Microsoft.Quantum.Canon namespace

This namespace contains a variety of useful operations and functions.

Description

To learn more about the operations in this namespace, see Higher-Order Control Flow and Quantum Fourier Transform.

Operations

Name	Summary
AndLadder	Performs a controlled "AND ladder" on a register of target qubits.
ApplyAnd	Inverts a given target qubit if and only if both control qubits are in the 1 state, using measurement to perform the adjoint operation.
ApplyCCNOTChain	Implements a cascade of CCNOT gates controlled on corresponding bits of two qubit registers, acting on the next qubit of one of the registers. Starting from the qubits at position 0 in both registers as controls, CCNOT is applied to the qubit at position 1 of the target register, then controlled by the qubits at position 1 acting on the qubit at position 2 in the target register, etc., ending with an action on the target qubit in position Length(nQubits)-1.
ApplyCNOTChain	Computes the parity of a register of qubits in-place.
ApplyCNOTChainWithTarget	Computes the parity of an array of qubits into a target qubit.
ApplyControlledOnBitString	Applies a unitary operation on the target register, controlled on a a state specified by a given bit mask.
ApplyControlledOnInt	Applies a unitary operation on the target register if the control register state corresponds to a specified positive integer.
ApplyDiagonalUnitary	Applies an array of complex phases to numeric basis states of a register of qubits.
ApplyFermionicSWAP	Applies the Fermionic SWAP.
ApplyIf	Applies an operation conditioned on a classical bit.
ApplyIfA	Applies a adjointable operation conditioned on a classical bit.
ApplyIfC	Applies a controllable operation conditioned on a classical bit.
ApplyIfCA	Applies a unitary operation conditioned on a classical bit.
ApplyIfElseB	Applies one of two operations, depending on the value of a classical bit.
ApplyIfElseBA	Applies one of two adjointable operations, depending on the value of a classical bit.
ApplyIfElseBC	Applies one of two controllable operations, depending on the value of a classical bit.
ApplyIfElseBCA	Applies one of two unitary operations, depending on the value of a classical bit.
ApplyIfElseR	Applies one of two operations, depending on the value of a classical result.
ApplyIfElseRA	Applies one of two adjointable operations, depending on the value of a classical result.
ApplyIfElseRC	Applies one of two controllable operations, depending on the value of a classical result.
ApplyIfElseRCA	Applies one of two unitary operations, depending on the value of a classical result.
ApplyIfOne	Applies an operation conditioned on a classical result value being one.
ApplyIfOneA	Applies an adjointable operation conditioned on a classical result value being one.
ApplyIfOneC	Applies a controllable operation conditioned on a classical result value being one.
ApplyIfOneCA	Applies a unitary operation conditioned on a classical result value being one.
ApplyIfZero	Applies an operation conditioned on a classical result value being zero.
ApplyIfZeroA	Applies an adjointable operation conditioned on a classical result value being zero.
ApplyIfZeroC	Applies a controllable operation conditioned on a classical result value being zero.
ApplyIfZeroCA	Applies a unitary operation conditioned on a classical result value being zero.
ApplyLowDepthAnd	Inverts a given target qubit if and only if both control qubits are in the 1 state, with T-depth 1, using measurement to perform the adjoint operation.
ApplyMultiControlledC	Applies a multiply controlled version of a singly controlled operation. The modifier C indicates that the single-qubit operation is controllable.
ApplyMultiControlledCA	Applies a multiply controlled version of a singly controlled operation. The modifier CA indicates that the single-qubit operation is controllable and adjointable.
