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decompose ¤

Some common decomposition methods for two-qubit and three-qubit gates.

Classes:

Name Description
ThreeQubitGateDecompose

A transpiler pass that decomposes three-qubit gates into combinations of single- and two-qubit gates.

Functions:

Name Description
u_dot_u

Carry out u @ u and return a new u information
h2u

Convert H gate to U3 gate tuple.
x2u

Convert X gate to U3 gate tuple.
sdg2u

Convert sdg gate to U3 gate tuple.
s2u

Convert S gate to U3 gate tuple.
rx2u

Convert RX gate to U3 gate tuple.
ry2u

Convert RY gate to U3 gate tuple.
rz2u

Convert RZ gate to U3 gate tuple.
cz_decompose

Decompose CZ gate to U3 gates and CZ gates.
cx_decompose

Decompose CX gate to U3 gates and CZ gates.
cy_decompose

Decompose CY gate to U3 gates and CZ gates.

swap_decompose

Decompose SWAP gate to U3 gates and CZ gates.
iswap_decompose

Decompose iswap gate with qiskit decompose algorithm.

rxx_decompose

Decompose RXX gate to U3 gates and CZ gates.
ryy_decompose

Decompose RYY gate to U3 gates and CZ gates.
rzz_decompose

Decompose RZZ gate to U3 gates and CZ gates.
cp_decompose

Decompose CPhase gate to U3 gates and CZ gates. ref: Quantum Sci. Technol. 7 (2022) 025021
ccx_decompose

Decompose ccx gate. Reference: A biological sequence comparison algorithm using quantum computers
cswap_decompose

Decompose cswap gate. Reference: http://threeplusone.com/gates
ccz_decompose

Decompose ccz gate. Reference: http://threeplusone.com/gates
ccx_decompose_mute_phase

Decompose ccx gate. it will lose some phase.

ThreeQubitGateDecompose() ¤

Bases: TranspilerPass

A transpiler pass that decomposes three-qubit gates into combinations of single- and two-qubit gates.

Methods:

Name Description
run

Decompose three-qubit gates in the quantum circuit into sequences of single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def __init__(self):
    super().__init__()

run(qc: QuantumCircuit) ¤

Decompose three-qubit gates in the quantum circuit into sequences of single- and two-qubit gates.

Parameters:

Name Type Description Default
qc QuantumCircuit

The quantum circuit to process.

 required

Returns:

Name Type Description
QuantumCircuit

A new quantum circuit with all three-qubit gates decomposed into single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def run(self,qc:QuantumCircuit):
    """Decompose three-qubit gates in the quantum circuit into sequences of single- and two-qubit gates.

    Args:
        qc (QuantumCircuit): The quantum circuit to process.

    Returns:
        QuantumCircuit: A new quantum circuit with all three-qubit gates decomposed into single- and two-qubit gates.
    """
    new = []
    for gate_info in qc.gates:
        if gate_info[0] == 'ccx':
            new += ccx_decompose(*gate_info[1:])
            #new += ccx_decompose_mute_phase(*gate_info[1:])
        elif gate_info[0] == 'ccz':
            new += ccz_decompose(*gate_info[1:])
        elif gate_info[0] == 'cswap':
            new += cswap_decompose(*gate_info[1:])
        else:
            new.append(gate_info)
    new_qc = qc.deepcopy()
    new_qc.gates = new
    return new_qc

u_dot_u(u_info1: tuple, u_info2: tuple) -> tuple ¤

Carry out u @ u and return a new u information

Parameters:

Name Type Description Default
u_info1 tuple

u gate information like ('u', 1.5707963267948966, 0.0, 3.141592653589793, 0)

 required
u_info2 tuple

u gate information like ('u', 1.5707963267948966, 0.0, 3.141592653589793, 0)

 required

Returns:

Name Type Description
tuple tuple

A new u gate information
Source code in quark/circuit/decompose.py 
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def u_dot_u(u_info1: tuple, u_info2: tuple) -> tuple:
    """Carry out u @ u and return a new u information

