Microsoft.Quantum.Arithmetic namespace

Warning

This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.

Please see https://aka.ms/qdk.api for the API documentation for the Modern QDK.

This namespace contains functions and operations used for coherently computing arithmetic.

Operations

Name	Summary
AddConstantFxP	Adds a classical constant to a quantum fixed-point number.
AddFxP	Adds two fixed-point numbers stored in quantum registers.
AddI	Automatically chooses between addition with carry and without, depending on the register size of ys.
ApplyLEOperationOnPhaseLE	Applies an operation that takes a PhaseLittleEndian user defined type register as input on a target register of type LittleEndian user defined type.
ApplyLEOperationOnPhaseLEA	Applies an operation that takes a PhaseLittleEndian user defined type register as input on a target register of type LittleEndian user defined type.
ApplyLEOperationOnPhaseLEC	Applies an operation that takes a PhaseLittleEndian user defined type register as input on a target register of type LittleEndian user defined type.
ApplyLEOperationOnPhaseLECA	Applies an operation that takes a PhaseLittleEndian user defined type register as input on a target register of type LittleEndian user defined type.
ApplyMajorityInPlace	Applies the three-qubit majority operation in-place on a register of qubits.
ApplyPhaseLEOperationOnLE	Applies an operation that takes a LittleEndian user defined type register as input on a target register of type PhaseLittleEndian user defined type.
ApplyPhaseLEOperationOnLEA	Applies an operation that takes a LittleEndian user defined type register as input on a target register of type PhaseLittleEndian user defined type.
ApplyPhaseLEOperationOnLEC	Applies an operation that takes a LittleEndian user defined type register as input on a target register of type PhaseLittleEndian user defined type.
ApplyPhaseLEOperationOnLECA	Applies an operation that takes a LittleEndian user defined type register as input on a target register of type PhaseLittleEndian user defined type.
ApplyReversedOpBE	Applies an operation that takes big-endian input to a register encoding an unsigned integer using little-endian format.
ApplyReversedOpBEA	Applies an operation that takes big-endian input to a register encoding an unsigned integer using little-endian format.
ApplyReversedOpBEC	Applies an operation that takes big-endian input to a register encoding an unsigned integer using little-endian format.
ApplyReversedOpBECA	Applies an operation that takes big-endian input to a register encoding an unsigned integer using little-endian format.
ApplyReversedOpLE	Applies an operation that takes little-endian input to a register encoding an unsigned integer using big-endian format.
ApplyReversedOpLEA	Applies an operation that takes little-endian input to a register encoding an unsigned integer using big-endian format.
ApplyReversedOpLEC	Applies an operation that takes little-endian input to a register encoding an unsigned integer using big-endian format.
ApplyReversedOpLECA	Applies an operation that takes little-endian input to a register encoding an unsigned integer using big-endian format.
ApplyXorInPlace	Applies a bitwise-XOR operation between a classical integer and an integer represented by a register of qubits.
AssertAllZeroFxP	Asserts that a quantum fixed-point number is initialized to zero.
AssertMostSignificantBit	Asserts that the most significant qubit of a qubit register representing an unsigned integer is in a particular state.
AssertPhaseLessThan	Asserts that the number encoded in PhaseLittleEndian is less than value.
AssertProbInt	Asserts that the probability of a specific state of a quantum register has the expected value.
Carry	Implements a reversible carry gate. Given a carry-in bit encoded in qubit carryIn and two summand bits encoded in summand1 and summand2, computes the bitwise xor of carryIn, summand1 and summand2 in the qubit summand2 and the carry-out is xored to the qubit carryOut.
CompareGTI	Wrapper for integer comparison: result = x > y.
CompareGTSI	Wrapper for signed integer comparison: result = xs > ys.
CompareGreaterThanFxP	Compares two fixed-point numbers stored in quantum registers, and controls a flip on the result.
CompareUsingRippleCarry	This operation tests if an integer represented by a register of qubits is greater than another integer, applying an XOR of the result onto an output qubit.
ComputeReciprocalFxP	Computes the reciprocal of a number stored in a quantum register with the fixed-point representation.
ComputeReciprocalI	Computes the reciprocal 1/x for an unsigned integer x using integer division. The result, interpreted as an integer, will be floor(2^(2*n-1) / x).
CopyMostSignificantBit	Copies the most significant bit of a qubit register from representing an unsigned integer into the qubit target.
DivideI	Divides two quantum integers.
EvaluateEvenPolynomialFxP	Evaluates an even polynomial in a fixed-point representation.
EvaluateOddPolynomialFxP	Evaluates an odd polynomial in a fixed-point representation.
EvaluatePolynomialFxP	Evaluates a polynomial in a fixed-point representation.
GreaterThan	Applies a greater-than comparison between two integers encoded into qubit registers, flipping a target qubit based on the result of the comparison.
IncrementByInteger	Increments an unsigned quantum register by a classical integer, using phase rotations.
IncrementByModularInteger	Performs a modular increment of a qubit register by an integer constant.
IncrementPhaseByInteger	Increments an unsigned quantum register by a classical integer, using phase rotations.
IncrementPhaseByModularInteger	Performs a modular increment of a qubit register by an integer constant.
Invert2sSI	Inverts a given integer modulo 2's complement.
InvertFxP	Computes the additive inverse of fp.
MAJ	This applies the in-place majority operation to 3 qubits.
MeasureFxP	Measure a fixed-point number, returns its value as Double, and resets all the register to zero.
MeasureInteger	Measures the content of a quantum register and converts it to an integer. The measurement is performed with respect to the standard computational basis, i.e., the eigenbasis of PauliZ.
MultiplyAndAddByModularInteger	Performs a modular multiply-and-add by integer constants on a qubit register.
MultiplyAndAddPhaseByModularInteger	The same as MultiplyAndAddByModularInteger, but assumes that the summand encodes integers in QFT basis.
MultiplyByModularInteger	Performs modular multiplication by an integer constant on a qubit register.
MultiplyFxP	Multiplies two fixed-point numbers in quantum registers.
MultiplyI	Multiply integer xs by integer ys and store the result in result, which must be zero initially.
MultiplySI	Multiply signed integer xs by signed integer ys and store the result in result, which must be zero initially.
PrepareFxP	Initialize a quantum fixed-point number to a classical constant.
ReflectAboutInteger	Reflects a quantum register about a given classical integer.
RippleCarryAdderCDKM	Reversible, in-place ripple-carry addition of two integers.
RippleCarryAdderD	Reversible, in-place ripple-carry addition of two integers.
RippleCarryAdderNoCarryTTK	Reversible, in-place ripple-carry addition of two integers without carry out.
RippleCarryAdderTTK	Reversible, in-place ripple-carry addition of two integers. Given two $n$-bit integers encoded in LittleEndian registers xs and ys, and a qubit carry, the operation computes the sum of the two integers where the $n$ least significant bits of the result are held in ys and the carry out bit is xored to the qubit carry.
SquareFxP	Squares a fixed-point number.
SquareI	Computes the square of the integer xs into result, which must be zero initially.
SquareSI	Square signed integer xs and store the result in result, which must be zero initially.
SubtractFxP	Computes minuend - subtrahend and stores the difference in minuend.
Sum	Implements a reversible sum gate. Given a carry-in bit encoded in qubit carryIn and two summand bits encoded in summand1 and summand2, computes the bitwise xor of carryIn, summand1 and summand2 in the qubit summand2.