ApplyOpRepeatedlyOver	Applies the same op over a qubit register multiple times.
ApplyOpRepeatedlyOverA	Applies the same op over a qubit register multiple times.
ApplyOpRepeatedlyOverC	Applies the same op over a qubit register multiple times.
ApplyOpRepeatedlyOverCA	Applies the same op over a qubit register multiple times.
ApplyP	Given a single-qubit Pauli operator, applies the corresponding operation to a single qubit.
ApplyPauli	Given a multi-qubit Pauli operator, applies the corresponding operation to a register.
ApplyPauliFromBitString	Applies a Pauli operator on each qubit in an array if the corresponding bit of a Boolean array matches a given input.
ApplyQuantumFourierTransform	Performs the Quantum Fourier Transform on a quantum register containing an integer in the little-endian representation.
ApplyReversedOpBigEndianA	> [!WARNING]
ApplyReversedOpBigEndianC	> [!WARNING]
ApplyReversedOpBigEndianCA	> [!WARNING]
ApplyReversedOpLittleEndianA	> [!WARNING]
ApplyReversedOpLittleEndianC	> [!WARNING]
ApplyReversedOpLittleEndianCA	> [!WARNING]
ApplyRippleCarryComparatorLE	> [!WARNING]
ApplySeriesOfOps	Applies a list of ops and their targets sequentially on an array.
ApplySeriesOfOpsA	Applies a list of ops and their targets sequentially on an array. (Adjoint)
ApplySeriesOfOpsC	Applies a list of ops and their targets sequentially on an array. (Controlled)
ApplySeriesOfOpsCA	Applies a list of ops and their targets sequentially on an array. (Adjoint + Controlled)
ApplyToEach	Applies a single-qubit operation to each element in a register.
ApplyToEachA	Applies a single-qubit operation to each element in a register. The modifier A indicates that the single-qubit operation is adjointable.
ApplyToEachC	Applies a single-qubit operation to each element in a register. The modifier C indicates that the single-qubit operation is controllable.
ApplyToEachCA	Applies a single-qubit operation to each element in a register. The modifier CA indicates that the single-qubit operation is controllable and adjointable.
ApplyToEachIndex	Applies a single-qubit operation to each indexed element in a register.
ApplyToEachIndexA	Applies a single-qubit operation to each indexed element in a register. The modifier A indicates that the single-qubit operation is adjointable.
ApplyToEachIndexC	Applies a single-qubit operation to each indexed element in a register. The modifier C indicates that the single-qubit operation is controllable.
ApplyToEachIndexCA	Applies a single-qubit operation to each indexed element in a register. The modifier CA indicates that the single-qubit operation is adjointable and controllable.
ApplyToElement	Applies an operation to a given element of an array.
ApplyToElementA	Applies an operation to a given element of an array.
ApplyToElementC	Applies an operation to a given element of an array.
ApplyToElementCA	Applies an operation to a given element of an array.
ApplyToFirstQubit	Applies an operation to the first qubit in the register.
ApplyToFirstQubitA	Applies an operation to the first qubit in the register. The modifier A indicates that the operation is adjointable.
ApplyToFirstQubitC	Applies operation op to the first qubit in the register. The modifier C indicates that the operation is controllable.
ApplyToFirstQubitCA	Applies operation op to the first qubit in the register. The modifier CA indicates that the operation is controllable and adjointable.
ApplyToFirstThreeQubits	Applies an operation to the first three qubits in the register.
ApplyToFirstThreeQubitsA	Applies an operation to the first three qubits in the register. The modifier A indicates that the operation is adjointable.
ApplyToFirstThreeQubitsC	Applies an operation to the first three qubits in the register. The modifier C indicates that the operation is controllable.
