Quantum Phase Estimation - Should be getting exact answer

Question

Having read the Qiskit demonstration in the Qiskit textbook on how to implement Quantum Phase Estimation, I tried to do so on PennyLane's framework. My code pretty well follows what was done in Qiskit, with a few nuances according to PennyLane, but when I run it over many shots, I get varying answers. For reference, I was implementing the T-Gate (exactly what is done in Qiskit textbook). While my code yields varying possibilities, Qiskit's strictly obtains 001 (which, through post-processing, shows that the applied phase was 1/8). Perhaps there is something wrong with the program I wrote? Is the code supposed to always yield 001?

dev = qml.device('default.qubit', wires = 4, shots=1)

@qml.qnode(dev)

def circuit():

    qml.PauliX(wires = 3)
    
    for qubit in range(3):
        qml.Hadamard(qubit)     
    
    def t_gate(j):
        qml.T(wires = j)
    
    repetitions = 1
    n = len(dev.wires) - 1
    for x in range(n-1, -1, -1):
        for i in range(repetitions):  
            qml.ctrl(t_gate, control = x)(3)
        repetitions *= 2
        
    def ops1(wires = [0, 2]):
        qml.templates.QFT(wires = [0, 2])
    qml.adjoint(ops1)(wires = [0, 2])   

    return qml.sample()

fig, ax = qml.draw_mpl(circuit)()

fig.show()

for i in range(0, 10):

    print(circuit())

Results:

[0 0 1 1]

[0 1 1 1]

[1 1 1 1]

[0 1 1 1]

[1 1 1 1]

[0 0 1 1]

[1 0 1 1]

[0 0 1 1]

[0 0 1 1]

[0 0 1 1]

Answer 1

Your circuit is very close, with only minor modifications needed to match the result from the Qiskit textbook.

• The counting registers are the first three wires of the circuit; so we need to apply the inverse QFT to wires 0, 1, and 2.

• Similarly, we want to measure samples only from wires 0, 1, and 2.

Here is an updated version of your code with these two changes:

import pennylane as qml
import numpy as np

dev = qml.device("default.qubit", wires=4, shots=10)


@qml.qnode(dev)
def circuit():
    qml.PauliX(wires=3)

    for qubit in range(3):
        qml.Hadamard(wires=qubit)

    repetitions = 1

    for x in range(2, -1, -1):
        for i in range(repetitions):
            qml.ControlledPhaseShift(np.pi / 4, wires=[x, 3])

        repetitions *= 2

    qml.adjoint(qml.QFT)(wires=[0, 1, 2])
    return qml.sample(wires=[0, 1, 2])


print(qml.draw(circuit)())
print(circuit())

This gives the results:

 0: ──H────────────────────────────────────────────────────────────────────────────────────────────╭ControlledPhaseShift(0.785)──╭ControlledPhaseShift(0.785)──╭ControlledPhaseShift(0.785)──╭ControlledPhaseShift(0.785)──╭QFT⁻¹──╭┤ Sample[basis]
 1: ──H────────────────────────────────╭ControlledPhaseShift(0.785)──╭ControlledPhaseShift(0.785)──│─────────────────────────────│─────────────────────────────│─────────────────────────────│─────────────────────────────├QFT⁻¹──├┤ Sample[basis]
 2: ──H──╭ControlledPhaseShift(0.785)──│─────────────────────────────│─────────────────────────────│─────────────────────────────│─────────────────────────────│─────────────────────────────│─────────────────────────────╰QFT⁻¹──╰┤ Sample[basis]
 3: ──X──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)──╰ControlledPhaseShift(0.785)───────────┤

[[0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]
 [0 0 1]]

matching the expected result from applying phase estimation.

---

Note that I also made some other minor modifications:

• Rather than looping over the QNode executions, if you set shots=N in the device, you will get a somewhat significant speed boost!

• While qml.ctrl(qml.T, control=x)(wires=x) works, I have slightly modified this to use qml.ControlledPhaseShift, simply because it prints out slightly nicer in the circuit drawer

• qml.T and qml.QFT are directly callables, so they can be passed directly to qml.ctrl and qml.adjoint, no need to wrap them in functions :)