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Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices. In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits.
A logical qubit specifies how a single qubit should behave in a quantum algorithm, subject to quantum logic operations which can be built out of quantum logic gates. However, issues in current technologies preclude single two-state quantum systems , which can be used as physical qubits, from reliably encoding and retaining this information for ...
Transversal gates, which perform a gate between two logical qubits each of which is encoded in N physical qubits by pairing up the physical qubits of each encoded qubit ("code block"), and performing independent gates on each pair, can be used to perform fault tolerant but not universal quantum computation because they guarantee that errors don ...
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Arbitrary single-qubit phase shift gates () are natively available for transmon quantum processors through timing of microwave control pulses. [13] It can be explained in terms of change of frame. [14] [15] As with any single qubit gate one can build a controlled version of the phase shift gate.
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Global single qubit gates on all the atoms can be done either by applying a microwave field for qubits encoded in the Hyperfine manifold such as Rb and Cs or by applying an RF magnetic field for qubits encoded in the nuclear spin such as Yb and Sr. Focused laser beams can be used to do single-site one qubit rotation using a lambda-type three level Raman scheme (see figure).
More recent motivation comes from quantum computing. In quantum mechanics the quantum state can evolve in two ways: by Schrödinger's equation (unitary transformations), or by their collapse. Logic operations for quantum computers, of which the Toffoli gate is an example, are unitary transformations and therefore evolve reversibly. [2]
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