qat.ir.gates.gates_1q module

class Gate1Q(**data)

Bases: GateBase, ABC

Base gate for single qubit operations.

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Gate1Q']

abstract property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

qubit: Annotated[int]

property qubits

class Hadamard(**data)

Bases: Gate1Q

Implements the Hadamard gate \(H\).

Matrix representation:

\[\begin{split}H = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}.\end{split}\]

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Hadamard']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Id(**data)

Bases: Gate1Q

The identity gate for a single qubit.

Matrix representation:

\[\begin{split}I = \begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}.\end{split}\]

Parameters:

qubit – Target qubit index.

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Id']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Phase(**data)

Bases: Gate1Q

The \({\rm Phase}(\theta)\) gate for some rotation angle \(\theta\).

Equivalent to the \(Rz(\theta)\) gate up to a global rotation. Matrix representation:

\[\begin{split}{\rm Phase}(\theta) = \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta}\end{bmatrix}.\end{split}\]

Parameters:

• qubit – Target qubit index.

• theta – Rotation angle

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Phase']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

theta: Annotated[float]

class Rx(**data)

Bases: Gate1Q

The \(R_{x}(\theta) = e^{-i\theta X/2}\) gate for some rotation angle \(\theta\).

Matrix representation:

\[\begin{split}R_{x}(\theta) = \begin{bmatrix} \cos(\theta/2) & -i\sin(\theta/2) \\ -i\sin(\theta/2) & \cos(\theta/2) \end{bmatrix}.\end{split}\]

Parameters:

• qubit – Target qubit index.

• theta – Rotation angle

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Rx']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

theta: Annotated[float]

class Ry(**data)

Bases: Gate1Q

The \(R_{y}(\theta) = e^{-i\theta Y/2}\) gate for some rotation angle \(\theta\).

Matrix representation:

\[\begin{split}R_{y}(\theta) = \begin{bmatrix} \cos(\theta/2) & -\sin(\theta/2) \\ \sin(\theta/2) & \cos(\theta/2) \end{bmatrix}.\end{split}\]

Parameters:

• qubit – Target qubit index.

• theta – Rotation angle

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Ry']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

theta: Annotated[float]

class Rz(**data)

Bases: Gate1Q

The \(R_{z}(\theta) = e^{-i\theta Z/2}\) gate for some rotation angle \(\theta\).

Matrix representation:

\[\begin{split}R_{z}(\theta) = \begin{bmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{bmatrix}.\end{split}\]

Parameters:

• qubit – Target qubit index.

• theta – Rotation angle

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Rz']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

theta: Annotated[float]

class S(**data)

Bases: Gate1Q

Implements the \(S\) gate.

This gate is identical to the \(R_{z}(\pi/2)\) gate up to global phase. Matrix representation:

\[\begin{split}S = \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix}.\end{split}\]

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['S']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Sdg(**data)

Bases: Gate1Q

Implements the adjoint of the \(S\) gate, \(S^{\dagger}\).

This gate is identical to the \(R_{z}(-\pi/2)\) gate up to global phase. Matrix representation:

\[\begin{split}S^{\dagger} = \begin{bmatrix} 1 & 0 \\ 0 & -i \end{bmatrix}.\end{split}\]

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Sdg']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class T(**data)

Bases: Gate1Q

Implements the \(T\) gate.

This gate is identical to the \(R_{z}(\pi/4)\) gate up to global phase. Matrix representation:

\[\begin{split}T = \begin{bmatrix} 1 & 0 \\ 0 & (1 + i)/\sqrt{2} \end{bmatrix}.\end{split}\]

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['T']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Tdg(**data)

Bases: Gate1Q

Implements the adjoint of the \(T\) gate, \(T^{\dagger}\).

This gate is identical to the \(R_{z}(-\pi/4)\) gate up to global phase. Matrix representation:

\[\begin{split}T^{\dagger} = \begin{bmatrix} 1 & 0 \\ 0 & (1 - i)/\sqrt{2} \end{bmatrix}.\end{split}\]

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Tdg']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class U(**data)

Bases: Gate1Q

Implements the \(U(\theta, \phi, \lambda)\) rotation gate defined by three rotation angles.

The gate can be expressed as

\[U(\theta, \phi, \lambda) = e^{\frac{1}{2}i\pi(\lambda+\phi)}R_{z}(\phi)R_{y}(\theta)R_{z}(\lambda)\]

Matrix representation:

\[\begin{split}U(\theta, \phi, \lambda) = \begin{bmatrix} \cos(\theta/2) & -e^{i\lambda} \sin(\theta/2) \\ e^{i\phi} \sin(\theta/2) & e^{i(\phi+\lambda)} \cos(\theta/2) \end{bmatrix}.\end{split}\]

Parameters:

• qubit – Target qubit index.

• theta – Rotation angle \(\theta\) around the Y-axis.

• phi – Rotation angle \(\phi\) around the Z-axis (final).

• lambd – Rotation angle \(\lambda\) around the Z-axis (first).

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

classmethod from_matrix(qubit, mat)

Returns a \(U(\theta, \phi, \lambda)\) gate directly from a 1Q matrix.

Determines the angles using simple algebra.

inst: Literal['U']

lambd: Annotated[float]

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

phi: Annotated[float]

theta: Annotated[float]

class X(**data)

Bases: Gate1Q

Implements the Pauli-X gate.

Matrix representation:

\[\begin{split}X = \begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix}.\end{split}\]

Parameters:

qubit – Target qubit index.

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['X']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Y(**data)

Bases: Gate1Q

Implements the Pauli-Y gate.

Matrix representation:

\[\begin{split}Y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}.\end{split}\]

Parameters:

qubit – Target qubit index.

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Y']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

class Z(**data)

Bases: Gate1Q

Implements the Pauli-Z gate.

Matrix representation:

\[\begin{split}X = \begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix}.\end{split}\]

Parameters:

qubit – Target qubit index.

Create a new model by parsing and validating input data from keyword arguments.

Raises [ValidationError][pydantic_core.ValidationError] if the input data cannot be validated to form a valid model.

self is explicitly positional-only to allow self as a field name.

inst: Literal['Z']

property matrix

model_config: ClassVar[ConfigDict] = {'extra': 'forbid', 'ser_json_inf_nan': 'constants', 'use_enum_values': False, 'validate_assignment': True}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].