# Microsoft.Quantum.Synthesis namespace

This namespace contains functions and operations for synthesizing quantum operations based on permutations and Boolean functions.

## Operations

Name Summary
Apply1C Given a single-qubit Clifford operator, applies the corresponding operation to a single qubit.
ApplyPermutationUsingDecomposition Permutes the amplitudes in a quantum state given a permutation using decomposition-based synthesis.
ApplyPermutationUsingDecompositionWithVariableOrder Permutes the amplitudes in a quantum state given a permutation using decomposition-based synthesis.
ApplyPermutationUsingTransformation Permutes the amplitudes in a quantum state given a permutation using transformation-based synthesis.
ApplyTransposition
ApplyUnitary Applies gate defined by a 2ⁿ × 2ⁿ unitary matrix.
ApplyXControlledOnTruthTable Applies the X operation operation on target, if the Boolean function func evaluates to true for the classical assignment in controlRegister.
ApplyXControlledOnTruthTableWithCleanTarget Applies the X operation operation on target, if the Boolean function func evaluates to true for the classical assignment in controlRegister.

## Functions

Name Summary
Action1C Returns the action by conjugation of a single-qubit Clifford operator on a single-qubit Pauli operator.
EqualityFact1C Requires that a single-qubit Clifford operator has the expected value.
Identity1C Returns a representation of the identity as a single-qubit Clifford operator.
IdentityFact1C Requires that a single-qubit Clifford operator is equal to the identity.
Inverse1C Returns the inverse of a single-qubit Clifford operators.
PauliAsSingleQubitClifford Returns a representation of a single-qubit Pauli operator as a single-qubit Clifford operator that acts by conjugation.
SingleQubitCliffordAsOperation Returns a representation of a single-qubit Clifford operator as an operation acting on a single qubit.
Times1C Returns the product of two single-qubit Clifford operators.
_TwoLevelDecomposition

## User-defined types

Name Summary
SingleQubitClifford An element of the single-qubit Clifford group.