Operations

Operation{N,M}

Abstract supertype for all the quantum operations acting on N qubits and M classical bits.

Methods

iswrapper, isunitary, numbits, numqubits, opname

See also

AbstractGate

cregsizes(operation)
cregsizes(operationtype)

Length of the classicalregisters the given operation acts on.

See also

qregsizes, numqubits, numbits

getparam(operation, name)

Value of the corresponding parameter in the given parametric operation.

Examples

getparam(GateRX(π/8), :θ)

See also

parnames, numparams, getparams

getparams(operation)

Value of the parameters in the given parametric operation.

Examples

getparam(GateU(π/8, 3.1, sqrt(2)))

See also

parnames, numparams, getparam

hilbertspacedim(operation)
hilbertspacedim(operationtype)
hilbertspacedim(N::Integer)

Hilbert space dimension for the given operation. For an operation actiing on N qubits, it is 2^N.

Examples

hilbertspacedim(Operation{2, 1})
hilbertspacedim(GateH)
hilbertspacedim(GateH())
hilbertspacedim(GateRX)
hilbertspacedim(GateCX)
hilbertspacedim(4)

See also

numqubits, numbits, Operation, AbstractGate

iswrapper(operation)
iswrapper(operationtype)

Checks if a given operation is a wrapper or not.

Examples

iswrapper(Control)
iswrapper(GateX)
iswrapper(GateSX) # SX is defined as Power(1//2, GateX())
iswrapper(GateCX) # CX is defined as Control(1, GateX())

See also

isunitary, getoperation

numparams(operation)
numparams(operationtype)

Number of parameters for the given parametric operation. Zero for non parametric operations.

By default it returns the number of fields of the operations.

Examples

julia> numparams(GateH)
0

julia> numparams(GateU)
4

julia> numparams(GateRX)
1

julia> numparams(Measure)
0

See also

parnames, getparam

parnames(operation)
parnames(operationtype)

Name of the parameters allowed for the given operation.

By default it returns the fieldnames of the operation type.

Examples

parnames(GateH)
parnames(GateRX)
parnames(GateCRX)
parnames(Measure)

See also

numparams, getparam

qregsizes(operation)
qregsizes(operationtype)

Length of the quantum registers the given operation acts on.

Examples

julia> qregsizes(GateRX(0.1))
(1,)

julia> qregsizes(GateCRX(0.1))
(1, 1)

julia> qregsizes(QFT(4))
(4,)

See also

cregsizes, numqubits, numbits

GATES

List of gates provided by the library.

Single qubit gates

GateID, GateX, GateY, GateZ, GateH, GateS, GateSDG, GateT, GateTDG, GateSX, GateSXDG.

Single qubit parametric gates

GateU, GateP, GateRX, GateRY, GateRZ, GateR, GateU1, GateU2, GateU3.

Two qubit gates

GateCX, GateCY, GateCZ, GateCH, GateSWAP, GateISWAP, GateCS, GateCSDG, GateCSX, GateCSXDG, GateECR, GateDCX,

Two qubit parametric gates

GateCP, GateCU, GateCRX, GateCRY, GateCRZ, GateRXX, GateRYY, GateRZZ, GateRZX, GateXXplusYY, GateXXminusYY.

Multi qubit Gates

GateCCX, GateC3X, GateCCP, GateCSWAP.

Generalized gates

These defines an unitary quantum operation on non fixed number of qubits.

See GENERALIZED for a list of them.

Operations

See OPERATIONS for a complete list of operations.

GENERALIZED

Definition of complex unitary quantum opteration on a not fixed number of qubits, or on multiple groups of qubits (registers).

Usually they are initialized with the number of qubits they operate on, or with the size of each group of qubits they act on

QFT, PhaseGradient

OPERATIONS

Phases and other unitaries

See GATES for a complete list unitary gates.

GateCustom

For gate definitions and calls, see GateDecl and GateCall

Other circuits elements

Barrier, IfStatement

Modifiers

Control, Parallel, Power, Inverse

Non-unitary operations

Measure, Reset

Algorithms or complex gate builders

See GENERALIZED for a complete list of generalized gates or algorithms.

AbstractGate{N} <: Operation{N,0}

Supertype for all the N-qubit unitary gates.

See also hilbertspacedim, inverse, isunitary, matrix, numqubits, opname

matrix(gate)

Matrix associated to the given gate.

Examples

Matrix of a simple gate

julia> matrix(GateH())
2×2 Matrix{Float64}:
 0.707107   0.707107
 0.707107  -0.707107

julia> matrix(GateRX(π/2))
2×2 Matrix{ComplexF64}:
 0.707107+0.0im            0.0-0.707107im
      0.0-0.707107im  0.707107+0.0im

julia> matrix(GateCX())
4×4 Matrix{Float64}:
 1.0  0.0  0.0  0.0
 0.0  1.0  0.0  0.0
 0.0  0.0  0.0  1.0
 0.0  0.0  1.0  0.0

Control(numcontrols, gate) <: AbstractGate

Control modifier, similar to OpenQASM 3.0 ctrl @ gate. It wraps a given gate and adds a number of controls to it.

See also Power, Inverse, getoperation, iswrapper, numcontrols, numtargets.

Examples

julia> Control(1, GateX())
CX

julia> Control(3, GateH())
C₃H

julia> Control(24, GateSWAP())
C₂₄SWAP

Decomposition

The default decomposition of a Control gate is build by applying recursively Lemma 7.3 of [1]. This requires to decompose multicontrolled-$X$ gates, which is done recursively, according to Lemma 7.2 and 7.3 of [1].