Functions

Name	Summary
ApplyFunctionWithLookupTable	This function creates a lookup table operator for the function that you want to approximate, as well as the parameters required to make the two FixedPoint registers that need to be used as inputs to the operator.
BigEndianAsLittleEndian	Converts a BigEndian qubit register to a LittleEndian qubit register by reversing the qubit ordering.
IdenticalFormatFactFxP	Assert that all fixed-point numbers in the provided array have identical point positions and qubit numbers.
IdenticalPointPosFactFxP	Assert that all fixed-point numbers in the provided array have identical point positions when counting from the least- significant bit. I.e., number of bits minus point position must be constant for all fixed-point numbers in the array.
LittleEndianAsBigEndian	Converts a LittleEndian qubit register to a BigEndian qubit register by reversing the qubit ordering.
ReversedOpBE	Given an operation that takes a big-endian input, returns a new operation that takes a little-endian input.
ReversedOpBEA	Given an operation that takes a big-endian input, returns a new operation that takes a little-endian input.
ReversedOpBEC	Given an operation that takes a big-endian input, returns a new operation that takes a little-endian input.
ReversedOpBECA	Given an operation that takes a big-endian input, returns a new operation that takes a little-endian input.
ReversedOpLE	Given an operation that takes a little-endian input, returns a new operation that takes a big-endian input.
ReversedOpLEA	Given an operation that takes a little-endian input, returns a new operation that takes a big-endian input.
ReversedOpLEC	Given an operation that takes a little-endian input, returns a new operation that takes a big-endian input.
ReversedOpLECA	Given an operation that takes a little-endian input, returns a new operation that takes a big-endian input.

User-defined types

Name	Summary
BigEndian	Register that encodes an unsigned integer in big-endian order. The qubit with index 0 encodes the highest bit of an unsigned integer.
FixedPoint	Represents a register of qubits encoding a fixed-point number. Consists of an integer that is equal to the number of qubits to the left of the binary point, i.e., qubits of weight greater than or equal to 1, and a quantum register.
FunctionWithLookupTable	The return type when making a lookup table. This contains the operation that makes the lookup table circuit, as well as all the parameters required to make the two FixedPoint registers that need to be used as inputs and outputs to the operator.
LittleEndian	Register that encodes an unsigned integer in little-endian order. The qubit with index 0 encodes the lowest bit of an unsigned integer.
PhaseLittleEndian	Little-endian unsigned integers in QFT basis.
SignedLittleEndian	Type of a signed integer stored in little endian (see LittleEndian). Negative numbers are stored using two's complement.