Adiabatic quantum transistors

Physical Review X

Volumn 3, Issue 2, 2013, Pages

  Bacon, Dave ^a,b,d   Flammia, Steven T ^a,c   Crosswhite, Gregory M ^b,e  

^a University of Washington   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

^c UNIVERSITY OF SYDNEY   (Australia)

^d GOOGLE INC   (United States)

^e UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Quantum Information; Quantum Physics; Strongly Correlated Materials

Indexed keywords

MANY-BODY QUANTUM SYSTEMS; NOISY ENVIRONMENT; QUANTUM COMPUTING DEVICES; QUANTUM INFORMATION; QUANTUM PHYSICS; QUANTUM TRANSISTORS; STRONGLY CORRELATED MATERIALS; TOPOLOGICAL ORDER;

QUANTUM COMPUTERS; QUANTUM ELECTRONICS;

QUANTUM OPTICS;

EID: 84883540511     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.3.021015     Document Type: Article

References (46)

1. W. Shockley, Circuit Element Utilizing Semiconductor Material, U.S. Patent No. 2569347, Bell Telephone Laboratories, 1948.
2. P.W. Shor, Algorithms for Quantum Computation: Discrete Log and Factoring, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 124-134.
3. D. Aharonov and M. Ben-Or, Fault-Tolerant Quantum Computation with Constant Error Rate, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (ACM Press, New York, 1997) pp. 176-188.
4. E. Knill, R. Laflamme, and W. H. Zurek, Resilent Quantum Computation, Science 279, 342 (1998).
5. E. Knill, R. Laflamme, and W. H. Zurek, Resilient Quantum Computation: Error Models and Thresholds, Proc. R. Soc. A 454, 365 (1998).
6. D. Deutsch, Quantum Computational Networks, Proc. R. Soc. A 425, 73 (1989).
7. Sougato Bose, Quantum Communication through an Unmodulated Spin Chain, Phys. Rev. Lett. 91, 207901 (2003).
8. E. Knill, R. Laflamme, and G. J. Milburn, A Scheme for Efficient Quantum Computation with Linear Optics, Nature (London) 409, 46 (2001).
9. R. Raussendorf and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001).
10. D. Aharonov,W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation, in 45th Annual IEEE Symposium on Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, 2004) pp. 42-51.
11. J. Kempe, A. Kitaev, and O. Regev, The Complexity of the Local Hamiltonian Problem, SIAM J. Comput. 35, 1070 (2006).
12. A. Mizel, D. A. Lidar, and M.W. Mitchell, Simple Proof of Equivalence between Adiabatic Quantum Computation and the Circuit Model, Phys. Rev. Lett. 99, 070502 (2007).
13. D. Kult, J. Åberg, and E. Sjoqvist, Noncyclic Geometric Changes of Quantum States, Phys. Rev. A 74, 022106 (2006).
14. W. Wootters and W. Zurek, A Single Quantum Cannot Be Cloned, Nature (London) 299, 802 (1982).
15. D. Bacon and S. T. Flammia, Adiabatic Gate Teleportation, Phys. Rev. Lett. 103, 120504 (2009).
16. D. Bacon and S. T. Flammia, Adiabatic Cluster State Quantum Computing, Phys. Rev. A 82, 030303(R) (2010).
17. O. Oreshkov, T. A. Brun, and D. A. Lidar, Fault-Tolerant Holonomic Quantum Computation, Phys. Rev. Lett. 102, 070502 (2009).
18. O. Oreshkov, Holonomic Quantum Computation in Subsystems, Phys. Rev. Lett. 103, 090502 (2009).
19. Hans J. Briegel and Robert Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett. 86, 910 (2001).
20. S. D. Bartlett and T. Rudolph, Simple Nearest-Neighbor Two-Body Hamiltonian System for which the Ground State Is a Universal Resource for Quantum Computation, Phys. Rev. A 74, 040302 (2006).
21. R. Oliveira and B. M. Terhal, The Complexity of Quantum Spin Systems on a Two-Dimensional Square Lattice, Quantum Inf. Comput. 8, 0900 (2008).
