Quantum Register in Quantum Computing

Quantum Register:

A quantum register is composed of several qubits. The size of the register is determined by the number of qubits. For example, a quantum register of size 4 can store individual numbers from 0 to 15. At any particular time, the 4-qubits can be in any one of 16 possible configurations:

0000, 0001, 0010, … … … … … 1111

Thus, a 4-qubit register can be represented in a superposition of the above 16 states:

|Ψ>=c₀ |0000> + c₁ | 0001 > + c₂ |0010>, … … … + c₁₄ |1110> + c₁₅ |1111>

Where the numbers c₀, c₁, c₂, … …, c₁₅ are complex coefficients such that

A unique advantage of the quantum system is that a linear increase in the number of qubits in a register leads to exponential growth in the state space of the register. The state of a quantum register with m qubits can be represented as 2^m-dimensional vector in complex vector space. Since all the states of a quantum register can be in all of its states at the same time. This allows parallel processing capability to solve certain problems in a time that is may-fold faster than that is possible in classical computers.