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APPENDIX SAMPLE CODE OF THE STABILIZER CIRCUIT SIMULATOR 101
# Sample code for testing the algorithm for correction of # Time-correlated errors using the stabilizer circuit simulator # GraphSim # Requires GraphSim from # http://homepage.uibk.ac.at/~c705213/work/graphsim.html # INPUT: Prepare the stabilizer circuits by using cnot, hadamard, # cphase gates and so on. Introduce errors by using bitflip and # phaseflip operations. # OUTPUT: Output the syndrome by printing the measurements on # different ancilla qubits. import graphsim import random random.seed() gr=graphsim.GraphRegister(22,random.randint(0,1E6)) # Prepare Steane |0> codeword on qubit 0-6 gr.hadamard (4) gr.hadamard (5) gr.hadamard (6) gr.cnot (6, 3) gr.cnot (6, 1) gr.cnot (6, 0) gr.cnot (5, 3) gr.cnot (5, 2) gr.cnot (5, 0) gr.cnot (4, 3) gr.cnot (4, 2) gr.cnot (4, 1) # Entangle qubit 3 with the extra ancilla gr.cnot(2,7) gr.hadamard(2) gr.cnot(2,8) gr.hadamard(2) # Errors happen on qubit ? 102
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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
Page 61 and 62: schedules: | � �� ST Cmax
Page 63 and 64: 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: correcting code capable of correcti
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 and 122: [RG05] B. W. Reichardt and L. K. Gr
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