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Quantum register

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A quantum register is a system comprising multiple qubits and is the quantum analog of the classical processor register.

Contents

Definition

An n size quantum register is a quantum system comprising n qubits.

The Hilbert space, H , in which the data stored in a quantum register is H = H n 1 H n 2 H 0 .

Quantum vs. Classical Register

First, there's a conceptual difference between the quantum and classical register. An n size classical register refers to an array of n flip flops. An n size quantum register is merely a collection of n qubits.

Moreover, while an n size classical register is able to store a single value of the 2 n possibilities spanned by n classical pure bits, a quantum register is able to store all 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 ) accordingly.

If we consider 2 pure qubits in superpositions | a 0 = 1 2 ( | 0 + | 1 ) and | a 1 = 1 2 ( | 0 | 1 ) , using the quantum register definition | a = | a 0 | a 1 = 1 2 ( | 00 | 01 + | 10 | 11 ) it follows that it is capable of storing all the possible values spanned by two qubits simultaneously.

References

Quantum register Wikipedia