Quantum Computational Basis Vectors
Quantum Computational Basis Vectors
A quantum computer is based on the notion of a quantum bit (or qubit). A qubit has two fundamental vector states denoted by and . These states represent basis vectors in the complex two-dimensional vector space (equivalent to the Hilbert space ). A quantum computer manipulates these states by unitary matrix transformations. Two qubits are defined in the four-dimensional complex vector space =⊗ associated with four basis vectors
|0〉=
1 |
0 |
|1〉=
0 |
1 |
2
2
4
2
2
00=0⊗0=
,01=0⊗1=
,10=1⊗0=
,11=1⊗1=
.
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
More generally, quantum bits have basis states, defined by 〉, where =0 or , .
n
n
2
|
ϵ
1
ϵ
2
…ϵ
n
ϵ
i
1
0≤i≤-1
n
2