. 397, 136 (2018). arXiv:1708.00419
Ikeda, K.: Topological Aspects of Matters and Langlands Program. arXiv:1812.11879
Hofstadter, D.R.: Energy levels and wave functions of bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239 (1976)
Hatsuda, Y., Katsura, H., Tachikawa, Y.: Hofstadter’s butterfly in quantum geometry. New J. Phys. 18, 103023 (2016). arXiv:1606.01894
Seki, Y., Nishimori, H.: Quantum annealing with antiferromagnetic fluctuations. Phys. Rev. E 85, 051112 (2012). arXiv:1203.2418
Bravyi, S., DiVincenzo, D.P., Oliveira, R.I., Terhal, B.M.: The Complexity of Stoquastic Local Hamiltonian Problems, arXiv e-prints (2006) quant [arXiv:quant-ph/0606140]
Damski, B., Rams, M.M.: Exact results for fidelity susceptibility of the quantum ising model: the interplay between parity, system size, and magnetic field. J. Phys. A Math. Theor. 47, 025303 (2013)
Dusuel, S., Vidal, J.: Continuous unitary transformations and finite-size scaling exponents in the lipkin-meshkov-glick model. Phys. Rev. B 71, 224420 (2005)
Susa, Y., Jadebeck, J.F., Nishimori, H.: Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic hamiltonian. Phys. Rev. A 95, 042321 (2017)
Larkin, A., Ovchinnikov, Y.N.: Quasiclassical method in the theory of superconductivity. Sov Phys JETP 28, 1200 (1969)
Maldacena, J., Shenker, S.H., Stanford, D.: A bound on chaos. JHEP 08, 106 (2016). arXiv:1503.01409
Kitaev, A.: Hidden correlations in the hawking radiation and thermal noise, talk at KITP, University of California, Santa Barbara, CA, U.S.A. http://online.kitp.ucsb.edu/online/joint98/kitaev/
Matsuki, Y., Ikeda, K.: Comments on the fractal energy spectrum of honeycomb lattice with defects. J. Phys. Commun. 3, 055003 (2019)
Sun, Z.-H., Cai, J.-Q., Tang, Q.-C., Hu, Y., Fan, H.: Out-of-time-order correlators and quantum phase transitions in the Rabi and Dicke model, arXiv e-prints (2018) [arXiv:1811.11191]
Bohigas, O., Giannoni, M.J., Schmit, C.: Characterization of chaotic quantum spectra and universality of level fluctuation laws. Phys. Rev. Lett. 52, 1 (1984)
Berry, M.V., Tabor, M., Ziman, J.M.: Level clustering in the regular spectrum. Proc. R. Soc. Lond. A Math. Phys. Sci. 356, 375 (1977). https://doi.org/10.1098/rspa.1977.0140