Enum OpType

Source

#[non_exhaustive]pub enum OpType {
Show 122 variants    Input,
    Output,
    Create,
    Discard,
    ClInput,
    ClOutput,
    Barrier,
    Label,
    Branch,
    Goto,
    Stop,
    ClassicalTransform,
    WASM,
    SetBits,
    CopyBits,
    RangePredicate,
    ExplicitPredicate,
    ExplicitModifier,
    MultiBit,
    Phase,
    Z,
    X,
    Y,
    S,
    Sdg,
    T,
    Tdg,
    V,
    Vdg,
    SX,
    SXdg,
    H,
    Rx,
    Ry,
    Rz,
    U3,
    U2,
    U1,
    TK1,
    TK2,
    CX,
    CY,
    CZ,
    CH,
    CV,
    CVdg,
    CSX,
    CSXdg,
    CS,
    CSdg,
    CRz,
    CRx,
    CRy,
    CU1,
    CU3,
    PhaseGadget,
    CCX,
    SWAP,
    CSWAP,
    BRIDGE,
    noop,
    Measure,
    Collapse,
    Reset,
    ECR,
    ISWAP,
    PhasedX,
    NPhasedX,
    ZZMax,
    XXPhase,
    YYPhase,
    ZZPhase,
    XXPhase3,
    ESWAP,
    FSim,
    Sycamore,
    ISWAPMax,
    PhasedISWAP,
    CnRx,
    CnRy,
    CnRz,
    CnX,
    CnY,
    CnZ,
    GPI,
    GPI2,
    AAMS,
    CircBox,
    Unitary1qBox,
    Unitary2qBox,
    Unitary3qBox,
    ExpBox,
    PauliExpBox,
    PauliExpPairBox,
    PauliExpCommutingSetBox,
    TermSequenceBox,
    CliffBox,
    PhasePolyBox,
    Conditional,
    StabiliserAssertionBox,
    ProjectorAssertionBox,
    CustomGate,
    QControlBox,
    UnitaryTableauBox,
    ClassicalExpBox,
    MultiplexorBox,
    MultiplexedRotationBox,
    MultiplexedU2Box,
    MultiplexedTensoredU2Box,
    ToffoliBox,
    ConjugationBox,
    DummyBox,
    StatePreparationBox,
    DiagonalBox,
    ClExpr,
    RNGInput,
    RNGOutput,
    RNGSeed,
    RNGBound,
    RNGIndex,
    RNGNum,
    JobShotNum,
}

Expand description

Operation types in a quantum circuit.

Variants (Non-exhaustive)§

This enum is marked as non-exhaustive

Non-exhaustive enums could have additional variants added in future. Therefore, when matching against variants of non-exhaustive enums, an extra wildcard arm must be added to account for any future variants.

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Input

Quantum input node of the circuit

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Output

Quantum output node of the circuit

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Create

Quantum node with no predecessors, implicitly in zero state.

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Discard

Quantum node with no successors, not composable with input nodes of other circuits.

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ClInput

Classical input node of the circuit

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ClOutput

Classical output node of the circuit

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Barrier

No-op that must be preserved by compilation

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Label

FlowOp introducing a target for Branch or Goto commands

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Branch

Execution jumps to a label if a condition bit is true (1), otherwise continues to next command

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Goto

Execution jumps to a label unconditionally

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Stop

Execution halts and the program terminates

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ClassicalTransform

A general classical operation where all inputs are also outputs

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WASM

Op containing a classical wasm function call.

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SetBits

An operation to set some bits to specified values

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CopyBits

An operation to copy some bit values

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RangePredicate

A classical predicate defined by a range of values in binary encoding

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ExplicitPredicate

A classical predicate defined by a truth table

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ExplicitModifier

An operation defined by a truth table that modifies one bit

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MultiBit

A classical operation applied to multiple bits simultaneously

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Phase

Global phase $\alpha \mapsto [\e^{i\pi\alpha}]$

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Z

\f$ \left[ \begin{array}{cc} 1 & 0 \ 0 & -1 \end{array} \right] \f$

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X

\f$ \left[ \begin{array}{cc} 0 & 1 \ 1 & 0 \end{array} \right] \f$

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Y

\f$ \left[ \begin{array}{cc} 0 & -i \ i & 0 \end{array} \right] \f$

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S

\f$ \left[ \begin{array}{cc} 1 & 0 \ 0 & i \end{array} \right] = \mathrm{U1}(\frac12) \f$

