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[TS06] E.M. Rains T.G. Draper, S.A. Kutin and K.M. Svore. “A Logarithmic-depth Quantum Carry-lookahead Adder.” Quantum Information and Computation, 6(4):351–369, 2006. [VRA99] F. Vatan, V.R. Raichowdry, and M. Anantram. “Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes.” IEEE Transactions on Information Theory, 45:1703–1708, 1999. [VSB01] 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, 414:883–887, December 2001. [Zal99] C. Zalka. “Grover’s Quantum Searching Algorithm Is Optimal.” Phys. Rev. A, 60(4):2746–2751, Oct 1999. 111
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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
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The makespan of schedule S1 is equa
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J1 J2 ... ... JN |0> |0> |0> ... ..
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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 and 116: # "Disentangle" the extra ancilla g
Page 117 and 118: LIST OF REFERENCES [AAK01] D. Aharo
Page 119 and 120: [Got97] D. Gottesman. “Stabilizer
Page 121: [RG05] B. W. Reichardt and L. K. Gr
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