This project investigates whether a minimal single-qubit quantum circuit can accurately reproduce two-flavor neutrino oscillation probabilities, and quantifies the circuit's noise robustness in both simulation and on real IBM Quantum hardware. Using atmospheric-channel parameters from NuFit 6.0, an exact statevector circuit matches the analytical oscillation formula to floating-point precision (MAE ≈ 6.8×10⁻¹⁷), and a combined noise model (averaged over 5 random seeds) places the circuit's failure threshold at severity 1.143 ± 0.017; converting this to a real-hardware safety margin is sensitive to calibration choice, with plausible estimates ranging from roughly 1× to roughly 38× current hardware noise. A repeated 4-trial paired statistical test on real IBM Quantum hardware (ibm_marrakesh) found no significant effect of standard error-mitigation techniques (dynamical decoupling, gate twirling; p = 0.523) — reversing an initial single-trial result and illustrating why repeated trials are needed on noisy NISQ hardware. This archive contains all three Jupyter notebooks (classical baseline, ideal qubit simulation, noise/hardware validation), raw hardware measurement data, the full research paper, and a research log documenting every finding, correction, and methodological lesson from the project.
This project investigates whether a minimal single-qubit quantum circuit can accurately reproduce two-flavor neutrino oscillation probabilities, and quantifies the circuit's noise robustness in both simulation and on real IBM Quantum hardware. Using atmospheric-channel parameters from NuFit 6.0, an exact statevector circuit matches the analytical oscillation formula to floating-point precision (MAE ≈ 6.8×10⁻¹⁷), and a combined noise model (averaged over 5 random seeds) places the circuit's failure threshold at severity 1.143 ± 0.017; converting this to a real-hardware safety margin is sensitive to calibration choice, with plausible estimates ranging from roughly 1× to roughly 38× current hardware noise. A repeated 4-trial paired statistical test on real IBM Quantum hardware (ibm_marrakesh) found no significant effect of standard error-mitigation techniques (dynamical decoupling, gate twirling; p = 0.523) — reversing an initial single-trial result and illustrating why repeated trials are needed on noisy NISQ hardware. This archive contains all three Jupyter notebooks (classical baseline, ideal qubit simulation, noise/hardware validation), raw hardware measurement data, the full research paper, and a research log documenting every finding, correction, and methodological lesson from the project.
We simulate three-flavor neutrino oscillations on two-qubit quantum circuits. The flavor space is embedded as ∣00⟩=νe, ∣01⟩=νμ, ∣10⟩=ντ with the ∣11⟩ channel kept inert, and the input mixing parameters (NuFIT~5.3, normal ordering, with SK-atm) follow the global fit. We verify three physical settings against analytic or exact references: vacuum propagation, reproduced by a mass-eigenstate phase circuit to ∼10−16; constant-density Mikheev--Smirnov--Wolfenstein (MSW) matter effects, showing resonant flavor conversion when the matter potential A crosses Δm312; and varying-density (supernova shock-shell) propagation by slicing plus second-order Suzuki--Trotter splitting, with per-slice Trotter error ∼10−6 and total accuracy ∼10−4 against the continuous profile. We report a Suzuki--Trotter precision--resource calibration varying order, step number, and matrix/probability error. It delimits brute-force Trotterization on solar baselines: we quantify both standard alternatives, coherence averaging and adiabatic MSW. We also compute quantum-information diagnostics from the same model parameters, namely mode entanglement and the CP asymmetry. Finally, we extend the framework to open quantum systems via a Lindblad master equation with dephasing and absorptive channels. These results provide a reproducible link between low-energy oscillation observables and quantum-information measures.
Noisy Intermediate-Scale Quantum (NISQ) computers suffer from gate errors, decoherence, and readout noise that can severely impact even small quantum circuits. In this work, the application of error mitigation techniques was investigated to a simple two-bit quantum comparator circuit executed on real IBM Quantum hardware. The 2-bit comparator is a basic quantum logic circuit that compares two 2-qubit binary numbers and outputs whether the first number is greater than, equal to, or less than the second. This comparator was implemented using Qiskit and studied its performance under realistic noise. This study on error mitigation concentrates on dynamical decoupling (DD), which is a coherent error suppression strategy that cancels coherent errors by inserting echo pulse sequences during idle time periods. The results demonstrate that dynamical decoupling improves accuracy for the comparator circuit - accurate outcomes are closer to the ideal outcome in the absence of noise. These results show that dynamical decoupling yields notable accuracy improvements for the comparator circuit - bringing measured outcomes closer to the ideal noiseless results. A performance analysis (including a bar-chart of accuracy after mitigation vs. before mitigation simulation) is presented to quantify these improvements. Finally, the implications of applying error mitigation in small quantum circuits and its relevance for near-term quantum computing are also discussed, where such techniques can enhance the reliability of quantum computations in the absence of full quantum error correction.
Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.
In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.
H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.