    Args:
        u_info1 (tuple): u gate information like ('u', 1.5707963267948966, 0.0, 3.141592653589793, 0)
        u_info2 (tuple): u gate information like ('u', 1.5707963267948966, 0.0, 3.141592653589793, 0)

    Returns:
        tuple: A new u gate information
    """
    assert(u_info1[-1] == u_info2[-1])
    u_mat1 = u_mat(*u_info1[1:-1])
    u_mat2 = u_mat(*u_info2[1:-1])

    new_u = u_mat2 @ u_mat1
    theta, phi, lamda, _ = u3_decompose(new_u)
    return ('u', theta, phi, lamda, u_info1[-1])

h2u(qubit: int) -> tuple ¤

Convert H gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def h2u(qubit: int) -> tuple:
    """Convert H gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u', np.pi/2, 0.0, np.pi, qubit)

x2u(qubit: int) -> tuple ¤

Convert X gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def x2u(qubit: int) -> tuple:
    """Convert X gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u', np.pi, np.pi/2, -np.pi/2, qubit)

sdg2u(qubit: int) -> tuple ¤

Convert sdg gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def sdg2u(qubit:int) -> tuple:
    """Convert sdg gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u', 0.0, -0.7853981633974483, -0.7853981633974483, qubit)

s2u(qubit: int) -> tuple ¤

Convert S gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def s2u(qubit: int) -> tuple:
    """Convert S gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u', 0.0, 0.7853981633974483, 0.7853981633974483, qubit)

rx2u(theta: float, qubit: int) -> tuple ¤

Convert RX gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def rx2u(theta:float,qubit:int) -> tuple:
    """Convert RX gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u',theta,-np.pi/2,np.pi/2,qubit)

ry2u(theta: float, qubit: int) -> tuple ¤

Convert RY gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def ry2u(theta:float,qubit:int) -> tuple:
    """Convert RY gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u',theta,0.0,0.0,qubit)

rz2u(theta: float, qubit: int) -> tuple ¤

Convert RZ gate to U3 gate tuple.

Parameters:

Name Type Description Default
qubit int

The qubit to apply the gate to.

 required

Returns:

Name Type Description
tuple tuple

u3 gate information.
Source code in quark/circuit/decompose.py 
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def rz2u(theta:float,qubit:int) -> tuple:
    """Convert RZ gate to U3 gate tuple.

    Args:
        qubit (int): The qubit to apply the gate to.

    Returns:
        tuple: u3 gate information.
    """
    return ('u',0.0,0.0,theta,qubit)

cz_decompose(control_qubit: int, target_qubit: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cx', 'cz', 'iswap']) -> list ¤

Decompose CZ gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
control_qubit int

The qubit used as control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def cz_decompose(control_qubit: int, target_qubit: int,convert_single_qubit_gate_to_u:bool,two_qubit_gate_basis:Literal['cx','cz','iswap']) -> list:
    """ Decompose CZ gate to U3 gates and CZ gates.

    Args:
        control_qubit (int): The qubit used as control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    gates = []
    if two_qubit_gate_basis == 'cz':
        gates.append(('cz',control_qubit,target_qubit))
    elif two_qubit_gate_basis == 'cx':
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(target_qubit))
        else:
            gates.append(('h',target_qubit))
        gates.append(('cx', control_qubit, target_qubit))
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(target_qubit))
        else:
            gates.append(('h',target_qubit))
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cz_to_iswap(control_qubit,target_qubit,convert_single_qubit_gate_to_u)

    return gates

cx_decompose(control_qubit: int, target_qubit: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cx', 'cz', 'iswap']) -> list ¤

Decompose CX gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
control_qubit int

The qubit used as control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def cx_decompose(control_qubit: int, target_qubit: int,convert_single_qubit_gate_to_u:bool,two_qubit_gate_basis:Literal['cx','cz','iswap']) -> list:
    """ Decompose CX gate to U3 gates and CZ gates.

