# Multi-Qubit Systems in Quantum Computing

## Multi-Qubit Systems:

A Multi-Qubit Quantum System can be formed by putting together several known quantum subsystems. A subsystem based on a single qubit is generally described by its state which is defined to be a unit vector in some complex Hilbert space.

The mathematical framework for describing a multi-qubit system utilizes the concept of a tensor product of vector spaces. The state space of the ith constituent of such a system is given by a separable Hilbert space Hi. Each Hilbert space Hi has an orthonormal basis given by –

{ |i, ki > ki = 1, 2, … }, i = 1, 2, …, n

The state space of the multi-bit system is then the tensor product space H defined by

H = H1 ⊗ H2 ⊗ … ⊗ Hn