ApplyToFirstThreeQubitsCA	Applies an operation to the first three qubits in the register. The modifier CA indicates that the operation is controllable and adjointable.
ApplyToFirstTwoQubits	Applies an operation to the first two qubits in the register.
ApplyToFirstTwoQubitsA	Applies an operation to the first two qubits in the register. The modifier A indicates that the operation is adjointable.
ApplyToFirstTwoQubitsC	Applies an operation to the first two qubits in the register. The modifier C indicates that the operation is controllable.
ApplyToFirstTwoQubitsCA	Applies an operation to the first two qubits in the register. The modifier CA indicates that the operation is controllable and adjointable.
ApplyToHead	Applies an operation to the first element of an array.
ApplyToHeadA	Applies an operation to the first element of an array.
ApplyToHeadC	Applies an operation to the first element of an array.
ApplyToHeadCA	Applies an operation to the first element of an array.
ApplyToMost	Applies an operation to all but the last element of an array.
ApplyToMostA	Applies an operation to all but the last element of an array.
ApplyToMostC	Applies an operation to all but the last element of an array.
ApplyToMostCA	Applies an operation to all but the last element of an array.
ApplyToPartition	Applies a pair of operations to a given partition of a register into two parts.
ApplyToPartitionA	Applies a pair of operations to a given partition of a register into two parts. The modifier A indicates that the operation is adjointable.
ApplyToPartitionC	Applies a pair of operations to a given partition of a register into two parts. The modifier C indicates that the operation is controllable.
ApplyToPartitionCA	Applies a pair of operations to a given partition of a register into two parts. The modifier CA indicates that the operation is controllable and adjointable.
ApplyToRest	Applies an operation to all but the first element of an array.
ApplyToRestA	Applies an operation to all but the first element of an array.
ApplyToRestC	Applies an operation to all but the first element of an array.
ApplyToRestCA	Applies an operation to all but the first element of an array.
ApplyToSubregister	Applies an operation to a subregister of a register, with qubits specified by an array of their indices.
ApplyToSubregisterA	Applies an operation to a subregister of a register, with qubits specified by an array of their indices. The modifier A indicates that the operation is adjointable.
ApplyToSubregisterC	Applies an operation to a subregister of a register, with qubits specified by an array of their indices. The modifier C indicates that the operation is controllable.
ApplyToSubregisterCA	Applies an operation to a subregister of a register, with qubits specified by an array of their indices. The modifier CA indicates that the operation is controllable and adjointable.
ApplyToTail	Applies an operation to the last element of an array.
ApplyToTailA	Applies an operation to the last element of an array.
ApplyToTailC	Applies an operation to the last element of an array.
ApplyToTailCA	Applies an operation to the last element of an array.
ApplyWith	Given two operations, applies one as conjugated with the other.
ApplyWithA	Given two operations, applies one as conjugated with the other.
ApplyWithC	Given two operations, applies one as conjugated with the other.
ApplyWithCA	Given two operations, applies one as conjugated with the other.
ApplyWithInputTransformation	Given an operation that accepts some input, a function that returns an output compatible with that operation, and an input to that function, applies the operation using the function to transform the input to a form expected by the operation.
