A Deutsch Gate, which is a specific quantum gate, is a rudimentary quantum circuit operating on a small number of qubits. They represent what analogues are for quantum computers as to what classical logic gates are for conventional digital computers.

A quantum logic gate is reversible, and can be mapped to classical logic gates, such as the Toffoli gate, which can provide reversibility, and can be mapped onto quantum logic gates. These are represented by unitary matrices, and operate on spaces of one or two qubits. As matrices, quantum gates can be described by 2x2 or 4x4 matrices with orthonormal rows.

A single-gate set of universal quantum gates can also be formulated using the three-qubit Deutsch gate. The Toffoli gate is reducible to the Deutsch gate, meaning that all classical logic operations can be performed on a universal quantum computer.

The Deutsch gate differs from Hadamard gate, the phase shifter gates, controlled gates, and uncontrolled gates, as it is a specific type of universal quantum gate that the Toffoli gate is reducible to.

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### Further Resources

Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms

Xiao-Feng Shi

October 5, 2017

Relationship between Toffoli gate and Deutsch gate

Web

August 27, 2015