# nLab quantum logic gate

Contents

### Context

#### Monoidal categories

monoidal categories

# Contents

## Idea

Analogously to how a classical logic gate is a function between (finite) sets of tuples of bits (truth values), so a quantum logic gate is a (unitary) linear operator on (finite-dimensional) Hilbert spaces of tensor products of qbits:

Specifically, one calls such a linear map a quantum gate if it is thought of as potentially implemented as a basic operation performed by a quantum computing machine.

As such, typical quantum logic gates operate on a small number of qbits, with more complicated such linear maps obtained by composing a given set of quantum logic gates into quantum logic circuits. Such compilation is hence one model of quantum computation.

## Examples

The first examples are linearizations of classical logic gates, or rather of their reversible versions:

NOT:

XOR and CNOT:

AND:

The following examples have no classical analog:

(…)

## References

The notion of quantum logic gates and quantum circuits originates with