    Args:
        control_qubit (int): The qubit used as control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    gates = []
    if two_qubit_gate_basis == 'cz':
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(target_qubit))
        else:
            gates.append(('h',target_qubit))
        gates.append(('cz', control_qubit, target_qubit))
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(target_qubit))
        else:
            gates.append(('h',target_qubit))
    elif two_qubit_gate_basis == 'cx':
        gates.append(('cx',control_qubit,target_qubit))
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(control_qubit,target_qubit,convert_single_qubit_gate_to_u)
    return gates

cy_decompose(control_qubit: int, target_qubit: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose CY gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
control_qubit int

The qubit used as control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def cy_decompose(control_qubit: int, target_qubit: int, convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """ Decompose CY gate to U3 gates and CZ gates. 

    Args:
        control_qubit (int): The qubit used as control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of U3 gates and CZ gates.
    """

    gates = []
    if convert_single_qubit_gate_to_u:
        gates.append(sdg2u(target_qubit))
    else:
        gates.append(('sdg',target_qubit))

    if two_qubit_gate_basis == 'cz':
        gates += cx_decompose(control_qubit,target_qubit,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'cx':
        gates.append(('cx',control_qubit,target_qubit))
    elif two_qubit_gate_basis =='iswap':
        gates += convert_cx_to_iswap(control_qubit,target_qubit,convert_single_qubit_gate_to_u)

    if convert_single_qubit_gate_to_u:
        gates.append(s2u(target_qubit))
    else:
        gates.append(('s',target_qubit))
    return gates

swap_decompose(qubit1: int, qubit2: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose SWAP gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
qubit1 int

The first qubit to apply the gate to.

 required
qubit2 int

The second qubit to apply the gate to.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def swap_decompose(qubit1: int, qubit2: int, convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """Decompose SWAP gate to U3 gates and CZ gates.

    Args:
        qubit1 (int): The first qubit to apply the gate to.
        qubit2 (int): The second qubit to apply the gate to.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    if two_qubit_gate_basis == 'cz':
        gates = []
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(qubit2))
        else:
            gates.append(('h',qubit2))
        gates.append(('cz',qubit1,qubit2))
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(qubit2))
            gates.append(h2u(qubit1))
        else:
            gates.append(('h',qubit2))
            gates.append(('h',qubit1))
        gates.append(('cz',qubit1,qubit2))
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(qubit1))
            gates.append(h2u(qubit2))
        else:
            gates.append(('h',qubit1))
            gates.append(('h',qubit2))
        gates.append(('cz',qubit1,qubit2))
        if convert_single_qubit_gate_to_u:
            gates.append(h2u(qubit2))
        else:
            gates.append(('h',qubit2))
    elif two_qubit_gate_basis == 'cx':
        gates = []
        gates.append(('cx',qubit1,qubit2))
        gates.append(('cx',qubit2,qubit1))
        gates.append(('cx',qubit1,qubit2))
    elif two_qubit_gate_basis == 'iswap':
        gates = []
        gates.append(('iswap',qubit1,qubit2))
        gates.append(('sx',qubit2))
        gates.append(('iswap',qubit1,qubit2))
        gates.append(('sx',qubit1))
        gates.append(('iswap',qubit1,qubit2))
        gates.append(('sx',qubit2))
    return gates

iswap_decompose(qubit1: int, qubit2: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose iswap gate with qiskit decompose algorithm.

Parameters:

Name Type Description Default
qubit1 int

The first qubit to apply the gate to.

 required
qubit2 int

The second qubit to apply the gate to.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def iswap_decompose(qubit1: int, qubit2: int, convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """ Decompose iswap gate with qiskit decompose algorithm. 

