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Quantum information processing with superconducting circuits: realizing and characterizing quantum gates and algorithms in open quantum systems (2401.07302v1)

Published 14 Jan 2024 in quant-ph

Abstract: This thesis focuses on quantum information processing using the superconducting device, especially, on realizing quantum gates and algorithms in open quantum systems. Such a device is constructed by transmon-type superconducting qubits coupled to a superconducting resonator. For the realization of quantum gates and algorithms, a one-step approach is used. We suggest faster and more efficient schemes for realizing $X$-rotation and entangling gates for two and three qubits. During these operations, the resonator photon number is canceled owing to the strong microwave field added. They do not require the resonator to be initially prepared in the vacuum state and the scheme is insensitive to resonator decay. Furthermore, the robustness of these operations is demonstrated by including the effect of the decoherence of transmon systems and the resonator decay in a master equation, and as a result, high fidelity will be achieved in quantum simulation. In addition, using the implemented x-rotation gates as well as the phase gates, we present an alternative way for implementing Grover's algorithm for two and three qubits, which does not require a series of single gates. As well, we also demonstrate by a numerical simulation the use of quantum process tomography to fully characterize the performance of a single-shot entangling gate for two and three qubits and obtain process fidelities greater than 0.93. These gates are used to create Bell and Greenberger-Horne-Zeilinger (GHZ) entangled states.

