In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register.
Definition
It is usually assumed that the register consists of qubits. It is also generally assumed that registers are not density matrices, but that they are pure, although the definition of "register" can be extended to density matrices. An n {\displaystyle n} size quantum register is a quantum system comprising n {\displaystyle n} pure qubits. The Hilbert space, H {\displaystyle {\mathcal {H}}} , in which the data is stored in a quantum register is given by H = H n − 1 ⊗ H n − 2 ⊗ … ⊗ H 0 {\displaystyle {\mathcal {H}}={\mathcal {H_{n-1}}}\otimes {\mathcal {H_{n-2}}}\otimes \ldots \otimes {\mathcal {H_{0}}}} where ⊗ {\displaystyle \otimes } is the tensor product. The number of dimensions of the Hilbert spaces depends on what kind of quantum systems the register is composed of. Qubits are 2-dimensional complex spaces ( C 2 {\displaystyle \mathbb {C} ^{2}} ), while qutrits are 3-dimensional complex spaces ( C 3 {\displaystyle \mathbb {C} ^{3}} ), etc. For a register composed of N number of d-dimensional (or d-level) quantum systems we have the Hilbert space H = ( C d ) ⊗ N = C d ⊗ C d ⊗ ⋯ ⊗ C d ⏟ N times ≅ C d N . {\displaystyle {\mathcal {H}}=(\mathbb {C} ^{d})^{\otimes N}=\underbrace {\mathbb {C} ^{d}\otimes \mathbb {C} ^{d}\otimes \dots \otimes \mathbb {C} ^{d}} _{N{\text{ times}}}\cong \mathbb {C} ^{d^{N}}.}
… excerpt ends here. Continue reading the full article.
