Phase shift gate

In quantum computing and specifically the quantum circuit model of computation, a quantum gate (or quantum logic gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits.

Unlike many classical logic gates, quantum logic gates are reversible. However, it is possible to perform classical computing using only reversible gates. For example, the reversible Toffoli gate can implement all Boolean functions, often at the cost of having to use ancillary bits. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits.

Quantum logic gates are represented by unitary matrices. The most common quantum gates operate on spaces of one or two qubits, just like the common classical logic gates operate on one or two bits. As matrices, quantum gates can be described by ${\displaystyle 2^{n}\times 2^{n}}$ sized unitary matrices, where ${\displaystyle n}$ is the number of qubits that the gate act on. The variables that the gates act upon, the quantum states, are vectors in ${\displaystyle 2^{n}}$ complex dimensions, where ${\displaystyle n}$ again is the number of qubits of the variable: The base vectors are the possible outcomes if measured, and a quantum state is a linear combinations of these outcomes.

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