Index
Aaronson, Scott, 261
addition of vectors, 30
additive inverse of a vector, 32
adjoint, 39
Aharonov, Dorit, 219
Aharonov, Yakhir, 112
algebraically complete, 14
algorithm
Deutsch–Jozsa, 4, 170, 179–187, 196, 218, 259, 321, 322
Deutsch’s, 4, 170–180, 218, 230, 233
Euclid’s, 217
Grover’s search, 4, 170, 195–204, 218, 235, 259, 260, 322, 367
Lempel–Ziv lossless compression, 296
modular-exponentiation, 218
Shor’s factoring, 4, 170, 204–219, 230, 259, 315, 322, 323, 361, 367
Simon’s periodicity, 4, 170, 187–196, 209, 218, 259, 322
analytic functions, 28
Argand plane, see complex plane
associativity of vector addition, 31
authentication, 267
Barenco, Adriano, 321
Barrow, John D., 239
orthogonal, 57
standard, see basis, canonical
BB84 protocol, 268–273, 275–277, 283, 323
Benioff, Paul, 320
Bennett, Charles, 153, 268, 273, 323, 324, 366
Berggren, Karl, 317
Berra, Yogi, 316
Bettelli, Stefano, 222
bijective, 15
bilinear map, 68
billiard ball
quantum, 91
bit, 138
Bloch sphere, 161
Bohm, David, 364
Bombelli, Rafael, 28
Boole, George, 277
Bouwmeester, Dik, 324
bra, 112
Caesar’s protocol, 263
Calderbank, A.R., 324
Cardano, Gerolamo, 28
Cartesian product
of sets, 45
of vector spaces, 45, 49, 66, 68
Cartesian representation, 18, 352
Cauchy sequence, 59
Chuang, Isaac L., xii, 315, 322
ciphertext, 262
Cirac, J.I., 311
Cirasella, Jill, xii, xiii, xvi, 319, 357
Collins, Graham P., 310
complex algebra, 42
complex analysis, 27
complex plane, 16, 17, 21, 362
complexity class, 243
configuration, 242, 247, 252–255
Crépeau, Claude, 323
Crow, Michael J., 363
D-Wave Systems, 316
dagger, see adjoint
data compression, 295–302, 304
lossless, 295
lossy, 295
De Broglie, Louis, 104
De Moivre’s formula, 25
decoherence, 5, 303, 305–317, 324, 371
decryption, 262
decryption key, 263
density operator, 288
Deutsch, David, 169, 320, 321, 366
Dick, Philip K., 103
Dijkstra, E.W., 170
Diogenes Laertius, vi
Dirac, P.A.M., 137
distance function, 57
DiVincenzo, David P., 310, 317, 321
division, 11
dot product, see inner product
Egan, Greg, 316
eigenspace, 62
Eilenberg, Samuel, xv
Einstein, Albert, 2, 104, 282, 364
elliptic curves, 267
encryption, 262
encryption key, 263
entanglement, 2, 4, 100, 103, 132–137, 144, 164, 262, 275–278, 282, 306, 364, 370
EPR paradox, 364
EQP, 258
Euler’s formula, 24
Everett, Hugh, 364
expected value, 120
experiment
diffraction, 104
double-slit, 74, 93, 96, 102, 104, 105, 241, 256, 363
Elitzur–Vaidman bomb-tester, 363
probabilistic double-slit, 85
Stern–Gerlach, 110
exponential form, 25
Feynman, Richard, 96, 100, 102, 319, 320
Fine, Arthur, 364
Fourier analysis, 1
fast, 368
Frost, Robert, 262
function
Fundamental theorem of algebra, 9
Galilei, Galileo, 29
gate
controlled-NOT, 153–155, 158, 165, 311, 313, 355, 366
Deutsch, 165
NOR, 147
NOT, 144, 145, 147, 149–151, 153, 155, 156, 158
Pauli, 366
square root of NOT, 159
Toffoli, 154–156, 158, 165, 166, 168, 366
Gay, J., 234
Gershenfeld, Neil, 322
Gibbs, Josia, 363
Gödel, Kurt, 239
Blog Search, 357
News, 357
Grassmann, Hermann, 363
group
Hamilton, Sir William Rowan, 363
Hamiltonian, 132
HAMILTONIAN GRAPH, 259
Heisenberg’s uncertainty principle, 3, 120, 124, 125
Held, Carsten, 365
Heller, Alex, xv
Heraclitus of Ephesus, vi
Huygens’ principle, 363
Holzscheiter, M., 317
Huygens, Christiaan, 363
infinite
countably, 49
uncountably, 49
complete, 60
instantaneous description, see configuration
interference, 89, 92–95, 105, 256
intrusion detection, 267
inversion about the average, see inversion about the mean
inversion about the mean, 198–204
isomorphism
of fields, 15
of graphs, 101
of matrices, 101
Jeans, Sir James, 138
Jones, J.A., 315
Josephson junctions, 315
Julius Caesar, 263
Kernaghan, M., 365
ket, 106
Kirk, Captain James T., 283
Kochen–Specker theorem, 365
