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gr.cnot(10+6,2) gr.cnot(10+6,5) gr.cnot(10+6,6) gr.cnot(11+6,0) gr.cnot(11+6,2) gr.cnot(11+6,4) gr.cnot(11+6,6) # X syndrome gr.cphase(12+6,3) gr.cphase(12+6,4) gr.cphase(12+6,5) gr.cphase(12+6,6) gr.cphase(13+6,1) gr.cphase(13+6,2) gr.cphase(13+6,5) gr.cphase(13+6,6) gr.cphase(14+6,0) gr.cphase(14+6,2) gr.cphase(14+6,4) gr.cphase(14+6,6) # Measure and output the syndrome for i in range(9+6,15+6): gr.hadamard(i) print gr.measure(i) print 105
LIST OF REFERENCES [AAK01] D. Aharonov, A. Ambainis, J. Kempe, and U. V. Vazirani. “Quantum walks on graphs.” In ACM Symposium on Theory of Computing, pp. 50–59, 2001. [Aar05] S. Aaronson. “Quantum Computing, Postselection, and Probabilistic Polynomial- Time.” Proceedings of the Royal Society A, 461(2063):3473–3482, December 2005. [AB06] S. Anders and H. J. Briegel. “Fast Simulation of Stabilizer Circuits Using a Graphstate Representation.” Phys. Rev. A, 73(2):022334–+, February 2006. [AG04] S. Aaronson and D. Gottesman. “Improved Simulation of Stabilizer Circuits.” Physical Review A (Atomic, Molecular, and Optical Physics), 70(5):052328, 2004. [AHH02] R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki. “Dynamical Description of Quantum Computing: Generic Nonlocality of Quantum Noise.” Phys. Rev. A, 65(6):062101–+, June 2002. [Amb07] A. Ambainis. “Quantum Walk Algorithm for Element Distinctness.” SIAM Journal on Computing, 37(1):210–239, 2007. [BBB92] C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. “Experimental Quantum Cryptography.” J. Cryptol., 5(1):3–28, 1992. [BBB97] C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. “Strengths and Weaknesses of Quantum Computing.” SIAM J. Comput., 26(5):1510–1523, 1997. [BBC93] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters. “Teleporting an Unknown Quantum State via Dual Classical and Einstein- Podolsky-Rosen Channels.” Phys. Rev. Lett., 70(13):1895–1899, Mar 1993. [BDE95] A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa. “Conditional Quantum Dynamics and Logic Gates.” Phys. Rev. Lett., 74(20):4083–4086, May 1995. [BHM02] G. Brassard, P. Høyer, M. Mosca, and A. Tapp. “Quantum Amplitude Amplification and Estimation.” AMS Contemporary Mathematics, 305:53–74, 2002. [BHT98] G. Brassard, P. Høyer, and A. Tapp. “Quantum Counting.” Lecture Notes in Computer Science, 1443:820+, 1998. 106
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STUDIES OF A QUANTUM SCHEDULING ALG
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ABSTRACT Quantum computation has be
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ACKNOWLEDGMENTS The first person I
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3.2 Amplitude Amplification . . . .
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LIST OF FIGURES 2.1 (a) The measure
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LIST OF TABLES 4.1 An example of 8
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lots of scientists to study on diff
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CHAPTER 2 BASIC CONCEPTS AND RELATE
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All these achievements continuously
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Different methods of implementing q
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| 11〉. For example, | 0〉⊗ | 1
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Suppose the state we want to copy i
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2.3 Quantum Circuits In the classic
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Operation U1 followed by U2 is equi
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c t c t ⊕ c c c Figure 2.3: Circu
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2.4 Physical Implementations of Qua
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an arbitrary number of qubits. A qu
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Up to date, there have been several
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iophysics and materials technology.
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In a key development for Topologica
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calculations many times. The advant
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very limited. To see the spectacula
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Example. Consider a 3-dimensional s
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CHAPTER 3 GROVER’S ALGORITHM 3.1
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lack box performs the following tra
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amplitude amplification is an opera
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Each iteration Q will rotate the sy
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CHAPTER 4 GROVER-TYPE QUANTUM SCHED
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4.2 Introduction to Scheduling Prob
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equires that the number of differen
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schedules: | � �� ST Cmax
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m index qubits to control the job-m
Page 65 and 66: The makespan of schedule S1 is equa
Page 67 and 68: J1 J2 ... ... JN |0> |0> |0> ... ..
Page 69 and 70: Max(| 5〉, | 7〉, | 4〉) =| 7〉
Page 71 and 72: the machine and remaining q qubits
Page 73 and 74: 1. Devise an encoding scheme for th
Page 75 and 76: state, a well-defined desired state
Page 77 and 78: Quantum error correction is used in
Page 79 and 80: discovered independently by Shor [S
Page 81 and 82: Since the first qubit was flipped,
Page 83 and 84: Let us take the C1 [7,4,3] Hamming
Page 85 and 86: For example, consider the case n =
Page 87 and 88: 2. The identity matrix multiplied b
Page 89 and 90: which means that the stabilizer M c
Page 91 and 92: example shows that the code cannot
Page 93 and 94: CHAPTER 6 QUANTUM ERROR-CORRECTION
Page 95 and 96: j Qubit flips i and j Qubit i is re
Page 97 and 98: of the model can be written as: H =
Page 99 and 100: We also assume that: • There are
Page 101 and 102: the original codeword. Now we need
Page 103 and 104: We use the Steane code to illustrat
Page 105 and 106: ... ... ... Extra XXX Codeword anci
Page 107 and 108: flip, 11 - bit-and-phase-flip, see
Page 109 and 110: Table 6.2: The syndromes for each o
Page 111 and 112: correcting code capable of correcti
Page 113 and 114: # Sample code for testing the algor
Page 115: # "Disentangle" the extra ancilla g
Page 119 and 120: [Got97] D. Gottesman. “Stabilizer
Page 121 and 122: [RG05] B. W. Reichardt and L. K. Gr
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