i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 331 — le-tex i i 331 Index a – nuclear 258 A-gate 218 – quantum number 258 abacus 10 – total 258 adiabatic passage 255 annihilation Adleman, Leonard 22 – operator 195 AlGaAs 223 anti-diagonally polarized photon 53 algorithm anti-Hermitian – Bernstein–Vazirani 286 –operator 43 – Deutsch–Jozsa 284 anti-Stokes – exponential speedup 286 – photon 265 – Deutsch’s 282 Antikythera mechanism 10 –eigenvalue argument – exponential speedup 293 –bit 27 – exponential time 293 astrolabe 10 – Euclid’s 288 atom –feasible 20 – interference 269 – field sieve 22, 287 atom–cavity – general number field sieve 155 – coupling 252, 256, 273 – GNFS 155, 287 – constant 256 – Grover’s 19, 293 atomic –intractable 20 – dipole matrix element 198 – Shor’s 19, 157, 214, 287, 288 – ensemble 262 – all optical 192 auxiliary qubit 181 – exponential speedup 288 axis – exponential time 288 –fast 53 – NMR 214, 287, 290 –slow 53 – Simon’s 287 – exponential speedup 287 b – subexponential 22 B92 165 Alice 81 B92 protocol 170, 171 – classical 141, 152 balanced function 282 – quantum 160 bandwidth 16 alkali-metal atoms 257 Bardeen all-optical 176 – John 236 analog computer 12 basis ancilla 103, 138, 146, 181 – computational 34 angular BB84 protocol 167, 170 – momentum BBN Technologies 157 – electron 215 BBO crystal 55 Companion to Quantum Computation and Communication, First Edition. M. Paviˇci´c. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA. Published 2013 by WILEY-VCH Verlag GmbH & Co. KGaA. i i i i i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 332 — le-tex i i 332 Index beam splitter c –BS 14 Calderbank–Shor–Steane code 144 – polarization-nonpreserving 71 carrier frequency 203 – polarization-preserving 71 carry 151 – polarizing 57, 260 carry bit 152 Bell cavity 37, 256 –inequality 77 – dark state 257 – state 64–66 – optical 252 – preparation 81 – spherical mirror 253 Bennett–Brassard protocol 167 – QED 176 Bernstein–Vazirani algorithm 286 CC-Uˆ gate biexciton 225 – quantum 138 bit 7 CCNOT –argument 27 –gate 28 – control 27 CCNOT gate –garbage 27 – quantum 145 – parity 141 cesium 257 – quantum 34 charge –result 27 – measurements 220 –sink 27 check matrix 143 –source 27 chip –target 27 –optical –train – integrated 192 – Kane computer 221 Chuang bit-flip 141 – Isaac 188 – correction 148 Church thesis 2 – quantum 144 Church’s general recursiveness 3 Bletchley Park 1 Cirac–Zoller phase gate 192, 230, 248, 306 blue sideband frequency 203 circuit Bob 81 – classical – classical 152 – reversible 138 – quantum 160 – entanglement 140 Bohm – quantum 145–147, 149, 206, 284, 289 – David 303 – diagram 289 Bohr circularly polarized photon 52 – magneton 233 classical –Niels 97 – Alice 141 Boltzmann cloning –entropy 26 –aqubit 94 Bomba 1 – no, theorem 109 Bombes 1 cluster state 300 Boolean – continuous variable 306 – algebra 3, 4, 6 CNOT – lattice model of classical logic 8 –operator 49 –logic 6 CNOT gate 28, 49, 140, 180 –operations 6 – destructive 183 bra 37 – f- 282 bra-ket notation 14 – full 186 broadcasting – interaction-free 266 – no, theorem 109 – pseudo 266 BS – quantum 138 – beam splitter 14 – ion trap 204 – semitransparent mirror 14 – Kane 221, 222 i i i i i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 333 — le-tex i i Index 333 – NMR 214 – Doppler 194 – silicon-based spin 221, 222 – Sisyphus 202 code 142 Cooper codeword 142 – Leon Neil 236 coding – pair 237 –dense 85 – box 240 –superdense 85 Cooper-pair – controlled 89 – number operator 242 coherence 54 coprime 288 collection efficiency 178, 251 correction communication – bit-flip 148 – quantum coset 172 – deterministic 161 counterfactual commutator 40 – measurement 110 complement 6 – reasoning 110 complementary subspace 44 counting rods complexities 17 – Chinese 10 – computational 19 coupler complexity – fiber 170 –class 18 coupling constant 214 – computational 19 creation –oforderO(f(n)) 21 – operator 195 – subexponential 22, 156, 287 critical – superpolynomial 22, 287 – Kochen–Specker set 120 computation cryptography – one-way 298 – interaction-free 280 –physical 17 – quantum 157, 167 –time 19 – continuous variables 177 computational – deterministic 161 –basis 34 – entangled pairs 177 condensation – free space transmission 177 – superconducting 236 – interaction-free 280 conjunction 6 – phase-coding 170 contextuality – roadmap 177 – quantum 110 – single-photon sources 177, 178 continued fraction expansion 292 – weak laser pulses 177 continuous variable crystal – cluster state 306 – BBO 55 continuous variable computation 302 – birefringent 53 continuous wave laser 16 –KDP 55 control –uniaxial 53 –bit 27 CSS code 144 – qubit 135, 138 CW laser 16 control mode 