ApplyWithInputTransformationA	Given an operation that accepts some input, a function that returns an output compatible with that operation, and an input to that function, applies the operation using the function to transform the input to a form expected by the operation.
ApplyWithInputTransformationC	Given an operation that accepts some input, a function that returns an output compatible with that operation, and an input to that function, applies the operation using the function to transform the input to a form expected by the operation.
ApplyWithInputTransformationCA	Given an operation that accepts some input, a function that returns an output compatible with that operation, and an input to that function, applies the operation using the function to transform the input to a form expected by the operation.
ApproximateQFT	Apply the Approximate Quantum Fourier Transform (AQFT) to a quantum register.
ApproximatelyApplyDiagonalUnitary	Applies an array of complex phases to numeric basis states of a register of qubits, truncating small rotation angles according to a given tolerance.
ApproximatelyMultiplexPauli	Applies a Pauli rotation conditioned on an array of qubits, truncating small rotation angles according to a given tolerance.
ApproximatelyMultiplexZ	Applies a Pauli Z rotation conditioned on an array of qubits, truncating small rotation angles according to a given tolerance.
AssertHighestBit	> [!WARNING]
AssertLessThanPhaseLE	> [!WARNING]
AssertPhase	> [!WARNING]
CNOTChain	> [!WARNING]
CNOTChainTarget	> [!WARNING]
CX	Applies the controlled-X (CX) gate to a pair of qubits.
CY	Applies the controlled-Y (CY) gate to a pair of qubits.
CZ	Applies the controlled-Z (CZ) gate to a pair of qubits.
CascadeCCNOT	> [!WARNING]
CascadeCNOT	> [!WARNING]
Delay	Applies a given operation with a delay.
DelayA	Applies a given operation with a delay.
DelayC	Applies a given operation with a delay.
DelayCA	Applies a given operation with a delay.
HY	Applies the Y-basis analog to the Hadamard transformation that interchanges the Z and Y axes.
InPlaceMajority	> [!WARNING]
InPlaceXorBE	> [!WARNING]
InPlaceXorLE	> [!WARNING]
IntegerIncrementLE	> [!WARNING]
IntegerIncrementPhaseLE	> [!WARNING]
IterateThroughCartesianPower	Applies an operation for each index in the Cartesian power of an integer range.
IterateThroughCartesianProduct	Applies an operation for each index in the Cartesian product of several ranges.
ModularAddProductLE	> [!WARNING]
ModularAddProductPhaseLE	> [!WARNING]
ModularIncrementLE	> [!WARNING]
ModularIncrementPhaseLE	> [!WARNING]
ModularMultiplyByConstantLE	> [!WARNING]
MultiplexOperations	Applies an array of operations controlled by an array of number states.
MultiplexOperationsBruteForceFromGenerator	Applies multiply-controlled unitary operation $U$ that applies a unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.
MultiplexOperationsFromGenerator	Applies a multiply-controlled unitary operation $U$ that applies a unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.
MultiplexPauli	Applies a Pauli rotation conditioned on an array of qubits.
MultiplexZ	Applies a Pauli Z rotation conditioned on an array of qubits.
NoOp	Performs the identity operation (no-op) on an argument.
PermuteQubits	Permutes qubits by using the SWAP operation.
QFT	Performs the Quantum Fourier Transform on a quantum register containing an integer in the big-endian representation.
QFTLE	Performs the Quantum Fourier Transform on a quantum register containing an integer in the little-endian representation.
RAll0	Rotates the all-zeros state by a given phase.
RAll1	Rotates the all-ones state by a given phase.
Repeat	Repeats an operation a given number of times.
RepeatA	Repeats an operation a given number of times.
RepeatC	Repeats an operation a given number of times.
RepeatCA	Repeats an operation a given number of times.
SwapReverseRegister	Uses SWAP gates to Reversed the order of the qubits in a register.