    Args:
        qubit1 (int): The first qubit to apply the gate to.
        qubit2 (int): The second qubit to apply the gate to.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    # iswap = R_{XX+YY}(-pi/2) = e^{i*pi/4*(X\otimesX + Y\otimesY)}
    if two_qubit_gate_basis == 'iswap':
        gates = []
        gates.append(('iswap',qubit1,qubit2))
    else:
        gates = []
        if convert_single_qubit_gate_to_u:
            gates.append(x2u(qubit1))
            gates.append(rx2u(np.pi/2,qubit1))
            gates.append(rx2u(-np.pi/2,qubit2))
        else:
            gates.append(('x', qubit1))
            gates.append(('rx', np.pi/2, qubit1))
            gates.append(('rx',-np.pi/2, qubit2))
        if two_qubit_gate_basis == 'cx':
            gates.append(('cx',  qubit1, qubit2))
        elif two_qubit_gate_basis == 'cz':
            gates += cx_decompose(qubit1, qubit2, convert_single_qubit_gate_to_u,two_qubit_gate_basis)
        if convert_single_qubit_gate_to_u:
            gates.append(rx2u(-np.pi/2,qubit1))
            gates.append(rz2u(-np.pi/2,qubit2))
        else:
            gates.append(('rx',-np.pi/2, qubit1))
            gates.append(('rz',-np.pi/2, qubit2)) 
        if two_qubit_gate_basis == 'cx':
            gates.append(('cx',  qubit1, qubit2))
        elif two_qubit_gate_basis == 'cz':
            gates += cx_decompose(qubit1, qubit2, convert_single_qubit_gate_to_u,two_qubit_gate_basis)
        if convert_single_qubit_gate_to_u:
            gates.append(rx2u(-np.pi/2, qubit1))
            gates.append(rx2u(np.pi/2, qubit2))
            gates.append(x2u(qubit1))
        else:
            gates.append(('rx',-np.pi/2, qubit1))
            gates.append(('rx', np.pi/2, qubit2))
            gates.append(('x', qubit1))
    return gates

rxx_decompose(theta: float, qubit1: int, qubit2: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose RXX gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
theta float

The rotation angle of the gate.

 required
qubit1 int

The first qubit to apply the gate to.

 required
qubit2 int

The second qubit to apply the gate to.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def rxx_decompose(theta:float,qubit1:int,qubit2:int,convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """Decompose RXX gate to U3 gates and CZ gates.

    Args:
        theta (float): The rotation angle of the gate.
        qubit1 (int): The first qubit to apply the gate to.
        qubit2 (int): The second qubit to apply the gate to.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    gates = []
    if convert_single_qubit_gate_to_u:
        gates.append(h2u(qubit1))
        gates.append(h2u(qubit2))
    else:
        gates.append(('h', qubit1))
        gates.append(('h', qubit2))
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx',qubit1,qubit2))
    elif two_qubit_gate_basis == 'cz':        
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)

    if convert_single_qubit_gate_to_u:
        gates.append(rz2u(theta,qubit2))
    else:
        gates.append(('rz', theta, qubit2))
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx',qubit1,qubit2))
    elif two_qubit_gate_basis == 'cz':        
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)

    if convert_single_qubit_gate_to_u:  
        gates.append(h2u(qubit1))
        gates.append(h2u(qubit2))
    else:
        gates.append(('h', qubit1))
        gates.append(('h', qubit2))      
    return gates

ryy_decompose(theta: float, qubit1: int, qubit2: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose RYY gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
theta float

The rotation angle of the gate.

 required
qubit1 int

The first qubit to apply the gate to.

 required
qubit2 int

The second qubit to apply the gate to.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def ryy_decompose(theta:float, qubit1:int, qubit2:int, convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """Decompose RYY gate to U3 gates and CZ gates.

    Args:
        theta (float): The rotation angle of the gate.
        qubit1 (int): The first qubit to apply the gate to.
        qubit2 (int): The second qubit to apply the gate to.

    Returns:
        list: A list of U3 gates and CZ gates.
    """
    gates = []
    if convert_single_qubit_gate_to_u:
        gates.append(rx2u(np.pi/2,qubit1))
        gates.append(rx2u(np.pi/2,qubit2))
    else:
        gates.append(('rx',np.pi/2,qubit1))
        gates.append(('rx',np.pi/2,qubit2))     
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx', qubit1, qubit2))
    elif two_qubit_gate_basis == 'cz':
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)
    if convert_single_qubit_gate_to_u:
        gates.append(rz2u(theta,qubit2))
    else:
        gates.append(('rz', theta, qubit2))
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx', qubit1, qubit2))
    elif two_qubit_gate_basis == 'cz':
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)
    if convert_single_qubit_gate_to_u:
        gates.append(rx2u(-np.pi/2,qubit1))
        gates.append(rx2u(-np.pi/2,qubit2))
    else:
        gates.append(('rx', -np.pi/2, qubit1))
        gates.append(('rx', -np.pi/2, qubit2))    
    return gates

rzz_decompose(theta: float, qubit1: int, qubit2: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose RZZ gate to U3 gates and CZ gates.