Here we give a simple example of a decomposition of a $C_5T$ gate.

julia> decompose(Control(3,GateT()))
4-qubit circuit with 9 instructions:
├── C(Z^(1//8)) @ q[3], q[4]
├── C₂X @ q[1:2], q[3]
├── C((Z^(1//8))†) @ q[3], q[4]
├── C₂X @ q[1:2], q[3]
├── C(Z^(1//16)) @ q[2], q[4]
├── CX @ q[1], q[2]
├── C((Z^(1//16))†) @ q[2], q[4]
├── CX @ q[1], q[2]
└── C(Z^(1//16)) @ q[1], q[4]

Control(gate)

Build a controlled gate with 1 control.

control([numcontrols], gate)

Build a multicontrolled gate.

The number of controls can be omitted to be lazily evaluated later.

Examples

Standard examples, with all the arguments spefcified.

julia> control(1, GateX())
CX

julia> control(2, GateX())
C₂X

julia> control(3, GateCH())
C₄H

numcontrols(control)

Number of controls of a given multicontrolled gate.

See also

Control, numtargets, numqubits

numtargets(control)

Get the number of targets of a given multicontrolled gate.

Examples

numcontro

See also

Control, numtargets, numqubits

Inverse(operation)

Inverse of the wrapped quantum operation.

The inversion is not performed right away, but only when the circuit is cached or executed.

Some simplifications are already carried out at construction, for example, Inverse(Inverse(op)) is simplified as Inverse(op).

See also inverse, iswrapper, Control, Power.

Examples

julia> Inverse(GateX())
X†

julia> Inverse(GateH())
H†

julia> Inverse(GateSX())
SX†

julia> Inverse(GateCSX())
(CSX)†

julia> Inverse(QFT(4))
QFT†

Decomposition

Decomposition of the inverse is carring out by inverting the decomposition of the wrapped operation.

julia> decompose(Inverse(GateCSX()))
2-qubit circuit with 3 instructions:
├── H @ q[2]
├── CU1(-1π/2) @ q[1], q[2]
└── H @ q[2]

Power(pow, operation)

Wraps an operation and raises it to the given power.

Some simplifications are already carried out at construction, for example Power(pow2, Power(pow1, op)) is simplified as Power(pow1 * pow2, op).

See also power, Inverse , inverse.

Example

julia> Power(GateZ(), 1//2)
S

julia> Power(GateZ(), 2)
Z^2

julia> Power(GateCH(), 1//2)
(CH)^(1//2)

julia> Power(GateCX(), 1//2)
(CX)^(1//2)

Decomposition

In the general case, if a decomposition is not known for a given operation and power, the Power operation is not decomposed.

If the exponent is an integer, then the gate is decomposed by repeating it.

julia> decompose(Power(GateH(), 2))
1-qubit circuit with 2 instructions:
├── H @ q[1]
└── H @ q[1]

julia> decompose(Power(GateH(), 1//2))
1-qubit circuit with 1 instructions:
└── U(π/2, 0, π)^(1//2) @ q[1]

julia> decompose(Power(GateX(), 1//2)) # same as decomposing GateSX
1-qubit circuit with 4 instructions:
├── S† @ q[1]
├── H @ q[1]
├── S† @ q[1]
└── U(0, 0, 0, π/4) @ q[1]

Parallel(repeats, operation)

Wrapper that applies the same operation on multiple qubits.

If the operation is a N-qubit operation, then the resulting operation is applied over N * repeats qubits.

Examples

julia> Parallel(5, GateX())
Parallel(5, X)

julia> Parallel(3, GateRX(λ))
Parallel(3, RX(λ))

julia> Parallel(2, Parallel(3, GateX()))
Parallel(2, Parallel(3, X))

Decomposition

A parallel is decomposed into a sequence of operation, one for each group of qubits.

julia> decompose(Parallel(2, GateX()))
2-qubit circuit with 2 instructions:
├── X @ q[1]
└── X @ q[2]

julia> decompose(Parallel(3, GateSWAP()))
6-qubit circuit with 3 instructions:
├── SWAP @ q[1:2]
├── SWAP @ q[3:4]
└── SWAP @ q[5:6]

numrepeats(paralleloperation)

Get the number of repetitions of a parallel operation.

See also Parallel.

Examples

julia> numrepeats(Parallel(5, GateX()))
5

julia> numrepeats(Parallel(3, GateSWAP()))
3

parallel(repeats, operation)

Build a parallel operation.

The resulting operation is applied over N * repeats qubits.

IfStatement(numbits, op, num)

Applies the wrapper operation, only if the classical register is equal to num.

Examples

push!(IfStatement(GateX(), 10), 1,1,2,3,4,5) is the equivalent of OpenQASM 2.0

creg c[5];
if (c==10) x q[0];

julia> IfStatement(10, GateX(), 999)
IF(c == 999) X

decompose(operation)
decompose(circuit)

Decompose the given operation or circuit into a circuit of more elementary gates. If applied recursively, it will decompose the given object into a circuit of GateCX and GateU gates.

See also decompose!.

decompose!(circuit, operation[, qtargets, ctargets])

In place version of decompose.

It decomposes the given object, appending all the resulting operations to the given circuit. The optional qtargets and ctargets arguments can be used to map the qubits and classical bits of the decomposed operation to the ones of the target circuit.