mimiqcircuits.operations.gates.standard.interactions¶

Interaction gates (RXX, RYY, RZZ, RZX, XX+YY, XX-YY).

Classes

`GateRXX`(theta)	Two qubit RXX gate (rotation about XX).
`GateRYY`(theta)	Two qubit RYY gate (rotation about YY).
`GateRZX`(theta)	Two qubit RZX gate.
`GateRZZ`(theta)	Two qubit RZZ gate (rotation about ZZ)..
`GateXXminusYY`(theta, beta)	Two qubit parametric GateXXminusYY gate.
`GateXXplusYY`(theta, beta)	Two qubit parametric XXplusYY gate.

class mimiqcircuits.operations.gates.standard.interactions.GateRXX(theta)[source]¶

Bases: Gate

Two qubit RXX gate (rotation about XX).

This gate is symmetric, and is maximally entangling at \((\theta = \frac{\pi}{2})\)

Matrix representation:

\[\begin{split}\operatorname{RXX}(\theta) =\begin{pmatrix} \cos(\frac{\theta}{2}) & 0 & 0 & -i\sin(\frac{\theta}{2}) \\ 0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 \\ 0 & -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 \\ -i\sin(\frac{\theta}{2}) & 0 & 0 & \cos(\frac{\theta}{2}) \end{pmatrix}\end{split}\]

Parameters:: theta – The angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRXX(theta)
RXX(theta)
>>> c = Circuit()
>>> c.push(GateRXX(theta), 0, 1)
2-qubit circuit with 1 instruction:
└── RXX(theta) @ q[0:1]

>>> GateRXX(theta).power(2), GateRXX(theta).inverse()
(RXX(theta)**2, RXX(-theta))
>>> GateRXX(theta).matrix()
[cos((1/2)*theta), 0, 0, -I*sin((1/2)*theta)]
[0, cos((1/2)*theta), -I*sin((1/2)*theta), 0]
[0, -I*sin((1/2)*theta), cos((1/2)*theta), 0]
[-I*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]

>>> GateRXX(theta).decompose()
2-qubit circuit with 7 instructions:
├── H @ q[0]
├── H @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
├── H @ q[1]
└── H @ q[0]

__init__(theta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.

class mimiqcircuits.operations.gates.standard.interactions.GateRYY(theta)[source]¶

Bases: Gate

Two qubit RYY gate (rotation about YY).

This gate is symmetric, and is maximally entangling at \((\theta = \frac{\pi}{2})\)

Matrix representation:

\[\begin{split}\operatorname{RYY}(\theta) =\begin{pmatrix} \cos(\frac{\theta}{2}) & 0 & 0 & i\sin(\frac{\theta}{2}) \\ 0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 \\ 0 & -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 \\ i\sin(\frac{\theta}{2}) & 0 & 0 & \cos(\frac{\theta}{2}) \end{pmatrix}\end{split}\]

Parameters:: theta (float) – The angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRYY(theta)
RYY(theta)
>>> GateRYY(theta).matrix()
[cos((1/2)*theta), 0, 0, I*sin((1/2)*theta)]
[0, cos((1/2)*theta), -I*sin((1/2)*theta), 0]
[0, -I*sin((1/2)*theta), cos((1/2)*theta), 0]
[I*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]

>>> c = Circuit().push(GateRYY(theta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── RYY(theta) @ q[0:1]

>>> GateRYY(theta).power(2), GateRYY(theta).inverse()
(RYY(theta)**2, RYY(-theta))
>>> GateRYY(theta).decompose()
2-qubit circuit with 7 instructions:
├── RX((1/2)*pi) @ q[0]
├── RX((1/2)*pi) @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
├── RX((-1/2)*pi) @ q[0]
└── RX((-1/2)*pi) @ q[1]

__init__(theta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.

class mimiqcircuits.operations.gates.standard.interactions.GateRZZ(theta)[source]¶

Bases: Gate

Two qubit RZZ gate (rotation about ZZ)..

This gate is symmetric, and is maximally entangling at \((\theta = \frac{\pi}{2})\)

Matrix representation:

\[\begin{split}\operatorname{RZZ}(\theta) = \begin{pmatrix} e^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\ 0 & e^{i\frac{\theta}{2}} & 0 & 0 \\ 0 & 0 & e^{i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & e^{-i\frac{\theta}{2}} \end{pmatrix}\end{split}\]

Parameters:: theta (float) – The angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRZZ(theta)
RZZ(theta)
>>> GateRZZ(theta).matrix()
[exp(-1/2*I*theta), 0, 0, 0]
[0, exp(1/2*I*theta), 0, 0]
[0, 0, exp(1/2*I*theta), 0]
[0, 0, 0, exp(-1/2*I*theta)]

>>> c = Circuit().push(GateRZZ(theta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── RZZ(theta) @ q[0:1]

>>> GateRZZ(theta).power(2), GateRZZ(theta).inverse()
(RZZ(theta)**2, RZZ(-theta))
>>> GateRZZ(theta).decompose()
2-qubit circuit with 3 instructions:
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
└── CX @ q[0], q[1]

__init__(theta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.

class mimiqcircuits.operations.gates.standard.interactions.GateRZX(theta)[source]¶

Bases: Gate

Two qubit RZX gate.

