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I have been trying to build a Shor's Algorithm simulation for N = 15 on Qiskit's framework. Having referenced the Qiskit textbook, I built a circuit that largely resembles what they have done, with a few minor caveats. I am getting some strange and unexpected measurements, could anybody find where my problem is? Below is my code.

N = 15 a = np.random.randint(2, 15) if math.gcd(a, N) != 1: raise ValueError("Non-trivial factor.") print(a) def a_mod15(a, x): if a not in [2,7,8,11,13]: raise ValueError("'a' must be 2,7,8,11 or 13") U = QuantumCircuit(4) for iteration in range(x): if a in [2, 13]: U.swap(0, 1) U.swap(1, 2) U.swap(2, 3) if a in [7, 8]: U.swap(2, 3) U.swap(1, 2) U.swap(0, 1) if a == 11: U.swap(1, 3) U.swap(0, 2) if a in [7, 11, 13]: for q in range(4): U.x(q) U = U.to_gate() U.name = "%i^%i mod 15" % (a, x) c_U = U.control() return c_U def mod_exp(qc, n, m, a): for x in range(n): qc.append(a_mod15(a, 2**x), [x] + list(range(n, n + m))) def iqft(qc, n): qc.append(QFT(len(n), do_swaps = False).inverse(), n) def circ(n, m, a): # Let n = 'X register' # Let m = 'W register' qc = QuantumCircuit(n + m, n) qc.h(range(n)) qc.x(n + m - 1) mod_exp(qc, n, m, a) iqft(qc, range(n)) qc.measure(range(n), range(n)) return qc n = 4 m = 4 qc = circ(n, m, a) qc.draw(fold=-1) simulator = Aer.get_backend('qasm_simulator') counts = execute(qc, backend=simulator).result().get_counts(qc) plot_histogram(counts)

enter image description here

These are the expected Qiskit results (note they used 8 counting qubits and I used 4): enter image description here

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    $\begingroup$ To better understand the issue, and since your code isn't commented, could you summarize the changes you made from the qiskit example, and also describe the measurement result that you expected? $\endgroup$ Commented Feb 5, 2022 at 17:46
  • $\begingroup$ for sure, the changes that I made were as follows; 1) Below the mod_exp function that I defined, I iterated through qubits using list(range(n, n + m))), whereas the Qiskit code used [i+n_count for i in range(4)]) - I wouldn't think this would make a difference, though. 2) Qiskit hardcoded the inverse QFT, while I simply used the built-in function and made it the conjugate transpose. 3) While Qiskit appended the modular exponentiation and the inverse QFT, I integrated them as functions, so called them in a slightly different way. (expected result above) Thanks so much! @ryanhill1 $\endgroup$ Commented Feb 6, 2022 at 18:32
  • $\begingroup$ Have you tried using 8 counting qubits like the original? $\endgroup$ Commented Feb 7, 2022 at 6:41

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Your error lies in the use of the built-in QFT inside your iqft function. It seems the issue gets resolved with either of the following two tweaks:

  1. Setting do_swaps=True, i.e.
def iqft(qc, n): qc.append(QFT(len(n), do_swaps=True).inverse(), n)
  1. Reverting back to using Qiskit's hard-coded inverse QFT method, i.e.
def qft_dagger(n): """n-qubit QFTdagger the first n qubits in circ""" qc = QuantumCircuit(n) # Don't forget the Swaps! for qubit in range(n//2): qc.swap(qubit, n-qubit-1) for j in range(n): for m in range(j): qc.cp(-np.pi/float(2**(j-m)), m, j) qc.h(j) qc.name = "QFT†" return qc def iqft(qc, n): qc.append(qft_dagger(len(n)), n)
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  • $\begingroup$ Thank you so much! $\endgroup$ Commented Feb 7, 2022 at 20:00

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