<p>Are there any <a href="https://en.wikipedia.org/wiki/Quantum_gate#Universal_quantum_gates" rel="nofollow noreferrer">universal quantum gates</a>?</p>

<p>Not for single gates.</p>

<p>{NAND} may also be represented as two gates {AND, NOT}, and remains a minimally functionally complete set of classical gates.</p>

<p>The Hadamard gate and Toffoli gate are one minimal set of universal quantum gates.</p>

CC BY-SA 3.0
2018-01-24T19:31:08.590Z
Wouldn't this imply that $U = H \otimes \mathrm{TOFFOLI}$ is an example of a single unitary operator which is (approximately) universal for quantum computation? One could similarly consider $U' = T \otimes H \otimes \mathrm{CNOT}$.
Niel de Beaudrap
CC BY-SA 3.0
2018-01-28T22:12:00.817Z
The answer directly contradicts the Wikipedia article it links to, which gives explicit examples of universal quantum single gates.
Emil Jeřábek
CC BY-SA 3.0
2018-01-24T12:28:33.160Z
2018-01-24T12:28:33.160Z
Nope
<p>In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates. </p>

<p>Is there an equivalent for quantum computing circuit? It should be possible imho to have such a complete set because any rotation ob Bloch sphere is reducible to <a href="https://en.wikipedia.org/wiki/Euler_angles" rel="nofollow noreferrer">Euler angles</a> based rotation matrices: $R=X(\alpha)Y(\beta)Z(\gamma)$. </p>

CC BY-SA 3.0
2018-04-04T00:34:59.877Z
You can ask this question at: https://quantumcomputing.stackexchange.com/ .
Rob
<quantum-computing>
What would be a complete QC circuit?
0x90
# What would be a complete QC circuit?

(Asked by: username_0 on 2018-01-23)

In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates.

Is there an equivalent for quantum computing circuit? It should be possible imho to have such a complete set because any rotation ob Bloch sphere is reducible to [Euler angles](https://en.wikipedia.org/wiki/Euler_angles) based rotation matrices: $R=X(\alpha)Y(\beta)Z(\gamma)$.

**Tags:** quantum-computing

> **Comments:**
> **username_1**: You can ask this question at: https://quantumcomputing.stackexchange.com/ .  

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## 1 answers

### Answer by username_2 on 2018-01-24. Score: -3

Are there any [universal quantum gates](https://en.wikipedia.org/wiki/Quantum_gate#Universal_quantum_gates)?

Not for single gates.

{NAND} may also be represented as two gates {AND, NOT}, and remains a minimally functionally complete set of classical gates.

The Hadamard gate and Toffoli gate are one minimal set of universal quantum gates.

> **Comments:**
> **username_3**: Wouldn't this imply that $U = H \otimes \mathrm{TOFFOLI}$ is an example of a single unitary operator which is (approximately) universal for quantum computation? One could similarly consider $U' = T \otimes H \otimes \mathrm{CNOT}$.  
> **username_4**: The answer directly contradicts the Wikipedia article it links to, which gives explicit examples of universal quantum single gates.  

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