Parameters:

Name Type Description Default
theta float

The rotation angle of the gate.

 required
qubit1 int

The first qubit to apply the gate to.

 required
qubit2 int

The second qubit to apply the gate to.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def rzz_decompose(theta:float, qubit1:int, qubit2:int, convert_single_qubit_gate_to_u:bool, two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """Decompose RZZ gate to U3 gates and CZ gates.

    Args:
        theta (float): The rotation angle of the gate.
        qubit1 (int): The first qubit to apply the gate to.
        qubit2 (int): The second qubit to apply the gate to.

    Returns:
        list: A list of U3 gates and CZ gates.
    """ 
    gates = []
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx', qubit1, qubit2))
    elif two_qubit_gate_basis == 'cz':
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)
    if convert_single_qubit_gate_to_u:
        gates.append(rz2u(theta,qubit2))
    else:
        gates.append(('rz', theta, qubit2))
    if two_qubit_gate_basis == 'cx':
        gates.append(('cx', qubit1, qubit2))
    elif two_qubit_gate_basis == 'cz':
        gates += cx_decompose(qubit1,qubit2,convert_single_qubit_gate_to_u,two_qubit_gate_basis)  
    elif two_qubit_gate_basis == 'iswap':
        gates += convert_cx_to_iswap(qubit1,qubit2,convert_single_qubit_gate_to_u)
    return gates

cp_decompose(theta: float, control_qubit: int, target_qubit: int, convert_single_qubit_gate_to_u: bool, two_qubit_gate_basis: Literal['cz', 'cx', 'iswap']) -> list ¤

Decompose CPhase gate to U3 gates and CZ gates. ref: Quantum Sci. Technol. 7 (2022) 025021

Parameters:

Name Type Description Default
theta float

The rotation angle of the gate.

 required
control_qubit int

The qubit used as control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list list

A list of U3 gates and CZ gates.
Source code in quark/circuit/decompose.py 
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def cp_decompose(theta:float, control_qubit:int, target_qubit:int, convert_single_qubit_gate_to_u:bool,two_qubit_gate_basis:Literal['cz','cx','iswap']) -> list:
    """Decompose CPhase gate to U3 gates and CZ gates. ref: Quantum Sci. Technol. 7 (2022) 025021

    Args:
        theta (float): The rotation angle of the gate.
        control_qubit (int): The qubit used as control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of U3 gates and CZ gates.
    """ 
    gates = []
    if convert_single_qubit_gate_to_u:
        gates.append(h2u(target_qubit))
    else:
        gates.append(('h',target_qubit))

    #gates.append(('cz', control_qubit, target_qubit))
    gates += cz_decompose(control_qubit,target_qubit,convert_single_qubit_gate_to_u,two_qubit_gate_basis)

    if convert_single_qubit_gate_to_u:
        gates.append(rx2u(theta/2,target_qubit))
    else:
        gates.append(('rx',theta/2,target_qubit))

    #gates.append(('cz', control_qubit, target_qubit))
    gates += cz_decompose(control_qubit,target_qubit,convert_single_qubit_gate_to_u,two_qubit_gate_basis)

    if convert_single_qubit_gate_to_u:
        gates.append(rz2u(-1*theta/2, control_qubit))
        gates.append(h2u(target_qubit))
        gates.append(rz2u(-1*theta/2,target_qubit))
    else:
        gates.append(('rz',-1*theta/2,control_qubit))
        gates.append(('h',target_qubit))
        gates.append(('rz',-1*theta/2,target_qubit))
    return gates

ccx_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int) ¤

Decompose ccx gate. Reference: A biological sequence comparison algorithm using quantum computers

