Operations

Operation{N,M,L}

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

zregsizes(operation)
zregsizes(operationtype)

Length of the zregisters the given operation acts on.

GATES

List of gates provided by the library.

Single qubit gates

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

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.

Noise channels

These define a non-unitary quantum operation based on the Kraus representation.

See NOISECHANNELS for a list of them.

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

NOISECHANNELS

List of noise channels provided by the library.

Not mixed-unitary noise channels

Kraus, AmplitudeDamping, GeneralizedAmplitudeDamping, PhaseAmplitudeDamping, ThermalNoise, Reset,

Mixed-Unitary noise channels

MixedUnitary, PauliNoise, PauliX, PauliY, PauliZ, Depolarizing,

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, MeasureX, MeasureY, MeasureZ, MeasureXX, MeasureYY, MeasureZZ MeasureReset, MeasureResetX, MeasureResetY, MeasureResetZ, Reset,

Algorithms or complex gate builders

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

AbstractGate{N} <: AbstractOperator{N}

Supertype for all the N-qubit unitary gates.

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

TODO

GateSY()

Single qubit $\sqrt{Y}$ gate.

See also GateSYDG, GateY, Power

Matrix representation

\[\operatorname{SY} = \sqrt{\operatorname{Y}} = \frac{1}{2} \begin{pmatrix} 1+i & -1-i \\ 1+i & 1+i \end{pmatrix}\]

Examples

julia> GateSY()
SY

julia> matrix(GateSY())
2×2 Matrix{ComplexF64}:
 0.5+0.5im  -0.5-0.5im
 0.5+0.5im   0.5+0.5im

julia> c = push!(Circuit(), GateSY(), 1)
1-qubit circuit with 1 instructions:
└── SY @ q[1]

julia> push!(c, GateSY, 2)
2-qubit circuit with 2 instructions:
├── SY @ q[1]
└── SY @ q[2]

julia> power(GateSY(), 2)
Y

Decomposition

julia> decompose(GateSY())
1-qubit circuit with 4 instructions:
├── S @ q[1]
├── S @ q[1]
├── H @ q[1]
└── U(0,0,0,π/4) @ q[1]

GateSYDG()

Single qubit $\sqrt{Y}^\dagger$ gate (conjugate transpose of the $\sqrt{Y}$ gate)

See also GateSY, GateY, Power, Inverse

Matrix representation

\[\operatorname{SYDG} = \sqrt{\operatorname{Y}}^\dagger = \frac{1}{2} \begin{pmatrix} 1-i & 1-i \\ -1+i & 1-i \end{pmatrix}\]

Examples

julia> GateSYDG()
SY†

julia> matrix(GateSYDG())
2×2 adjoint(::Matrix{ComplexF64}) with eltype ComplexF64:
  0.5-0.5im  0.5-0.5im
 -0.5+0.5im  0.5-0.5im

julia> c = push!(Circuit(), GateSYDG(), 1)
1-qubit circuit with 1 instructions:
└── SY† @ q[1]

julia> push!(c, GateSYDG, 2)
2-qubit circuit with 2 instructions:
├── SY† @ q[1]
└── SY† @ q[2]

julia> power(GateSYDG(), 2)
(SY†)^2

julia> inverse(GateSYDG())
SY

MeasureXX()

The MeasureXX operation measures the joint parity of two qubits in the X-basis, determining whether the qubits are in the same or different states within this basis. The operation begins by applying a controlled-X (CX) gate between the two qubits to entangle them. Following this, a Hadamard (H) gate is applied to the first qubit, rotating it into the X-basis. The second qubit, designated as the target, is then measured to extract the parity information. After the measurement, the Hadamard gate is applied again to the first qubit to reverse the rotation, and a second controlled-X (CX) gate is applied to disentangle the qubits, restoring the system to its original state. Through this sequence, the MeasureXX operation efficiently captures the parity relationship of the qubits in the X-basis.

A result of 0 indicates that the qubits are in the same state, while a result of 1 indicates that they are in different states.

See Also MeasureYY, MeasureZZ

Examples

julia> c = Circuit()
empty circuit

julia> push!(c, MeasureXX(), 1, 2, 1)
2-qubit circuit with 1 instructions:
└── MXX @ q[1:2], c[1]

MeasureYY()

The MeasureYY operation measures the joint parity of two qubits in the Y-basis, determining whether they are in the same or different states in this basis. This is achieved by first applying an S gate (a π/2 phase shift) to both qubits, followed by a controlled-X (CX) gate. A Hadamard gate (H) is then applied to the first qubit, and the second qubit is measured. To restore the system, a Z gate is applied to the first qubit, followed by another Hadamard gate, another CX gate, and finally another S gate to both qubits. The measurement result reflects whether the qubits are in the same or different states in the Y-basis.

A result of 0 indicates that the qubits are in the same state, while a result of 1 indicates that they are in different states.

See Also MeasureXX, MeasureZZ

Examples

julia> c = Circuit()
empty circuit

julia> push!(c, MeasureYY(), 1, 2, 1)
2-qubit circuit with 1 instructions:
└── MYY @ q[1:2], c[1]

MeasureZZ()

The MeasureZZ operation measures the joint parity of two qubits in the Z-basis. This is achieved by applying a controlled-X (CX) gate, measuring the target qubit, and then applying another CX gate to undo the entanglement. The measurement result indicates whether the qubits are in the same or different states in the Z-basis.

See Also MeasureYY, MeasureXX

Examples

julia> c = Circuit()
empty circuit

julia> push!(c, MeasureZZ(), 1, 2, 1)
2-qubit circuit with 1 instructions:
└── MZZ @ q[1:2], c[1]

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(1.0471975511966005,-0.9553166181245096,2.1862760354652835,0.16991845472706107) @ 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())
⨷ ⁵ X

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

julia> Parallel(2, Parallel(3, GateX()))
⨷ ² (⨷ 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(op, bs::BitString)

Applies the provided operation only if the classical register matches the specified BitString.

IfStatement enables conditional operations in a quantum circuit based on the state of a classical register. If the classical register's state matches the BitString, the operation (op) is applied to the target qubits.

Arguments

• op: The quantum operation to apply, such as GateX() or another gate.
• bs: A BitString object representing the target state of the classical register that triggers op.

Examples

Basic Usage

julia> using MimiqCircuitsBase

# Define a condition as a BitString
julia> condition = BitString("01011")
5-bits BitString with integer value 26:
  01011

# Apply GateX only if the condition is met
julia> if_statement = IfStatement(GateX(), condition)
IF(c==01011) X

# Add this conditional operation to a circuit
julia> c = Circuit()
julia> push!(c, if_statement, 1, 2, 3, 4, 5, 6)
1-qubit circuit with 1 instructions:
└── IF(c==01011) X @ q[1], c[2:6]

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.

struct Not <: Operation{0,1,0}