This gate is maximally entangling at \((\theta = \frac{\pi}{2})\)

Matrix representation:

\[\begin{split}\operatorname{RZX}(\theta) =\begin{pmatrix} \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) & 0 & 0 \\ -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) & 0 & 0 \\ 0 & 0 & \cos(\frac{\theta}{2}) & i\sin(\frac{\theta}{2}) \\ 0 & 0 & i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) \end{pmatrix}\end{split}\]

Parameters:: theta (float) – The angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRZX(theta)
RZX(theta)
>>> GateRZX(theta).matrix()
[cos((1/2)*theta), -I*sin((1/2)*theta), 0, 0]
[-I*sin((1/2)*theta), cos((1/2)*theta), 0, 0]
[0, 0, cos((1/2)*theta), I*sin((1/2)*theta)]
[0, 0, I*sin((1/2)*theta), cos((1/2)*theta)]

>>> c = Circuit().push(GateRZX(theta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── RZX(theta) @ q[0:1]

>>> GateRZX(theta).power(2), GateRZX(theta).inverse()
(RZX(theta)**2, RZX(-theta))
>>> GateRZX(theta).decompose()
2-qubit circuit with 5 instructions:
├── H @ q[1]
├── CX @ q[0], q[1]
├── RZ(theta) @ q[1]
├── CX @ q[0], q[1]
└── H @ q[1]

__init__(theta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.

class mimiqcircuits.operations.gates.standard.interactions.GateXXplusYY(theta, beta)[source]¶

Bases: Gate

Two qubit parametric XXplusYY gate.

Also known as an XY gate. Its action is to induce a coherent rotation by some angle between \(\ket{10}\) and \(\ket{01}\).

Matrix representation:

\[\begin{split}\operatorname{(XX+YY)}(\theta, \beta)= \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2})e^{i\beta} & 0\\ 0 & -i\sin(\frac{\theta}{2})e^{-i\beta} & \cos(\frac{\theta}{2}) & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}\end{split}\]

Parameters:

theta – The angle in radians.
beta – The phase angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, beta = symbols('theta beta')
>>> GateXXplusYY(theta, beta)
XXplusYY(theta, beta)
>>> GateXXplusYY(theta, beta).matrix()
[1.0, 0, 0, 0]
[0, cos((1/2)*theta), (sin(beta) - I*cos(beta))*sin((1/2)*theta), 0]
[0, I*(I*sin(beta) - cos(beta))*sin((1/2)*theta), cos((1/2)*theta), 0]
[0, 0, 0, 1.0]

>>> c = Circuit().push(GateXXplusYY(theta, beta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── XXplusYY(theta, beta) @ q[0:1]

>>> GateXXplusYY(theta, beta).power(2), GateXXplusYY(theta, beta).inverse()
(XXplusYY(theta, beta)**2, XXplusYY(-theta, beta))
>>> GateXXplusYY(theta, beta).decompose()
2-qubit circuit with 14 instructions:
├── RZ(beta) @ q[0]
├── RZ((-1/2)*pi) @ q[1]
├── SX @ q[1]
├── RZ((1/2)*pi) @ q[1]
├── S @ q[0]
├── CX @ q[1], q[0]
├── RY((-1/2)*theta) @ q[1]
├── RY((-1/2)*theta) @ q[0]
├── CX @ q[1], q[0]
├── S† @ q[0]
├── RZ((-1/2)*pi) @ q[1]
├── SX† @ q[1]
├── RZ((1/2)*pi) @ q[1]
└── RZ(-beta) @ q[0]

__init__(theta, beta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.

class mimiqcircuits.operations.gates.standard.interactions.GateXXminusYY(theta, beta)[source]¶

Bases: Gate

Two qubit parametric GateXXminusYY gate.

Its action is to induce a coherent rotation by some angle between \(\ket{00}\) and \(\ket{11}\)

Matrix representation:

\[\begin{split}\operatorname{(XX-YY)}(\theta, \beta)=\begin{pmatrix} \cos(\frac{\theta}{2}) & 0 & 0 & -i\sin(\frac{\theta}{2})e^{-i\beta} \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ -i\sin(\frac{\theta}{2})e^{i\beta} & 0 & 0 & \cos(\frac{\theta}{2}) \end{pmatrix}\end{split}\]

Parameters:

theta (float) – The angle in radians.
beta (float) – The angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, beta = symbols('theta beta')
>>> GateXXminusYY(theta, beta)
XXminusYY(theta, beta)
>>> GateXXminusYY(theta, beta).matrix()
[cos((1/2)*theta), 0, 0, I*(I*sin(beta) - cos(beta))*sin((1/2)*theta)]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[(sin(beta) - I*cos(beta))*sin((1/2)*theta), 0, 0, cos((1/2)*theta)]

>>> c = Circuit().push(GateXXminusYY(theta, beta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── XXminusYY(theta, beta) @ q[0:1]

>>> GateXXminusYY(theta, beta).power(2), GateXXminusYY(theta, beta).inverse()
(XXminusYY(theta, beta)**2, XXminusYY(-theta, beta))
>>> GateXXminusYY(theta, beta).decompose()
2-qubit circuit with 14 instructions:
├── RZ(-beta) @ q[1]
├── RZ((-1/2)*pi) @ q[0]
├── SX @ q[0]
├── RZ((1/2)*pi) @ q[0]
├── S @ q[1]
├── CX @ q[0], q[1]
├── RY((1/2)*theta) @ q[0]
├── RY((-1/2)*theta) @ q[1]
├── CX @ q[0], q[1]
├── S† @ q[1]
├── RZ((-1/2)*pi) @ q[0]
├── SX† @ q[0]
├── RZ((1/2)*pi) @ q[0]
└── RZ(beta) @ q[1]

__init__(theta, beta)[source]¶

inverse()[source]¶

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:: NotImplementedError – If the method is called.