Quantum Circuit

Circuit

Circuit classes for encoding quantum operations.

This module provides:

• BaseCircuit: An abstract base class for quantum circuits.

• MBQCCircuit: A circuit class composed solely of a unit gate set.

• Circuit: A class for circuits that include macro instructions.

• CircuitScheduleStrategy: Scheduling strategies for circuit conversion.

• circuit2graph: A function that converts a circuit to a graph state, gflow, and scheduler.

class graphqomb.circuit.CircuitScheduleStrategy

Bases: Enum

Enumeration for manual scheduling strategies derived from circuit structure.

PARALLEL = 1

MINIMIZE_SPACE = 2

class graphqomb.circuit.BaseCircuit

Bases: ABC

Abstract base class for quantum circuits.

This class defines the interface for quantum circuit objects. It enforces implementation of core methods that must be present in any subclass representing a specific type of quantum circuit.

abstract property num_qubits: int

Get the number of qubits in the circuit.

Returns:

The number of qubits in the circuit

Return type:

int

abstractmethod instructions()

Get the list of gate instructions in the circuit.

Returns:

List of gate instructions in the circuit.

Return type:

list[Gate]

abstractmethod unit_instructions()

Get the list of unit gate instructions in the circuit.

Returns:

List of unit gate instructions in the circuit.

Return type:

list[UnitGate]

class graphqomb.circuit.MBQCCircuit

Bases: BaseCircuit

A circuit class composed solely of a unit gate set.

__init__(num_qubits)

property num_qubits: int

Get the number of qubits in the circuit.

Returns:

The number of qubits in the circuit.

Return type:

int

instructions()

Get the list of gate instructions in the circuit.

Returns:

List of gate instructions in the circuit.

Return type:

list[Gate]

unit_instructions()

Get the list of unit gate instructions in the circuit.

Returns:

List of unit gate instructions in the circuit.

Return type:

list[UnitGate]

j(qubit, angle)

Add a J gate to the circuit.

Parameters:

• qubit (int) – The qubit index.

• angle (float) – The angle of the J gate.

cz(qubit1, qubit2)

Add a CZ gate to the circuit.

Parameters:

• qubit1 (int) – The first qubit index.

• qubit2 (int) – The second qubit index.

phase_gadget(qubits, angle)

Add a phase gadget to the circuit.

Parameters:

• qubits (collections.abc.Sequence[int]) – The qubit indices.

• angle (float) – The angle of the phase gadget

class graphqomb.circuit.Circuit

Bases: BaseCircuit

A class for circuits that include macro instructions.

__init__(num_qubits)

property num_qubits: int

Get the number of qubits in the circuit.

Returns:

The number of qubits in the circuit.

Return type:

int

instructions()

Get the list of gate instructions in the circuit.

Returns:

List of gate instructions in the circuit.

Return type:

list[Gate]

unit_instructions()

Get the list of unit gate instructions in the circuit.

Returns:

The list of unit gate instructions in the circuit.

Return type:

list[UnitGate]

apply_macro_gate(gate)

Apply a macro gate to the circuit.

Parameters:

gate (Gate) – The macro gate to apply.

graphqomb.circuit.circuit2graph(circuit, schedule_strategy=CircuitScheduleStrategy.PARALLEL)

Convert a circuit to a graph state, gflow, and scheduler.

Parameters:

• circuit (BaseCircuit) – The quantum circuit to convert.

• schedule_strategy (CircuitScheduleStrategy, optional) –

  Strategy for scheduling preparation and measurement times derived from the circuit, by default CircuitScheduleStrategy.PARALLEL. The strategies are:

  • CircuitScheduleStrategy.PARALLEL: schedule each qubit independently to reduce depth

  • CircuitScheduleStrategy.MINIMIZE_SPACE: serialize operations to reduce prepared qubits

Returns:

The graph state, gflow, and scheduler converted from the circuit. The scheduler is configured with automatic time scheduling derived from circuit structure.

Return type:

tuple[GraphState, dict[int, set[int]], Scheduler]

Gate

Module for gates used in circuit representation.

This module provides:

• Gate: Abstract class for gates.

• UnitGate: Abstract class for unit gates.

• J: Class for the J gate.

• CZ: Class for the CZ gate.

• PhaseGadget: Class for the PhaseGadget gate.

• Identity: Class for the Identity gate.

• X: Class for the X gate.

• Y: Class for the Y gate.

• Z: Class for the Z gate.

• H: Class for the H gate.

• S: Class for the S gate.

• T: Class for the T gate.

• Tdg: Class for the Tdg gate.

• Rx: Class for the Rx gate.

• Ry: Class for the Ry gate.

• Rz: Class for the Rz gate.

• U3: Class for the U3 gate.

• CNOT: Class for the CNOT gate.

• SWAP: Class for the SWAP gate.

• CRz: Class for the CRz gate.

• CRx: Class for the CRx gate.

• CU3: Class for the CU3 gate.

• Toffoli: Class for the Toffoli gate.

• CCZ: Class for the CCZ gate.

class graphqomb.gates.Gate

Abstract class for gates.

abstractmethod unit_gates()

Get the unit gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

abstractmethod matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

class graphqomb.gates.SingleGate

Base class for single qubit macro gates.

class graphqomb.gates.TwoQubitGate

Base class for two qubit macro gates.

class graphqomb.gates.MultiGate

Base class for multi qubit macro gates.

class graphqomb.gates.J

Class for the J gate.

qubit

The qubit the gate acts on.

Type:

int

angle

The angle of the J gate.

\[\begin{split}J = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & e^{i\theta} \\ 1 & -e^{i\theta} \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit, angle)

class graphqomb.gates.CZ

Class for the CZ gate.

qubits

The qubits the gate acts on.

\[\begin{split}CZ = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}\end{split}\]

Type:

tuple[int, int]

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits)

class graphqomb.gates.PhaseGadget

Class for the PhaseGadget gate.

qubits

The qubits the gate acts on.

