Adder, 102
Adleman, Leonard, 172
Algorithms
Deutsch, 145–149
Deutsch-Jozsa, 152–157
Grover, 176–181
Shor, 174–176
Simon, 157–168
Amplitude amplification, 179
Ancilla bit, 108
BB84 protocol, 53–55
Bell, John Stewart, 72, 76, 84
Bell basis, 128
Bell circuit, 127
Bell’s inequality, 79–84
Bell test, loophole-free, 66, 183
Bennett, Charles, 54
Billiard ball computer, 90, 111–115
Bit
ancilla, 108
classical, 1
garbage, 109
quantum, 1, 50
Bitwise addition, 157
Black box, 145
Bohm, David, 76
Bohmian mechanics, 85
Bohr, Niels, 1, 71, 76, 82, 84
Boole, George, 89, 90
Boolean algebra, 91–93
Boolean function, 94
Bounded quantum polynomial. See Complexity classes, BQP
Bra, 19
Bra-ket
length of vectors, 24
notation, 23
orthogonality of vectors, 24–25
Brassard, Gilles, 54
Chemistry. See Computational chemistry
Circuit, 99
Classical bit, 1
Classical mechanics, 9–11
Clauser, John, 82
Clay Mathematics Institute, 144
Cloning, 124
Complexity classes
BPP, 167
BQP, 167
EQP, 166
NP, 142–144
P, 142–144
QP, 166
Complex numbers, 17–18, 35, 38
Computational chemistry, 181–182
Cooper pair, 183
Copenhagen interpretation, 71
Cryptanalysis, 172
Darwin, Charles, 188
Database search, 181
Decoherence, 182
Deutsch, David, 85, 145, 169, 187
Dimension, 19, 38
Dirac, Paul, 17, 19, 181
D-Wave, 185–186
Einstein, Albert, 69, 71, 75–77, 82
Ekert, Artur, 86
Ekert protocol, 86–87
Encryption, RSA, 172–173
Entanglement, 59
Entropy, 105
EPR paradox, 76–77
Equivalent state vectors, 41–42
Error correction, 135–140
Everett, Hugh, 187
Exact quantum polynomial. See Complexity classes, EQP
Exponential time, 143
Fan-out, 100
Feynman, Richard, 89, 115, 182
Flip about the mean, 179
Flip-flop, 103
Fredkin, Edward, 89, 111, 115
Freedman, Stuart, 82
Function
balanced, 146
constant, 146
Functional completeness, 94–96
Garbage bit, 109
Gate
AND, 98
controlled not (CNOT), 67, 105
Fredkin, 109
Hadamard, 122
NAND, 99
NOT, 98
OR, 99
Pauli, 121
quantum, 117, 120
reversible, 102
switch, 111
Toffoli, 107
universal, 101, 108, 110, 123
XOR, 102
Gerlach, Walther, 1
Google, 184
Gravity, 75–76
Grover, Lov, 176
Half-adder, 102–103
Hidden variables, 11, 71, 77–78
IBM, 182, 184
ID Quantique, 176
Interference, 52–53, 174
Ion-trap, 183
Josephson junction, 183
Ket, 19
Kronecker product, 149–152
Landauer limit, 105
Linear algebra toolbox, 35
Linearly independent, 165
Linear superposition, 50
Local realism, 71, 75–76
Logical equivalence, 93
Many-worlds view, 85
Matrix, 30
Hadamard, 159–160
identity, 32
Kronecker product, 149–152
main diagonal, 32
multiplication, 31, 32
not commutative, 32
orthogonal, 34
square, 32
transpose, 31
unitary, 34
Micius, 176
Millennium Prize, 144
NMR machine, 185
No cloning theorem, 124–126, 134, 138
Non-commutative operation, 32, 58
NVision Imaging Technologies, 185
Oracle, 145
Ordered basis, 29
Orthonormal basis, 25
Parallelogram law, 22
Parallel universes, 187
Parity check, 137–139
Pauli, Wolfgang, 121
Pauli transformations, 121
Peirce, Charles Sanders, 97
Petzold, Charles, 101
Photosynthesis, 182
Podolsky, Boris, 76
Polarization, 11–15
Polarized filters, 12–15
Polynomial time, 142–144
Post-quantum cryptography, 175
Probability, 37–38
Probability amplitude, 29, 39, 52
Pseudorandom numbers, 15
P versus NP, 144
Pythagorean theorem, 20
Quadratic speedup, 180
Quantized spin, 15
Quantum annealing, 185–186
Quantum bit, 1, 49–50
Quantum bit-flip correction, 137–140
Quantum clock, 6, 14, 68–69, 78
Quantum Fourier transform, 174
Quantum key distribution (QKD), 53, 86, 175–176
Quantum parallelism, 141, 168–169
Quantum speedup, 141
Quantum supremacy, 184, 186–188
Quantum teleportation, 132–135, 176
Quantum tunneling, 186
Qubit. See Quantum bit
Query complexity, 145
Randomness, 10–11
Relative phase, 122
Repetition code, 136–137
Reversible gate, 102–108
Rivest, Ronald, 172
Roots of unity, 174
Rosen, Nathan, 76
RSA encryption, 172–174
RSA Laboratories, 143
Scalar multiplication, 21
Schrödinger, Irwin, 71, 85, 176
Schrödinger equation, 85
Sensitive dependence on initial conditions, 11, 77
Shamir, Adi, 172
Shannon, Claude, 89, 98, 105
Sheffer, Henry, 97
Sheffer stroke, 97
Shor, Peter, 144, 170, 172
Simon, Daniel, 169
Spin, 3
Spin state, 39
Spontaneous parametric down-conversion, 65
Spooky action at a distance, 69, 76–77
Standard basis, 26, 35
State, 39
Stern, Otto, 1
Stern-Gerlach apparatus, 2
Superdense coding, 129–132
Superluminal communication, 62–64
Teleportation. See Quantum teleportation
Tensor product, 57–58
Theory of relativity, 62, 76
Toffoli, Tommaso, 107
Truth tables
and, 90–91
exclusive or, 91
inclusive or, 91
Nand, 96
negation (not), 90
Turing, Alan, 171, 187–188
Turing machine, 188
Universal gate (classical), 101, 108, 110, 123
Universal quantum gate, 123–124
Vector, 19
addition, 21–22
dot product, 24
length, 20, 30
linear combination, 28
orthogonal, 23
space, 38
state, 39
tensor product, 57–58
unit, 20
Wineland, David, 183