Quantum register

In quantum computing, a quantum registeris a system comprising multiple qubits. It is the quantum analog of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. In quantum computing, a quantum registeris a system comprising multiple qubits. It is the quantum analog of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register. An n {displaystyle n} size quantum register is a quantum system comprising n {displaystyle n} qubits. The Hilbert space, H {displaystyle {mathcal {H}}} , in which the data 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}}}} . First, there's a conceptual difference between the quantum and classical register.An n {displaystyle n} size classical register refers to an array of n {displaystyle n} flip flops. An n {displaystyle n} size quantum register is merely a collection of n {displaystyle n} qubits. Moreover, while an n {displaystyle n} size classical register is able to store a single value of the 2 n {displaystyle 2^{n}} possibilities spanned by n {displaystyle n} classical pure bits, a quantum register is able to store all 2 n {displaystyle 2^{n}} possibilities spanned by quantum pure qubits in the same time. For example, consider a 2-bit-wide register. A classical register is able to store only one of the possible values represented by 2 bits - 00 , 01 , 10 , 11 ( 0 , 1 , 2 , 3 ) {displaystyle 00,01,10,11quad (0,1,2,3)} accordingly. If we consider 2 pure qubits in superpositions | a 0 ⟩ = 1 2 ( | 0 ⟩ + | 1 ⟩ ) {displaystyle |a_{0} angle ={frac {1}{sqrt {2}}}(|0 angle +|1 angle )} and | a 1 ⟩ = 1 2 ( | 0 ⟩ − | 1 ⟩ ) {displaystyle |a_{1} angle ={frac {1}{sqrt {2}}}(|0 angle -|1 angle )} , using the quantum register definition | a ⟩ = | a 0 ⟩ ⊗ | a 1 ⟩ = 1 2 ( | 00 ⟩ − | 01 ⟩ + | 10 ⟩ − | 11 ⟩ ) {displaystyle |a angle =|a_{0} angle otimes |a_{1} angle ={frac {1}{2}}(|00 angle -|01 angle +|10 angle -|11 angle )} it follows that it is capable of storing all the possible values spanned by two qubits simultaneously.