162 CZ 192 controlled-controlled-NOT gate CZ gate 192, 230, 248, 306 – quantum 145 controlled-controlled-Û gate d – quantum 138 dark controlled-NOT gate – counts 178 – quantum 138 – state 255–257 controlled superdense coding 89 – cavity 257 cooling – mixing angle 255 –laser – teleportation 257 i i i i i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 334 — le-tex i i 334 Index DARPA quantum network 158 edge 20 Decidable theories 3 eigenbra 44 decoherence 175 eigenket 44 decomposition of unity 45 eigenvalue 44, 293 decoy – algorithm – pulse 178 – exponential speedup 293 delay – exponential time 293 – gate 152 eigenvector 44, 293 demand Einstein – photons on 178 –Albert 77 dense coding 85 – “element of physical reality” 77 density operator 47 Einstein–Podolsky–Rosen 303 destructive CNOT gate 183 – Gedankenexperiment (EPR) 78 deterministic Ekert protocol 165 – quantum electric dipole moment 256 – communication 161 electric field vector 51 – cryptography 161 electron Deutsch–Jozsa algorithm 284 –angular – exponential speedup 286 – momentum 215 Deutsch’s algorithm 282 –magnetic diagonally polarized photon 52 – moment 215 diode laser 177 –single dipole – transistor 220 – approximation 197, 199 – spin 215 –matrixelement electron commutation relations 199 – atomic 198 emission, spontaneous 54 –moment encoder – electric 256 – gate 186 direct product 40 – quantum 183 discrete Fourier transform 281 – quantum 182 disjunction 6 encoding distributivity 9 – quantum 182 DiVincenzo entangled – Criteria 176 –photons 50 – D. 231 – state 65, 140, 147 DLCZ protocol 262 – on demand 204 donor entanglement – phosphorus 218 – circuit 140 Doppler cooling 194 – swapping 262, 263 Doppler laser cooling 194 entropy 26 dot –Boltzmann 26 – quantum 179 EPR (Einstein–Podolsky–Rosen) 78, 303 down-conversion error – parametric 55 – correction –type-I 55 – classical 141 –type-II 56 – Hadamard gate 145 Duan–Lukin–Cirac–Zoller protocol 262 – quantum 144 dyad 40 – weight 143 Euclid’s algorithm 288 e Euler tour 20 Earnshaw’s theorem 193 Eve 81 eavesdropping – quantum 167 – quantum 167 evolution operator 130 i i i i i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 335 — le-tex i i Index 335 exciton 223, 225 free space transmission – state 226 – cryptography exponential – quantum 177 – matrix 134 Frege – speedup – Gottlob 4 – Deutsch–Jozsa algorithm 286 frequency – eigenvalue algorithm 293 –angular 51 – Shor’s algorithm 288 –ofawave 51 – Simon’s algorithm 287 full –time – adder 151 – eigenvalue algorithm 293 – CNOT gate 186 – Shor’s algorithm 288 EXPTIME 19 g extraordinary ray 166 GaAs 223 GaInP 224 f garbage f-CNOT gate 282 –bit 27 factoring a number 287 gas factoring number 17 – van der Waals 296 false (0, ?)6 fan-out gate 6 –gate 30 – A 218 fault-tolerant computation 149 –AND 7 feasible – CCNOT 28 – algorithm 20 – classical 6 –problem 20 – CNOT 28, 49, 140 Fermi – destructive 183 – operator 200 – full 186 Fert, Albert 225 – interaction-free 266 Feynman – ion trap 204 – Richard 28 – Kane 221, 222 fiber 191 – NMR 214 – coupler 170 – quantum 138 fictitious magnetic – silicon-based spin 221, 222 –dipole – CZ 192, 230, 248, 306 – ion trap 200 – delay 152 –field – encoder 186 – ion trap 200 – quantum 183 field –fan-out 30 – sieve algorithm 287 –Fredkin 27 Field Sieve algorithm 22 – H 132 flip – Hadamard 81, 132, 248, 283, 285, 292 – parity 304 – ion trap 203 – spatial 304 – NMR 213 Fock – J 218, 219 – state –logic 7 – single-photon 178 –operations 7 Fourier transform 10, 292 –symbols 7 – discrete 281 – NMR 213 – quantum 281, 290 – NOT 7, 28, 132 FP7 158 p– ion trap 203 Franson, James D. 180 – NOT 132 Fredkin –OR 7 –gate 27 – parity check 180 i i i i i i Mladen Paviˇci´c: Companion to Quantum Computation and Communication — 2013/3/5 — page 336 — le-tex i i 336 Index – phase 132, 230, 248 – distance 142 – phase shift 132 – rule 142 – quantum 6, 222 – scheme 142 – rotation 132 harmonic oscillator 195 – S 132, 221 – Hamiltonian 195 – Toffoli 28, 138 Heisenberg microscope 270 –universal Hermitian – quantum 136 –matrix 43 – X 132 –operator 43 –XNOR 7 hexagon – Y 132 – lattice model of classical logic 8 – Z 132 Hilbert gcd 288 –David 4 general number field sieve algorithm –program 4 155, 287 Holevo limit 165 generator home qubit 161 – rotation gate 133 Hong–Ou–Mandel dip 90, 304 giant magnetoresistance 225 HWP (half-wave plate) 80 Ginzburg hyperfine interaction 215, 218, 258 – Vitaly 237 hyperfine structure 36 GNFS algorithm 155, 287 hypergraph 20, 115 Goldberg–Vaidman protocol 165 – MMP 116 Gottesman Hänsch, T.W. 194 – Daniel 188 i graph 20 identity operator 40, 130 – state 306 idler 55 greatest common divisor 288 idQuantique 157 Grover’s algorithm 19, 293 inconsistent mathematics