Parameters:

Name Type Description Default
control_qubit1 int

The qubit used as the first control.

 required
control_qubit2 int

The qubit used as the second control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list

A list of single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def ccx_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int,):
    """Decompose ccx gate. Reference: A biological sequence comparison algorithm using quantum computers

    Args:
        control_qubit1 (int): The qubit used as the first control.
        control_qubit2 (int): The qubit used as the second control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of single- and two-qubit gates.
    """
    gates = [
        ('h',target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('t',target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('t',control_qubit2),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('cx',control_qubit1,control_qubit2),
        ('t',target_qubit),
        ('t',control_qubit1),
        ('tdg',control_qubit2),
        ('h',target_qubit),
        ('cx',control_qubit1,control_qubit2),
    ]
    return gates

cswap_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int) ¤

Decompose cswap gate. Reference: http://threeplusone.com/gates

Parameters:

Name Type Description Default
control_qubit1 int

The qubit used as the first control.

 required
control_qubit2 int

The qubit used as the second control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list

A list of single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def cswap_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int,):
    """Decompose cswap gate. Reference: http://threeplusone.com/gates

    Args:
        control_qubit1 (int): The qubit used as the first control.
        control_qubit2 (int): The qubit used as the second control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of single- and two-qubit gates.
    """
    gates = [
        ('cx',target_qubit,control_qubit2),
        ('h',target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('t',target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('t',control_qubit2),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('cx',control_qubit1,control_qubit2),
        ('t',target_qubit),
        ('t',control_qubit1),
        ('tdg',control_qubit2),
        ('h',target_qubit),
        ('cx',control_qubit1,control_qubit2),
        ('cx',target_qubit,control_qubit2),
    ]
    return gates

ccz_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int) ¤

Decompose ccz gate. Reference: http://threeplusone.com/gates

Parameters:

Name Type Description Default
control_qubit1 int

The qubit used as the first control.

 required
control_qubit2 int

The qubit used as the second control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list

A list of single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def ccz_decompose(control_qubit1: int, control_qubit2: int, target_qubit: int,):
    """Decompose ccz gate. Reference: http://threeplusone.com/gates

    Args:
        control_qubit1 (int): The qubit used as the first control.
        control_qubit2 (int): The qubit used as the second control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of single- and two-qubit gates.
    """
    gates = [
        ('cx',control_qubit2,target_qubit),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('t',target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('t',control_qubit2),
        ('tdg',target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('cx',control_qubit1,control_qubit2),
        ('t',target_qubit),
        ('t',control_qubit1),
        ('tdg',control_qubit2),
        ('h',target_qubit),
        ('cx',control_qubit1,control_qubit2),
        ('h',target_qubit)
    ]
    return gates

ccx_decompose_mute_phase(control_qubit1: int, control_qubit2: int, target_qubit: int) ¤

Decompose ccx gate. it will lose some phase.

Parameters:

Name Type Description Default
control_qubit1 int

The qubit used as the first control.

 required
control_qubit2 int

The qubit used as the second control.

 required
target_qubit int

The qubit targeted by the gate.

 required

Returns:

Name Type Description
list

A list of single- and two-qubit gates.
Source code in quark/circuit/decompose.py 
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def ccx_decompose_mute_phase(control_qubit1: int, control_qubit2: int, target_qubit: int,):
    """Decompose ccx gate. it will lose some phase.

    Args:
        control_qubit1 (int): The qubit used as the first control.
        control_qubit2 (int): The qubit used as the second control.
        target_qubit (int): The qubit targeted by the gate.

    Returns:
        list: A list of single- and two-qubit gates.
    """
    gates = [
        ('u',np.pi/4,0,0,target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('u',np.pi/4,0,0,target_qubit),
        ('cx',control_qubit1,target_qubit),
        ('u',np.pi/4,-np.pi,-np.pi,target_qubit),
        ('cx',control_qubit2,target_qubit),
        ('u',np.pi/4,-np.pi,-np.pi,target_qubit),
    ]
    return gates[::-1]