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xi | |
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xv | |
Preface |
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xvii | |
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1 | (56) |
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2 | (2) |
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Classical Error Correcting Codes |
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4 | (13) |
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Linear Error Correcting Codes |
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4 | (3) |
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Errors, Hamming Weight and Distance |
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7 | (3) |
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Error Detection and Correction |
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10 | (2) |
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12 | (2) |
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Bounds on Code Parameters |
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14 | (3) |
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Using Quantum Systems to Store and Process Data |
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17 | (14) |
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Linear Superposition and Quantum Parallelism |
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17 | (3) |
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20 | (1) |
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21 | (2) |
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Distinguishing Quantum States |
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23 | (1) |
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24 | (4) |
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Noise: Errors and Decoherence |
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28 | (3) |
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Quantum Error Correcting Codes---First Pass |
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31 | (26) |
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Redundancy without Cloning |
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31 | (9) |
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Necessary and Sufficient Conditions |
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40 | (8) |
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48 | (3) |
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51 | (6) |
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Quantum Error Correcting Codes |
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57 | (26) |
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57 | (16) |
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Operator-Sum Representation |
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58 | (12) |
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70 | (1) |
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71 | (2) |
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Quantum Error Correcting Codes: Definitions |
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73 | (2) |
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Example: Calderbank-Shor-Steane [ 7, 1, 3] Code |
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75 | (8) |
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77 | (3) |
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80 | (3) |
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83 | (32) |
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83 | (10) |
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83 | (2) |
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85 | (5) |
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Quantum Error Correction Reprise |
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90 | (1) |
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91 | (2) |
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93 | (3) |
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93 | (2) |
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95 | (1) |
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95 | (1) |
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Alternate Formulation: Finite Geometry |
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96 | (4) |
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100 | (15) |
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101 | (3) |
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104 | (6) |
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110 | (3) |
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113 | (2) |
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Quantum Stabilizer Codes: Efficient Encoding and Decoding |
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115 | (22) |
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115 | (6) |
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121 | (6) |
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127 | (10) |
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131 | (3) |
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134 | (3) |
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Fault-Tolerant Quantum Computing |
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137 | (58) |
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137 | (4) |
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To Encode or Not to Encode |
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139 | (1) |
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139 | (2) |
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141 | (12) |
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144 | (4) |
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148 | (3) |
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151 | (2) |
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Encoded Operations in N(Gn) ∩ N (S) |
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153 | (9) |
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155 | (3) |
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158 | (4) |
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162 | (4) |
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166 | (3) |
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Multi-Qubit Stabilizer Codes |
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169 | (4) |
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Operations Outside N(Gn)---Toffoli Gate |
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173 | (7) |
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180 | (6) |
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186 | (9) |
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Fault-Tolerant Quantum Computing |
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186 | (1) |
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Fault-Tolerant Encoded Operations |
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187 | (1) |
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188 | (4) |
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192 | (3) |
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Accuracy Threshold Theorem |
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195 | (28) |
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195 | (4) |
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196 | (1) |
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197 | (2) |
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199 | (24) |
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Recursion - Relation for pop(j) |
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200 | (8) |
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Clifford Group Gates and Storage Registers |
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208 | (2) |
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210 | (9) |
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219 | (1) |
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220 | (3) |
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Bounds on Quantum Error Correcting Codes |
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223 | (38) |
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223 | (2) |
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Quantum Gilbert-Varshamov Bound |
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225 | (2) |
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227 | (2) |
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Linear Programming Bounds for QECCs |
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229 | (11) |
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230 | (3) |
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Quantum MacWilliams Identity |
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233 | (3) |
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236 | (3) |
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Bounds via Linear Programming |
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239 | (1) |
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Entanglement Purification and QECCs |
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240 | (21) |
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241 | (14) |
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255 | (2) |
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257 | (1) |
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258 | (3) |
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261 | (8) |
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261 | (4) |
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261 | (1) |
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262 | (3) |
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265 | (1) |
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265 | (1) |
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265 | (1) |
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266 | (3) |
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266 | (1) |
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Fundamental Homomorphism Theorem |
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267 | (1) |
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268 | (1) |
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269 | (14) |
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270 | (1) |
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271 | (1) |
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271 | (1) |
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272 | (1) |
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Measurement and State Preparation |
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273 | (3) |
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276 | (7) |
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280 | (3) |
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283 | (6) |
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283 | (2) |
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285 | (1) |
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Universal Sets of Quantum Gates |
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286 | (3) |
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288 | (1) |
Index |
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289 | |