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References (51)
  1. R. P. Feynman. “Simulating physics with computers.” Int. J. Theor. Phys., 21, 467–488 (1982).
  2. D. Deutsch. “Quantum theory, the Church-Turing principle and the universal quantum computer.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 400, 97–117 (1985).
  3. P. W. Shor. “Algorithms for quantum computation: Discrete logarithms and factoring.” In “Proceedings, 35th Annual Symposium on Foundations of Computer Science, Santa Fe,” 124. IEEE Computer Society Press (1994). Cited on page 2.
  4. S. Takeuchi. “Experimental demonstration of a three-qubit quantum computation algorithm using a single photon and linear optics.” Phys. Rev. A, 62, 032301– (2000). Cited on page 3.
  5. L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf. “Demonstration of two-qubit algorithms with a superconducting quantum processor.” Nature, 460, 240–244 (2009).
  6. L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang. “Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance.” Nature, 414, 883 (2001).
  7. B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist, and A. G. White. “Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement.” Phys. Rev. Lett., 99, 250505 (2007).
  8. C.-Y. Lu, D. E. Browne, T. Yang, and J.-W. Pan. “Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits.” Phys. Rev. Lett., 99, 250504 (2007).
  9. A. Politi, J. C. F. Matthews, and J. L. O’Brien. “Shor’s quantum factoring algorithm on a photonic chip.” Science, 325, 1221 (2009).
  10. D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo. “Experimental quantum error correction.” Phys. Rev. Lett., 81, 2152–2155 (1998).
  11. T. B. Pittman, B. C. Jacobs, and J. D. Franson. “Demonstration of quantum error correction using linear optics.” Phys. Rev. A, 71, 052332 (2005).
  12. J. Chiaverini, D. Leibfried, T. Schaetz, M. Barrett, R. Blakestad, J. Britton, W. Itano, J. Jost, E. Knill, C. Langer, R. Ozeri, and D. Wineland. “Realization of quantum error correction.” Nature, 432, 602–605 (2004).
  13. P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, and R. Blatt. “Experimental repetitive quantum error correction.” Science, 332, 1059–1061 (2011).
  14. M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf. “Realization of three-qubit quantum error correction with superconducting circuits.” Nature, 482, 382–385 (2012).
  15. M. Feng. ”Grover search with pairs of trapped ions.” Phys. Rev. A 63, 052308 (2001).
  16. Z.Y. Xu, M. Feng,”Addendum to “Grover search with pairs of trapped ions”.” Phys. Rev. A 78, 014301 (2008).
  17. T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo. “Superconducting persistent-current qubit.” Phys. Rev. B 60, 15398 (1999).
  18. Y. Makhlin, G. Scöhn, and A. Shnirman, “Josephson-junction qubits with controlled couplings,” Nature 398, 305-307(1999).
  19. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. “Charge-insensitive qubit design derived from the Cooper pair box.” Phys. Rev. A 76, 042319 (2007).
  20. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf. “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation.” Physical Review A, 69, 062320 (2004).
  21. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf. “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics.” Nature, 431, 162–167 (2004).
  22. P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraff. “Observation of Berry’s phase in a solid-state qubit.” Science, 318, 1889 (2007).
  23. P. J. Leek, M. Baur, J. M. Fink, R. Bianchetti, L. Steffen, S. Filipp, and A. Wallraff. “Cavity quantum electrodynamics with separate photon storage and qubit readout modes.” Phys. Rev. Lett.” 104, 100504 (2010).
  24. L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf. “Preparation and measurement of three-qubit entanglement in a superconducting circuit.” Nature, 467, 574–578 (2010).
  25. M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis. “Generation of three-qubit entangled states using superconducting phase qubits.” Nature, 467, 570–573 (2010).
  26. M. Baur, A. Fedorov, L. Steffen, S. Filipp, M. P. da Silva, and A. Wallraff. “Benchmarking a quantum teleportation protocol in superconducting circuits using tomography and an entanglement witness.” Phys. Rev. Lett., 108, 040502 (2012).
  27. J. L. O’Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, “Quantum process tomography of a controlled-not gate,” Phys. Rev. Lett. 93, 0805025(2004).
  28. A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff. “Implementation of a toffoli gate with superconducting circuits.” Nature, 481, 170–172 (2012).
  29. M. Mariantoni, H. Wang, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, T. Yamamoto, Y. Yin, J. Zhao, and A. N. Cleland. “Photon shell game in three-resonator circuit quantum electrodynamics.” Nat Phys, 7, 287–293 (2011).
  30. D. P. DiVincenzo. ”Elementary gates for quantum computation.” Phys. Rev. A 51, 1015-1022 (1995).
  31. D. Deutsch and R. Jozsa. “Rapid solution of problems by quantum computation.” Proceedings: Mathematical and Physical Sciences, 439, 553–558 (1992).
  32. B. D. Josephson. “Possible new effects in superconductive tunnelling.” Physics Letters, 1, 251–253 (1962).
  33. P. Anderson and J. Rowell. “Probable observation of the josephson superconducting tunneling effect.” Phys. Rev. Lett., 10, 230 (1963).
  34. D. E. McCumber. “Effect of ac impedance on dc voltage-current characteristics of superconductor weak-link junctions.” J. Appl. Phys. 39, 3113–3118 (1968).
  35. M. Büttiker. “Zero-current persistent potential drop across smallcapacitance josephson junctions.” Phys. Rev. B, 36, 3548–3555 (1987).
  36. V. Bouchiat, D. Vion, P. Joyez, D. Esteve, and M. H. Devoret. “Quantum coherence with a single Cooper pair.” Phys. Scr. T76, 165–170 (1998).
  37. M. Tinkham. Introduction to Superconductivity. McGraw-Hill International Editions (1996).
  38. E. Jaynes and F. Cummings. “Comparison of quantum and semiclassical radiation theories with application to the beam maser.” Proceedings of the IEEE, 51, 89–109 (1963).
  39. V. V. Shende and I. L. Markov. ”On the CNOT-cost of TOFFOLI gates.” Quantum Inf. Comput. 9, 461 (2009).
  40. H Sakhouf, M Daoud and R Ahl Laamara. ”Simple scheme for implementing the Grover search algorithm with superconducting qubits.” J. Phys. B: At. Mol. Opt. Phys. 54 175501(2021).
  41. Shi-Biao Zheng. ”Generation of entangled states for many multilevel atoms in a thermal cavity and ions in thermal motion.” Phys. Rev. A 68, 035801(2003).
  42. A. Sørensen and K. Mølmer. ”Quantum computation with ions in thermal motion.” Phys. Rev. A 62, 022311 (2000).
  43. J. R. Johansson, P. D. Nation, and F. Nori, “QuTiP: An open-source Python framework for the dynamics of open quantum systems”, Comp. Phys. Comm. 183, 1760 (2012).
  44. J. R. Johansson, P. D. Nation, and F. Nori, “QuTiP 2: A Python framework for the dynamics of open quantum systems”, Comp. Phys. Comm. 184, 1234 (2013).
  45. Chui-Ping Yang. ”Quantum information transfer with superconducting flux qubits coupled to a resonator.” Phys. Rev. A 82, 054303(2010). .
  46. T. Sleator and H. Weinfurter. ”Realizable universal quantum logic gates.” Phys. Rev. Lett. 74, 4087 (1995)
  47. A. G. Kofman and A. N. Korotkov. ”Two-qubit decoherence mechanisms revealed via quantum process tomography.” Phys. Rev. A 80, 042103(2009).
  48. I. L. Chuang and M. A. Nielsen.”Prescription for experimental determination of the dynamics of a quantum black box.” J. Mod. Opt. 44, 2455 (1997).
  49. G. M. D’Ariano and P. Lo Presti. ”Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation.” Phys. Rev. Lett. 86, 4195-4198(2001).
  50. D. P. DiVincenzo. “Fault-tolerant architectures for superconducting qubits.” Phys. Scr., 2009, 014020 (2009).
  51. A. Y. Kitaev. “Fault-tolerant quantum computation by anyons.” Annals of Physics, 303, 2 – 30 (2003).

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