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Sdg

\f$ \left[ \begin{array}{cc} 1 & 0 \ 0 & -i \end{array} \right] = \mathrm{U1}(-\frac12) \f$

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T

\f$ \left[ \begin{array}{cc} 1 & 0 \ 0 & e^{i\pi/4} \end{array} \right] = \mathrm{U1}(\frac14) \f$

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Tdg

\f$ \left[ \begin{array}{cc} 1 & 0 \ 0 & e^{-i\pi/4} \end{array} \right] \equiv \mathrm{U1}(-\frac14) \f$

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V

\f$ \frac{1}{\sqrt 2} \left[ \begin{array}{cc} 1 & -i \ -i & 1 \end{array} \right] = \mathrm{Rx}(\frac12) \f$

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Vdg

\f$ \frac{1}{\sqrt 2} \left[ \begin{array}{cc} 1 & i \ i & 1 \end{array} \right] = \mathrm{Rx}(-\frac12) \f$

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SX

\f$ \frac{1}{2} \left[ \begin{array}{cc} 1+i & 1-i \ 1-i & 1+i \end{array} \right] = e^{\frac{i\pi}{4}}\mathrm{Rx}(\frac12) \f$

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SXdg

\f$ \frac{1}{2} \left[ \begin{array}{cc} 1-i & 1+i \ 1+i & 1-i \end{array} \right] = e^{\frac{-i\pi}{4}}\mathrm{Rx}(-\frac12) \f$

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H

\f$ \frac{1}{\sqrt 2} \left[ \begin{array}{cc} 1 & 1 \ 1 & -1 \end{array} \right] \f$

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Rx

\f$ \mathrm{Rx}(\alpha) = e^{-\frac12 i \pi \alpha X} = \left[ \begin{array}{cc} \cos\frac{\pi\alpha}{2} & -i\sin\frac{\pi\alpha}{2} \ -i\sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} \end{array} \right] \f$

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Ry

\f$ \mathrm{Ry}(\alpha) = e^{-\frac12 i \pi \alpha Y} = \left[ \begin{array}{cc} \cos\frac{\pi\alpha}{2} & -\sin\frac{\pi\alpha}{2} \ \sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} \end{array} \right] \f$

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Rz

\f$ \mathrm{Rz}(\alpha) = e^{-\frac12 i \pi \alpha Z} = \left[ \begin{array}{cc} e^{-\frac12 i \pi\alpha} & 0 \ 0 & e^{\frac12 i \pi\alpha} \end{array} \right] \f$

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U3

\f$ \mathrm{U3}(\theta, \phi, \lambda) = \left[ \begin{array}{cc} \cos\frac{\pi\theta}{2} & -e^{i\pi\lambda} \sin\frac{\pi\theta}{2} \ e^{i\pi\phi} \sin\frac{\pi\theta}{2} & e^{i\pi(\lambda+\phi)} \cos\frac{\pi\theta}{2} \end{array} \right] = e^{\frac12 i\pi(\lambda+\phi)} \mathrm{Rz}(\phi) \mathrm{Ry}(\theta) \mathrm{Rz}(\lambda) \f$

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U2

\f$ \mathrm{U2}(\phi, \lambda) = \mathrm{U3}(\frac12, \phi, \lambda) = e^{\frac12 i\pi(\lambda+\phi)} \mathrm{Rz}(\phi) \mathrm{Ry}(\frac12) \mathrm{Rz}(\lambda) \f$

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U1

\f$ \mathrm{U1}(\lambda) = \mathrm{U3}(0, 0, \lambda) = e^{\frac12 i\pi\lambda} \mathrm{Rz}(\lambda) \f$

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TK1

\f$ \mathrm{TK1}(\alpha, \beta, \gamma) = \mathrm{Rz}(\alpha) \mathrm{Rx}(\beta) \mathrm{Rz}(\gamma) \f$

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TK2

\f$ \mathrm{TK2}(\alpha, \beta, \gamma) = \mathrm{XXPhase}(\alpha) \mathrm{YYPhase}(\beta) \mathrm{ZZPhase}(\gamma) \f$

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CX

Controlled OpType::X.

