Index
227
Quantum convolutional Singleton bound,
168
Quantum error-correcting code, 37
Quantum error group, 36, 37
Quantum error operators, 35
Quantum Hamming bound, 38
Quantum NOT gate, 20
Quantum operation, 32
Quantum Singleton bound, 37
Quantum synchronizable codes, 118
Quantum Z gate, 21
Quotient group, 214
Quotient ring, 51
R
Reduced matrix, 164
Reed–Solomon code, 138, 139
Riemann–Roch space, 54
Ring, 214
S
Self-dual basis of F q m over F q , 48
Sequence in metric spaces, 9
Simultaneous diagonalization theorem, 15
Stabilizer code, 36
State space of quantum systems, 17
State vector, 17
Steane’s code, 32
Steane’s construction, 64
Subgroup, 214
Submodule, 7
Subspace, 2
Subspaces spanned by a set, 2
Support of a divisor, The, 54
Symplectic weight, 36
T
Tensor product, 5, 6
Tensor product of linear transformations, 13
Theorem of spectral decomposition, 12
The Shor code, 29, 30
The (u|u + v) construction, 47
Three qubit bit flip code, 26
Three qubit phase flip code, 28, 29
Toffoli gate, 22
Tower of function fields, 113
Trace map, 34
Tracesymplectic form, 128
U
Unitary operator, 12
Universal quantum gates, 20
V
Valuation ring, 53
Vector space, 1
W
Weierstrass semigroup, 55
Weil differential, 54