22. Gernot Schaller, Sarah Mostame, and Ralf Schutzhold, General Error Estimate for Adiabatic Quantum Computing, Phys. Rev. A 73, 062307 (2006).
23. A. C. Doherty and S. D. Bartlett, Identifying Phases of Quantum Many-Body Systems that Are Universal for Quantum Computation, Phys. Rev. Lett. 103, 020506 (2009).
24. J. K. Pachos and M. B. Plenio, Three-Spin Interactions in Optical Lattices and Criticality in Cluster Hamiltonians, Phys. Rev. Lett. 93, 056402 (2004).
25. E. Lieb, T. Schultz, and D. Mattis, Two Soluble Models of an Antiferromagnetic Chain, Ann. Phys. (Amsterdam) 16, 407 (1961).
26. F. Verstraete, D. Porras, and J. I. Cirac, Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective, Phys. Rev. Lett. 93, 227205 (2004).
27. Steven R. White, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett. 69, 2863 (1992).
28. U. Schollwock, The Density-Matrix Renormalization Group, Rev. Mod. Phys. 77, 259 (2005).
29. J. Dorier, F. Becca, and F. Mila, Quantum Compass Model on the Square Lattice, Phys. Rev. B 72, 024448 (2005).
30. Gerardo A. Paz-Silva, Gavin K. Brennen, and Jason Twamley, Fault Tolerance with Noisy and Slow Measurements and Preparation, Phys. Rev. Lett. 105, 100501 (2010).
31. A. Childs, E. Farhi, and J. Preskill, Robustness of Adiabatic Quantum Computation, Phys. Rev. A 65, 012322 (2001).
32. P. Pfeuty, The One-Dimensional Ising Model with a Transverse Field, Ann. Phys. (Berlin) 57, 79 (1970).
33. Jeremie Roland and Nicolas J. Cerf, Quantum Search by Local Adiabatic Evolution, Phys. Rev. A 65, 042308 (2002).
34. W. Son, L. Amico, and V. Vedral, Topological Order in 1D Cluster State Protected by Symmetry, Quantum Inf. Process. 11, 1961 (2012).
35. Norbert Schuch, David Perez-Garca, and Ignacio Cirac, Classifying Quantum Phases Using Matrix Product States and Projected Entangled Pair States, Phys. Rev. B 84, 165139 (2011).
36. Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, Symmetry Protected Topological Orders and the Group Cohomology of Their Symmetry Group, Phys. Rev. B 87, 155114 (2013).
37. Sergey Bravyi, Matthew Hastings, and Spyridon Michalakis, Topological Quantum Order: Stability under Local Perturbations, J. Math. Phys. (N.Y.) 51, 093512 (2010).
38. S. Michalakis and J. Pytel, Stability of Frustration-free Hamiltonians, arXiv:1109.1588.
39. Dominic V. Else, Ilai Schwarz, Stephen D. Bartlett, and Andrew C. Doherty, Symmetry-Protected Phases for Measurement-Based Quantum Computation, Phys. Rev. Lett. 108, 240505 (2012).
40. Akimasa Miyake, Quantum Computation on the Edge of a Symmetry-Protected Topological Order, Phys. Rev. Lett. 105, 040501 (2010).
41. G. Brennen and A. Miyake, Measurement-Based Quantum Computer in the Gapped Ground State of a Two-Body Hamiltonian, Phys. Rev. Lett. 101, 010502 (2008).
42. S. D. Bartlett, G. K. Brennen, A. Miyake, and J. Renes, Quantum Computational Renormalization in the Haldane Phase, Phys. Rev. Lett. 105, 110502 (2010).
43. Joseph M. Renes, Akimasa Miyake, Gavin K. Brennen, and Stephen D. Bartlett, Holonomic Quantum Computing in Ground States of Spin Chains with Symmetry-Protected Topological Order, New J. Phys. 15, 025020 (2013).
44. J. A. Smolin and D. P. DiVincenzo, Five Two-Bit Quantum Gates Are Sufficient to Implement the Quantum Fredkin Gate, Phys. Rev. A 53, 2855 (1996).
45. Iulia Buluta and Franco Nori, Quantum Simulators, Science 326, 108 (2009)
46. P. Jordan and E. Wigner, ü ber das Paulische Ä quivalenzverbot (On the Pauli Exclusion Principle), Z. Phys. 47, 631 (1928).