Kronecker delta function, 57, 336
Kryptonite, 262
Kubinec, Mark, 322
Kuhn, D. Richard, 370
length (of a vector), see norm
linear map, 43
linearly dependent, 47
linearly independent, 46
Lloyd, Seth, 321
Lomonaco, Samuel J., 371
Luthor, Lex, 262
MATLAB, xii, xiii, xvi, 206, 260, 351–356
matrix
Boolean adjacency, 76
change of basis, 51
controlled-NOT, 226
doubly stochastic, 80, 83–85, 87
invertible, 64
Pauli, 158
phase shift, 226
transition, see matrix, change of basis
unitary, 64–66, 89–96, 129–132, 171–173, 180, 181, 186, 188, 196–198, 200, 201, 214, 215, 217, 218, 336
Vandermonde, 213
Maxwell’s demon, 365
mean value, 126
Meyer, David, 370
Möbius transformation, 27, 362
Monroe, C., 311
Mosca, M., 315
Musil, Robert, 7
Nagarajan, R., 225
negative of a vector, 32
No-cloning theorem, 166–169, 224, 268, 271, 278
nonlocality, 2
normalized, 109
NP-complete problem, 259
numbers
tractably computable, 251, 252
natural, 8
positive, 8
rational, 8
real, 8
tractably computable, 246, 252
whole, 8
observables, 129
Ömer, Bernhard, 234
One-Time-Pad protocol, 265
operations
parallel, 148
sequential, 147
operator, 44
oracle computation, 369
orthogonal, 57
P, 243–246, 250, 251, 258, 369
Papanikolaou, N., 225
parallelogram rule, 17
pdf, see probability distribution
period (of a function), 188–195
phase, 19
phase change, 162
phase shift, 356
plaintext, 262
pointwise, 44
polar representation, 18, 19, 352
polarization, 313
Pollard’s rho heuristic, 367
Pratt certificate, 369
primality testing, 369
probability distribution, 285
Pythagoras’ theorem, 16
QFC, 236
sequential, 368
QSPACE, 258
Quantiki, 357
quantum assembler, 222
quantum data compression scheme, 299
quantum eraser, 363
quantum error-correction, 371
quantum error-detection, 371
quantum finite automata, 369
quantum games, 370
quantum hardware interface, 223, 224
quantum machine language, 222
quantum register, 224
Rüdiger, R., 234
rational functions, 27
reduced Planck constant, 117
reflection
imaginary axis, 14
real axis, 14
representation of an operator, 44
Riemann sphere, 362
Rohit Parikh, xv
roots of unity, 25
Saint Exupry, Antoine de, 305
SAT, 259
Sayood, Kahil, 304
scalar, 33
scalar multiplication, 33
scalar product, see inner product
Schrödinger equation, 131, 132
Schrödinger’s cat, 365
Schumacher, Benjamin, 301, 324
Schumacher’s quantum coding theorem, 301, 304
Shannon, Claude, 5, 284, 297, 304, 324
Shannon’s noiseless channel coding theorem, 297, 301
Shor, Peter, 204, 219, 303, 322–324
Simon, Daniel R., 322
skew symmetric, 54
Smart Quantum, 323
snapshot, see configuration
Spectral theorem for self-adjoint operators, 64, 292
SQP, 315
stabilizer codes, 371
state
entangled, 135
entangled, 71
mixed, 307
pure, 306
statistical mechanics, 2
Steane, Andrew M., 324
subfield, 14
subtraction, 11
Sudoku game, 316
Suetonius, 263
superconductor, 315
superposition, 2–4, 96, 97, 107, 256
Tartaglia, Niccol Fontana, 28
Taylor expansion, 24
Technorati, 357
teleportation, 5, 262, 277–283, 324
tensor product
of matrices, 71, 99–101, 150, 354
of vector spaces, 66–73, 102, 132–137
thesis
classical Church–Turing, 241
Cook–Karp, 243
strong Church–Turing, 251, 259
time symmetry, 82
transporting, 167
transpose, 39
triangle inequality, 56, 57, 295
Turing, Alan, 239
nondeterministic, 239, 243–246
probabilistic, 239, 246–253, 260
quantum, 5, 223, 239, 252–260, 320, 369, 370
well-formed, 255
unit circle, 24
unit sphere, 65
universal logical gates, 165
universal quantum gates, 165
vectors, 16
vector space, 362
F2, 183
, 183
Vernam cipher, see One-Time-Pad protocol
Wang, Hao, 239
Wiesner, Stephen, 323
Wigner’s friend, 365
Wikipedia, 358
Williams, D., 225
Wineland, D., 311
Yao, Andrew Chi-Chih, 321
zero vector, 32
Zizzi, Paola, 316
Zoller, P., 311
Zurek, Wojciech H., 317