Low Fidelity For QFT on IBM

Low Fidelity For QFT on IBM Ask Question Asked 9 months ago Modified today Viewed 226 times 2 I implemented a 5-qubit QFT circuit using Qiskit and performed quantum state tomography using an IBM backend. However, the reported process fidelity is only ~20%, which seems very low. I am trying to understand the potential reasons behind this. from qiskit import QuantumCircuit from qiskit_ibm_runtime import QiskitRuntimeService service = QiskitRuntimeService( channel='ibm_quantum_platform', instance='', token='', ) backend = service.backend("ibm_brisbane") def qft_circuit(n): qc = QuantumCircuit(n, n) for j in range(n): qc.h(j) for k in range(1, n - j): qc.cp(2 * 3.141592653589793 / 2**(k + 1), j + k, j) for i in range(n // 2): qc.swap(i, n - i - 1) return qc qft_20 = qft_circuit(5) qft_20.draw('mpl') qstexp1 = StateTomography(qft_20, backend=backend) qstdata1 = qstexp1.run(backend).block_for_results() # Print results display(qstdata1.analysis_results(dataframe=True)) ``` qiskitquantum-stateprogrammingqiskit-runtime Share Improve this question Follow edited Jul 13, 2025 at 15:36 asked Jul 11, 2025 at 18:04 physicino 1315 5 bronze badges Can you provide some reasoning as to why you say it "seems very low". And based on this analysis, what value were you expecting to get? –  diemilio Commented Jul 11, 2025 at 19:25 Which backend did you use? How did you perform tomography? –  Tristan Nemoz ♦ Commented Jul 12, 2025 at 15:34 Thank you for your responses. I actually expected with higher fidelity about 50 to 70 percent, as I run it with a noise model using Aersimulator of the same backend. Regarding the backed, I have tested on Brisbane and Fez. I do the tommograpphy using the following piece of code: qft_20 = qft_circuit(5) qft_20.draw('mpl') qstexp1 = StateTomography(qft_20, backend=backend) qstdata1 = qstexp1.run(backend).block_for_results() display(qstdata1.analysis_results(dataframe=True)) –  physicino Commented Jul 12, 2025 at 16:29 Can you post your full code within your post please? –  Tristan Nemoz ♦ Commented Jul 13, 2025 at 4:52 I edited the post with the full code. –  physicino Commented Jul 13, 2025 at 15:36 Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 0 You can get a bit pessimistic fidelity about 50 to 70 percent, just by running the QFT circuit without the tomagraphy. For tomagraph you need measuring circuits. For each qubit you must measure along the three Pauli axes Z, X and Y. That means three different measurement bases per qubit. If you have n qubits, every qubit can be measured in any of the three bases, so the total number of basis-combinations (i.e. distinct measurement circuits) is 3 n 3 𝑛 . Example for n =3 You need 3 3 =27 3 3 = 27 different circuits. In any basis a single qubit has two eigenstates (eigenvalues ± 1): Z basis: |0⟩,|1⟩ | 0 ⟩ , | 1 ⟩ X basis: |+⟩,|−⟩ | + ⟩ , | − ⟩ *Y basis: |+i⟩,|−i⟩ | + 𝑖 ⟩ , | − 𝑖 ⟩ Thus each basis provides 2 projectors, so there are 6 single-qubit projectors in total. When you measure n 𝑛 qubits simultaneously you get 2 n 2 𝑛 possible bit-string outcomes per circuit. Example for n = 3: 2 3 =8 2 3 = 8 different bit-strings per circuit. How many projectors do we need in the full POVM? The full, information-complete POVM is the tensor product of the six single-qubit projectors over all qubits, giving 6 n 6 𝑛 multi-qubit projectors. With n = 3 we need 6 3 =216 6 3 = 216 projectors. There will be a lot of SPAM errors and shotnoise. For reference the following qiskit circuit shows a fidelity of 0.65 without the Tomography. from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector, state_fidelity, Operator, process_fidelity, DensityMatrix from qiskit_aer import AerSimulator from qiskit_aer.noise import NoiseModel, depolarizing_error, ReadoutError import numpy as np # --- QFT‑circuit en ideale fideliteit --- def qft_circuit(n): qc = QuantumCircuit(n) for j in range(n): qc.h(j) for k in range(1, n - j): qc.cp(2 * np.pi / 2**(k + 1), j + k, j) for i in range(n // 2): qc.swap(i, n - i - 1) return qc n = 5 qc = qft_circuit(n) # Ideale staatvector en fideliteit statevector = Statevector.from_instruction(qc) ideal = np.ones(2**n) / np.sqrt(2**n) print(statevector, "Statevector") print("State fidelity (ideal):", state_fidelity(statevector, ideal)) print("Process fidelity (ideal):", process_fidelity(Operator(qc), Operator(qc))) # --- Ruis­model (depolarisatie + meetfouten) --- noise_model = NoiseModel() error_1q = depolarizing_error(0.005, 1) # 0.5% 1‑qubit depolariserende fout error_2q = depolarizing_error(0.03, 2) # 3% 2‑qubit depolariserende fout noise_model.add_all_qubit_quantum_error(error_1q, ['u1','u2','u3','rx','ry','rz','h','t','sx','x','y','z','s','sdg']) noise_model.add_all_qubit_quantum_error(error_2q, ['cx','cp','swap']) readout_error = ReadoutError([[0.9, 0.1], [0.1, 0.9]]) # 10% meetfout noise_model.add_all_qubit_readout_error(readout_error) sim = AerSimulator(noise_model=noise_model) # Ruis­simulatie met density matrix qc_dm = qc.copy() qc_dm.save_density_matrix() job = sim.run(qc_dm) result = job.result() rho = result.data(qc_dm)['density_matrix'] print("Noisy fidelity (density matrix):", state_fidelity(DensityMatrix(rho), ideal)) Output: State fidelity (ideal): 0.9999999999999991 Process fidelity (ideal): 0.9999999999999996 Noisy fidelity (density matrix): 0.6887759418623769 Share Improve this answer Follow edited Jul 27, 2025 at 6:52 answered Jul 25, 2025 at 16:31 Bram 1,5418 8 silver badges 10 10 bronze badges Thank you so much for your response. I think you have run your circuit on a simulator, which also, if you do tomography on a simulator with the noise data from a real device, you can get the same or even better results. –  physicino Commented Jul 27, 2025 at 16:08 Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions qiskitquantum-stateprogrammingqiskit-runtime See similar questions with these tags. 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