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\f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \frac{1}{\sqrt 2} & -i \frac{1}{\sqrt 2} \ 0 & 0 & -i \frac{1}{\sqrt 2} & \frac{1}{\sqrt 2} \end{array} \right] \f$

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CVdg

Controlled OpType::Vdg

\f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \frac{1}{\sqrt 2} & i \frac{1}{\sqrt 2} \ 0 & 0 & i \frac{1}{\sqrt 2} & \frac{1}{\sqrt 2} \end{array} \right] \f$

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CSX

Controlled OpType::SX

\f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \frac{1+i}{2} & \frac{1-i}{2} \ 0 & 0 & \frac{1-i}{2} & \frac{1+i}{2} \end{array} \right] \f$

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CSXdg

Controlled OpType::SXdg

\f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \frac{1-i}{2} & \frac{1+i}{2} \ 0 & 0 & \frac{1+i}{2} & \frac{1-i}{2} \end{array} \right] \f$

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CS

Controlled OpType::S gate

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CSdg

Controlled OpType::Sdg gate

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CRz

Controlled OpType::Rz

\f$ \mathrm{CRz}(\alpha) = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & e^{-\frac12 i \pi\alpha} & 0 \ 0 & 0 & 0 & e^{\frac12 i \pi\alpha} \end{array} \right] \f$

The phase parameter \f$ \alpha \f$ is defined modulo \f$ 4 \f$.

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CRx

Controlled OpType::Rx

\f$ \mathrm{CRx}(\alpha) = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \cos \frac{\pi \alpha}{2} & -i \sin \frac{\pi \alpha}{2} \ 0 & 0 & -i \sin \frac{\pi \alpha}{2} & \cos \frac{\pi \alpha}{2} \end{array} \right] \f$

The phase parameter \f$ \alpha \f$ is defined modulo \f$ 4 \f$.

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CRy

Controlled OpType::Ry

\f$ \mathrm{CRy}(\alpha) = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & \cos \frac{\pi \alpha}{2} & -\sin \frac{\pi \alpha}{2} \ 0 & 0 & \sin \frac{\pi \alpha}{2} & \cos \frac{\pi \alpha}{2} \end{array} \right] \f$

The phase parameter \f$ \alpha \f$ is defined modulo \f$ 4 \f$.

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CU1

Controlled OpType::U1

\f$ \mathrm{CU1}(\alpha) = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & e^{i\pi\alpha} \end{array} \right] \f$

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CU3

Controlled OpType::U3

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PhaseGadget

\f$ \alpha \mapsto e^{-\frac12 i \pi\alpha Z^{\otimes n}} \f$

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CCX

Controlled OpType::CX

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SWAP

Swap two qubits

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CSWAP

Controlled OpType::SWAP

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BRIDGE

Three-qubit gate that swaps the first and third qubits

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noop

Identity

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Measure

Measure a qubit, producing a classical output

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Collapse

Measure a qubit producing no output

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Reset

Reset a qubit to the zero state

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ECR

\f$ \frac{1}{\sqrt 2} \left[ \begin{array}{cccc} 0 & 0 & 1 & i \ 0 & 0 & i & 1 \ 1 & -i & 0 & 0 \ -i & 1 & 0 & 0 \end{array} \right] \f$

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ISWAP

\f$ \alpha \mapsto e^{\frac14 i \pi\alpha (X \otimes X + Y \otimes Y)} = \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & \cos\frac{\pi\alpha}{2} & i\sin\frac{\pi\alpha}{2} & 0 \ 0 & i\sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} & 0 \ 0 & 0 & 0 & 1 \end{array} \right] \f$

Also known as an XY gate.

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PhasedX

\f$ (\alpha, \beta) \mapsto \mathrm{Rz}(\beta) \mathrm{Rx}(\alpha) \mathrm{Rz}(-\beta) \f$

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NPhasedX

PhasedX gates on multiple qubits

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ZZMax

\f$ \mathrm{ZZPhase}(\frac12) \f$

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XXPhase

\f$ \alpha \mapsto e^{-\frac12 i \pi\alpha (X \otimes X)} = \left[ \begin{array}{cccc} \cos\frac{\pi\alpha}{2} & 0 & 0 & -i\sin\frac{\pi\alpha}{2} \ 0 & \cos\frac{\pi\alpha}{2} & -i\sin\frac{\pi\alpha}{2} & 0 \ 0 & -i\sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} & 0 \ -i\sin\frac{\pi\alpha}{2} & 0 & 0 & \cos\frac{\pi\alpha}{2} \end{array} \right] \f$

