Pauli Exponentiation for Quantum Simulation¶

In this example, we will consider a simple Pauli Exponentiation circuit.

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import math

from bloqade import qasm2

import math from bloqade import qasm2

First, we define the zzzz_gadget function which is a simple implementation of Pauli Z exponentiation with a parameterized angle gamma.

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@qasm2.extended
def zzzz_gadget(targets: tuple[qasm2.Qubit, ...], gamma: float):
    for i in range(len(targets) - 1):
        qasm2.cx(targets[i], targets[i + 1])

    qasm2.rz(targets[-1], gamma)

    for j in range(len(targets) - 1):
        qasm2.cx(targets[-j - 1], targets[-j - 2])

@qasm2.extended def zzzz_gadget(targets: tuple[qasm2.Qubit, ...], gamma: float): for i in range(len(targets) - 1): qasm2.cx(targets[i], targets[i + 1]) qasm2.rz(targets[-1], gamma) for j in range(len(targets) - 1): qasm2.cx(targets[-j - 1], targets[-j - 2])

Next, we define the pauli_basis_change function which is a simple implementation of Pauli basis change with a parameterized start and end Pauli basis.

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@qasm2.extended
def pauli_basis_change(targets: tuple[qasm2.Qubit, ...], start: str, end: str):
    # assert len(targets) == len(start)
    # assert len(targets) == len(end)

    # for qubit, start_pauli, end_pauli in zip(targets, start, end):
    for i in range(len(targets)):
        qubit = targets[i]
        start_pauli = start[i]
        end_pauli = end[i]

        target = start_pauli + end_pauli
        if target == "ZX":
            qasm2.ry(qubit, math.pi / 2)
        elif target == "ZY":
            qasm2.rx(qubit, -math.pi / 2)
        # elif target == "ZZ":
        #     pass
        # elif target == "XX":
        #     pass
        elif target == "XY":
            qasm2.rz(qubit, math.pi / 2)
        elif target == "XZ":
            qasm2.ry(qubit, -math.pi / 2)
        elif target == "YX":
            qasm2.rz(qubit, -math.pi / 2)
        # elif target == "YY":
        #     pass
        elif target == "YZ":
            qasm2.rx(qubit, math.pi / 2)

@qasm2.extended def pauli_basis_change(targets: tuple[qasm2.Qubit, ...], start: str, end: str): # assert len(targets) == len(start) # assert len(targets) == len(end) # for qubit, start_pauli, end_pauli in zip(targets, start, end): for i in range(len(targets)): qubit = targets[i] start_pauli = start[i] end_pauli = end[i] target = start_pauli + end_pauli if target == "ZX": qasm2.ry(qubit, math.pi / 2) elif target == "ZY": qasm2.rx(qubit, -math.pi / 2) # elif target == "ZZ": # pass # elif target == "XX": # pass elif target == "XY": qasm2.rz(qubit, math.pi / 2) elif target == "XZ": qasm2.ry(qubit, -math.pi / 2) elif target == "YX": qasm2.rz(qubit, -math.pi / 2) # elif target == "YY": # pass elif target == "YZ": qasm2.rx(qubit, math.pi / 2)

Putting it all together, we define the pauli_exponential function which is a simple implementation of Pauli Exponentiation with a parameterized Pauli basis and angle gamma.

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@qasm2.extended
def pauli_exponential(targets: tuple[qasm2.Qubit, ...], pauli: str, gamma: float):
    # assert len(targets) == len(pauli)

    pauli_basis_change(targets=targets, start="Z" * len(targets), end=pauli)
    zzzz_gadget(targets=targets, gamma=gamma)
    pauli_basis_change(targets=targets, start=pauli, end="Z" * len(targets))

@qasm2.extended def pauli_exponential(targets: tuple[qasm2.Qubit, ...], pauli: str, gamma: float): # assert len(targets) == len(pauli) pauli_basis_change(targets=targets, start="Z" * len(targets), end=pauli) zzzz_gadget(targets=targets, gamma=gamma) pauli_basis_change(targets=targets, start=pauli, end="Z" * len(targets))

Finally, we define the main function as the entry point of the program.

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@qasm2.extended
def main():
    register = qasm2.qreg(4)
    pauli_exponential((register[0], register[1], register[2]), "ZXY", 0.5)

@qasm2.extended def main(): register = qasm2.qreg(4) pauli_exponential((register[0], register[1], register[2]), "ZXY", 0.5)

we can now ask the compiler to emit the QASM2 code for the main function.

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target = qasm2.emit.QASM2()
ast = target.emit(main)
qasm2.parse.pprint(ast)

target = qasm2.emit.QASM2() ast = target.emit(main) qasm2.parse.pprint(ast)