Functions

Name	Summary
BigEndianToLittleEndian	> [!WARNING]
Bound	Given an array of operations acting on a single input, produces a new operation that performs each given operation in sequence.
BoundA	Given an array of operations acting on a single input, produces a new operation that performs each given operation in sequence. The modifier A indicates that all operations in the array are adjointable.
BoundC	Given an array of operations acting on a single input, produces a new operation that performs each given operation in sequence. The modifier C indicates that all operations in the array are controllable.
BoundCA	Given an array of operations acting on a single input, produces a new operation that performs each given operation in sequence. The modifier CA indicates that all operations in the array are adjointable and controllable.
CControlled	Given an operation op, returns a new operation which applies the op if a classical control bit is true. If false, nothing happens.
CControlledA	Given an operation op, returns a new operation which applies the op if a classical control bit is true. If false, nothing happens. The modifier A indicates that the operation is adjointable.
CControlledC	Given an operation op, returns a new operation which applies the op if a classical control bit is true. If false, nothing happens. The modifier C indicates that the operation is controllable.
CControlledCA	Given an operation op, returns a new operation which applies the op if a classical control bit is true. If false, nothing happens. The modifier CA indicates that the operation is controllable and adjointable.
Compose	Returns the composition of two functions.
ConjugatedBy	Given outer and inner operations, returns a new operation that conjugates the inner operation by the outer operation.
ConjugatedByA	Given outer and inner operations, returns a new operation that conjugates the inner operation by the outer operation.
ConjugatedByC	Given outer and inner operations, returns a new operation that conjugates the inner operation by the outer operation.
ConjugatedByCA	Given outer and inner operations, returns a new operation that conjugates the inner operation by the outer operation.
ControlledOnBitString	Returns a unitary operation that applies an oracle on the target register if the control register state corresponds to a specified bit mask.
ControlledOnInt	Returns a unitary operator that applies an oracle on the target register if the control register state corresponds to a specified positive integer.
CurriedOp	Returns a curried version of an operation on two inputs.
CurriedOpA	Returns a curried version of an operation on two inputs.
CurriedOpC	Returns a curried version of an operation on two inputs.
CurriedOpCA	Returns a curried version of an operation on two inputs.
DecomposeIntoTimeStepsCA	> [!WARNING]
DecomposedIntoTimeStepsCA	Returns an operation implementing the Trotter–Suzuki integrator for a given operation.
Delayed	Returns an operation that applies given operation with given argument.
DelayedA	Returns an operation that applies given operation with given argument.
DelayedC	Returns an operation that applies given operation with given argument.
DelayedCA	Returns an operation that applies given operation with given argument.
EmbedPauli	Given a single-qubit Pauli operator and the index of a qubit, returns a multi-qubit Pauli operator with the given single-qubit operator at that index and PauliI at every other index.
Fst	Given a pair, returns its first element.
Ignore	Ignores the output of an operation or function.
IsRangeEmpty	Returns true if and only if input range is empty.
IsResultOne	Tests if a given Result value is equal to One.
IsResultZero	Tests if a given Result value is equal to Zero.
LittleEndianToBigEndian	> [!WARNING]
MultiplexerBruteForceFromGenerator	Returns a multiply-controlled unitary operation $U$ that applies a unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.
MultiplexerFromGenerator	Returns a multiply-controlled unitary operation $U$ that applies a unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.
OperationPow	Raises an operation to a power.
OperationPowA	Raises an operation to a power. The modifier A indicates that the operation is adjointable.
OperationPowC	Raises an operation to a power. The modifier C indicates that the operation is controllable.
OperationPowCA	Raises an operation to a power. The modifier A indicates that the operation is controllable and adjointable.
RestrictedToSubregister	Restricts an operation to an array of indices of a register, i.e., a subregister.
RestrictedToSubregisterA	Restricts an operation to an array of indices of a register, i.e., a subregister. The modifier A indicates that the operation is adjointable.
RestrictedToSubregisterC	Restricts an operation to an array of indices of a register, i.e., a subregister. The modifier C indicates that the operation is controllable.
RestrictedToSubregisterCA	Restricts an operation to an array of indices of a register, i.e., a subregister. The modifier CA indicates that the operation is controllable and adjointable.
SinglyControlled	Given a controllable operation, returns a controlled version of that operation accepting exactly one control qubit.
SinglyControlledA	Given a controllable operation, returns a controlled version of that operation accepting exactly one control qubit.
Snd	Given a pair, returns its second element.
TransformedOperation	Given a function and an operation, returns a new operation whose input is transformed by the given function.
TransformedOperationA	Given a function and an operation, returns a new operation whose input is transformed by the given function.
TransformedOperationC	Given a function and an operation, returns a new operation whose input is transformed by the given function.
TransformedOperationCA	Given a function and an operation, returns a new operation whose input is transformed by the given function.
UncurriedOp	Given a function which returns operations, returns a new operation which takes both inputs as a tuple.
UncurriedOpA	Given a function which returns operations, returns a new operation which takes both inputs as a tuple. The modifier A indicates that the operations are adjointable.
UncurriedOpC	Given a function which returns operations, returns a new operation which takes both inputs as a tuple. The modifier C indicates that the operations are controllable.
UncurriedOpCA	Given a function which returns operations, returns a new operation which takes both inputs as a tuple. The modifier CA indicates that the operations are controllable and adjointable.
WeightOnePaulis	Returns an array of all weight-1 Pauli operators on a given number of qubits.
XOR	> [!WARNING]

User-defined types

Name	Summary
CCNOTop	The signature type of CCNOT gate.