Type:

list[int]

angle

The angle of the PhaseGadget gate.

\[PhaseGadget(\theta) = \exp\left(-i\frac{\theta}{2}\prod_{j}Z_j\right)\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits, angle)

graphqomb.gates.UnitGate: TypeAlias = graphqomb.gates.J | graphqomb.gates.CZ | graphqomb.gates.PhaseGadget

Unit gate type

class graphqomb.gates.Identity

Class for the Identity gate.

qubit

The qubit the gate acts on.

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

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Identity matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.X

Class for the X gate.

qubit

The qubit the gate acts on.

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

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

X gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.Y

Class for the Y gate.

qubit

The qubit the gate acts on.

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

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Y gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.Z

Class for the Z gate.

qubit

The qubit the gate acts on.

\[\begin{split}Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\end{split}\]

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Z gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.H

Class for the H gate.

qubit

The qubit the gate acts on.

\[\begin{split}H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}\end{split}\]

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

H gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.S

Class for the S gate.

qubit

The qubit the gate acts on.

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

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

S gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.T

Class for the T gate.

qubit

The qubit the gate acts on.

\[\begin{split}T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}\end{split}\]

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

T gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.Tdg

Class for the Tdg gate.

qubit

The qubit the gate acts on.

\[\begin{split}T^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & e^{-i\pi/4} \end{pmatrix}\end{split}\]

Type:

int

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Tdg gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit)

class graphqomb.gates.Rx

Class for the Rx gate.

qubit

The qubit the gate acts on.

Type:

int

angle

The angle of the Rx gate.

\[\begin{split}R_x(\theta) = \begin{pmatrix} \cos(\theta/2) & -i\sin(\theta/2) \\ -i\sin(\theta/2) & \cos(\theta/2) \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Rx gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit, angle)

class graphqomb.gates.Ry

Class for the Ry gate.

qubit

The qubit the gate acts on.

Type:

int

angle

The angle of the Ry gate.

\[\begin{split}R_y(\theta) = \begin{pmatrix} \cos(\theta/2) & -\sin(\theta/2) \\ \sin(\theta/2) & \cos(\theta/2) \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Ry gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit, angle)

class graphqomb.gates.Rz

Class for the Rz gate.

qubit

The qubit the gate acts on.

Type:

int

angle

The angle of the Rz gate.

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

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Rz gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit, angle)

class graphqomb.gates.U3

Class for the U3 gate.

qubit

The qubit the gate acts on.

Type:

int

angle1

The first angle of the U3 gate.

Type:

float

angle2

The second angle of the U3 gate.

Type:

float

angle3

The third angle of the U3 gate.

\[\begin{split}U3(\theta, \phi, \lambda) = \begin{pmatrix} \cos(\theta/2) & -e^{i\lambda}\sin(\theta/2) \\ e^{i\phi}\sin(\theta/2) & e^{i(\phi+\lambda)}\cos(\theta/2) \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

U3 gate matrix.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubit, angle1, angle2, angle3)

class graphqomb.gates.CNOT

Class for the CNOT gate.

qubits

The qubits the gate acts on [control target].

\[\begin{split}CNOT = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}\end{split}\]

Type:

tuple[int, int]

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits)

class graphqomb.gates.SWAP

Class for the SWAP gate.

qubits

The qubits the gate acts on [control target].

\[\begin{split}SWAP = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\end{split}\]

Type:

tuple[int, int]

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits)

class graphqomb.gates.CRz

Class for the CRz gate.

qubits

The qubits the gate acts on [control target].

Type:

tuple[int, int]

angle

The angle of the CRz gate.

\[\begin{split}CR_z(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\theta/2} & 0 \\ 0 & 0 & 0 & e^{i\theta/2} \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits, angle)

class graphqomb.gates.CRx

Class for the CRx gate.

qubits

The qubits the gate acts on [control target].

Type:

tuple[int, int]

angle

The angle of the CRx gate.

\[\begin{split}CR_x(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\theta/2) & -i\sin(\theta/2) \\ 0 & 0 & -i\sin(\theta/2) & \cos(\theta/2) \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits, angle)

class graphqomb.gates.CU3

Class for the CU3 gate.

qubits

The qubits the gate acts on.

Type:

tuple[int, int]

angle1

The first angle of the CU3 gate.

Type:

float

angle2

The second angle of the CU3 gate.

Type:

float

angle3

The third angle of the CU3 gate.

\[\begin{split}CU3(\theta, \phi, \lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\theta/2) & -e^{i\lambda}\sin(\theta/2) \\ 0 & 0 & e^{i\phi}\sin(\theta/2) & e^{i(\phi+\lambda)}\cos(\theta/2) \end{pmatrix}\end{split}\]

Type:

float

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits, angle1, angle2, angle3)

class graphqomb.gates.Toffoli

Class for the Toffoli gate.

qubits

The qubits the gate acts on [control1, control2, target].

\[\begin{split}Toffoli = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix}\end{split}\]

Type:

list[int]

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]

__init__(qubits)

class graphqomb.gates.CCZ

Class for the CCZ gate.

qubits

The qubits the gate acts on [control1, control2, target].

\[\begin{split}CCZ = \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \end{pmatrix}\end{split}\]

Type:

list[int]

unit_gates()

Get the unit_gates that make up the gate.

Returns:

List of unit gates that make up the gate.

Return type:

list[UnitGate]

__init__(qubits)

matrix()

Get the matrix representation of the gate.

Returns:

Matrix representation of the gate.

Return type:

numpy.typing.NDArray[numpy.complex128]