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YYPhase

\f$ \alpha \mapsto e^{-\frac12 i \pi\alpha (Y \otimes Y)} = \left[ \begin{array}{cccc} \cos\frac{\pi\alpha}{2} & 0 & 0 & i\sin\frac{\pi\alpha}{2} \ 0 & \cos\frac{\pi\alpha}{2} & -i\sin\frac{\pi\alpha}{2} & 0 \ 0 & -i\sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} & 0 \ i\sin\frac{\pi\alpha}{2} & 0 & 0 & \cos\frac{\pi\alpha}{2} \end{array} \right] \f$

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ZZPhase

\f$ \alpha \mapsto e^{-\frac12 i \pi\alpha (Z \otimes Z)} = \left[ \begin{array}{cccc} e^{-\frac12 i \pi\alpha} & 0 & 0 & 0 \ 0 & e^{\frac12 i \pi\alpha} & 0 & 0 \ 0 & 0 & e^{\frac12 i \pi\alpha} & 0 \ 0 & 0 & 0 & e^{-\frac12 i \pi\alpha} \end{array} \right] \f$

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XXPhase3

Three-qubit phase MSGate

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ESWAP

\f$ \alpha \mapsto e^{-\frac12 i\pi\alpha \cdot \mathrm{SWAP}} = \left[ \begin{array}{cccc} e^{-\frac12 i \pi\alpha} & 0 & 0 & 0 \ 0 & \cos\frac{\pi\alpha}{2} & -i\sin\frac{\pi\alpha}{2} & 0 \ 0 & -i\sin\frac{\pi\alpha}{2} & \cos\frac{\pi\alpha}{2} & 0 \ 0 & 0 & 0 & e^{-\frac12 i \pi\alpha} \end{array} \right] \f$

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FSim

\f$ (\alpha, \beta) \mapsto \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & \cos \pi\alpha & -i\sin \pi\alpha & 0 \ 0 & -i\sin \pi\alpha & \cos \pi\alpha & 0 \ 0 & 0 & 0 & e^{-i\pi\beta} \end{array} \right] \f$

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Sycamore

Fixed instance of a OpType::FSim gate with parameters \f$ (\frac12, \frac16) \f$: \f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 0 & -i & 0 \ 0 & -i & 0 & 0 \ 0 & 0 & 0 & e^{-i\pi/6} \end{array} \right] \f$

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ISWAPMax

Fixed instance of a OpType::ISWAP gate with parameter \f$ 1.0 \f$: \f$ \left[ \begin{array}{cccc} 1 & 0 & 0 & 0 \ 0 & 0 & i & 0 \ 0 & i & 0 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] \f$

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PhasedISWAP

ISwap gate with extra Rzs on each qubit

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CnRx

N-controlled OpType::Rx

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CnRy

N-controlled OpType::Ry

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CnRz

N-controlled OpType::Rz

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CnX

Multiply-controlled OpType::X

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CnY

Multiply-controlled OpType::Y

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CnZ

Multiply-controlled OpType::Z

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GPI

GPi gate

\f$ (\phi) \mapsto \left[ \begin{array}{cc} 0 & e^{-i\pi\phi} \\ e^{i\pi\phi} & 0 \end{array} \right] \f$

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GPI2

GPi2 gate

\f$ (\phi) \mapsto \frac{1}{\sqrt 2} \left[ \begin{array}{cc} 1 & -ie^{-i\pi\phi} \\ -ie^{i\pi\phi} & 1 \end{array} \right] \f$

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AAMS

AAMS gate

\f$

(\theta, \phi_0, \phi_1) \mapsto \left[ “ \begin{array}{cccc} \cos\frac{\pi\theta}{2} & 0 & 0 & -ie^{-i\pi(\phi_0+\phi_1)}\sin\frac{\pi\theta}{2} \\ 0 & \cos\frac{\pi\theta}{2} & -ie^{i\pi(\phi_1-\phi_0)}\sin\frac{\pi\theta}{2} & 0 \\ 0 & -ie^{i\pi(\phi_0-\phi_1)}\sin\frac{\pi\theta}{2} & \cos\frac{\pi\theta}{2} & 0 \\ -ie^{i\pi(\phi_0+\phi_1)}\sin\frac{\pi\theta}{2} & 0 & 0 & \cos\frac{\pi\theta}{2} \end{array} \right]` \f$

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