Quantum Gates#

Due to the physical nature of quantum systems, all operations with quantum information are subject to a few constraints:
- All operations must be norm-preserving because they take a quantum state as an input and also produce a quantum state as an output and all quantum states must have a norm of \(1\).
- With the exception of measurement, all operations must be linear.
- With the exception of measurement, all operations must be reversible.

Since quantum states are complex vectors, all of the above criteria are satisfied by unitary matrices, i.e. every quantum operation can be represented by a unitary matrix and every unitary matrix represents some quantum operation.