In fact, many physical realizations of quantum computers can not perform arbitrary unitary operations, but can only perform the **standard set** of universal gates which consists of the **Hadamard, phase, controlled-NOT, and $\pi/8$ gates**.

## QCQI notes: Why single qubit and CNOT gates are universal?

We know that the combination of single-qubit and CNOT gates are universal, they can be used to implement arbitrary operation on *n* qubits. In this post, we go through this part of QCQI (section 4.5.2).

## QCQI notes: How to decompose unitary matrices and quantum gates?

Any unitary operator \(U\), can be decomposed into a product of two-level unitary matrices. Here we introduce the universal method of this procedure.

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