Quantum computation of trapped spectra for nuclear scattering requires resource-efficient circuits and reliable energy inputs. We present a cross-platform benchmark of ancilla-recycled RODEO filtering for a four-dimensional effective Hamiltonian describing a trapped neutron--proton model. Static circuits on IonQ Forte-1 and dynamic circuits on IBM Aachen implement the same ideal ten-cycle all-zero accepted filter using twelve and three active qubits, respectively. Mid-circuit measurement and reset reduce the active qubit count by 75\% while retaining all controlled evolutions. The interleaved IBM peak-center offset from the exact level is $-0.017 \pm 0.507~\mathrm{keV}$, compared with $-0.568 \pm 0.694~\mathrm{keV}$ for IonQ (finite-shot bootstrap uncertainties). At \(ω=3.7~\mathrm{MeV}\), the modified effective range expansion maps both centers to finite-confinement scattering inputs consistent with the exact reference within propagated uncertainties. Three IBM batches exhibit center variations beyond finite-shot uncertainties (\(p=0.015\)), despite comparatively stable postselection amplitudes. Calibration-derived noisy simulations do not consistently reproduce the measured centers. Complete sampled support enables sample-based quantum diagonalization to recover the exact effective-space level, whereas larger-space simulator tests expose substantial errors from omitted configurations. The calculation validates one finite-confinement input, not a free-space phase shift. This benchmark provides a reusable circuit and validation protocol separating spectral precision, hardware repeatability, and sampled-subspace completeness for multilevel nuclear-scattering calculations.
Quantum computation of trapped spectra for nuclear scattering requires resource-efficient circuits and reliable energy inputs. We present a cross-platform benchmark of ancilla-recycled RODEO filtering for a four-dimensional effective Hamiltonian describing a trapped neutron--proton model. Static circuits on IonQ Forte-1 and dynamic circuits on IBM Aachen implement the same ideal ten-cycle all-zero accepted filter using twelve and three active qubits, respectively. Mid-circuit measurement and reset reduce the active qubit count by 75% while retaining all controlled evolutions. The interleaved IBM peak-center offset from the exact level is −0.017±0.507keV, compared with −0.568±0.694keV for IonQ (finite-shot bootstrap uncertainties). At (ω=3.7~\mathrm{MeV}), the modified effective range expansion maps both centers to finite-confinement scattering inputs consistent with the exact reference within propagated uncertainties. Three IBM batches exhibit center variations beyond finite-shot uncertainties ((p=0.015)), despite comparatively stable postselection amplitudes. Calibration-derived noisy simulations do not consistently reproduce the measured centers. Complete sampled support enables sample-based quantum diagonalization to recover the exact effective-space level, whereas larger-space simulator tests expose substantial errors from omitted configurations. The calculation validates one finite-confinement input, not a free-space phase shift. This benchmark provides a reusable circuit and validation protocol separating spectral precision, hardware repeatability, and sampled-subspace completeness for multilevel nuclear-scattering calculations.
We reconstruct elastic s-wave neutron-proton (np) phase shifts from trapped spectra measured on IBM Aachen using a compressed RODEO circuit. For a schematic square-well interaction represented by classically constructed four-dimensional effective Hamiltonians, four positive-energy levels at five trap strengths supply twenty inputs to classical modified effective range expansion (MERE) extrapolation to free space. The six-cycle factorized geometric-time RODEO implementation (FG-R6) combines ancilla reuse, exact query-phase separation, post-compilation binding, and six numerically optimized geometric evolution times. Numerical cycle-count tests support this choice within the adopted local spectral tolerances. At the same three-qubit width and equal shot budgets, FG-R6 reduces median compiled depth and two-qubit-gate count by 33.1% and 37.2% relative to ten-cycle dynamic direct RODEO (direct R10), increases the median fitted amplitude, and lowers median finite-shot energy uncertainty from 0.610 to 0.534 keV. For this dataset's primary fit on the 0.1-30.0 MeV grid, the maximum central phase-shift deviation from exact-energy MERE decreases from 0.842∘ to 0.163∘, despite a larger root-mean-square (RMS) trapped-energy deviation. The full-grid gain arises mainly in the low-energy extrapolation region; direct R10 has slightly smaller residuals relative to the same reference on the 10.0-30.0 MeV common energy-interpolation subset. The FG-R6 central curve differs from the analytical square-well solution by at most 0.156∘. Fit-form sensitivity remains appreciable and is assessed separately from finite-shot uncertainty. This reduced-space benchmark connects RODEO circuit compression to nuclear continuum observables and shows why circuit performance must be assessed through the scattering reconstruction and its energy range, not spectral RMS errors alone.
Qudits, the multi-level generalization of qubits, provide a natural extension of the binary paradigm in quantum computation and offer new opportunities to enhance algorithmic performance. Beyond their direct applicability to the simulation of multi-level quantum systems, higher-dimensional ancillae can improve sampling efficiency in quantum algorithms by enabling the simultaneous implementation of multiple control operations, thereby reducing circuit complexity. In this work, we pursue three main objectives. First, we present a formulation of the Rodeo algorithm employing a general d-level ancilla qudit. Second, we introduce the concept of the \emph{Rodeo kernel}, defined as a two-frequency interferometer, which acts as a spectral filter in the energy domain. Finally, we propose a microcanonical protocol for the Rodeo algorithm. This protocol enables the estimation of entropic quantities through a single energy sweep and admits a natural interpretation as a Gaussian convolution of the density of states. To support the theoretical analysis, we perform numerical evaluations of the corresponding quantum circuit using ancilla qudits of dimensions three, four, and five. The simulations are performed for the one-dimensional Ising model, considering both spin-$\sfrac{1}{2}$ and spin-1 particles. The ancilla qutrit implementation exhibits an 18% reduction in fluctuations compared to the qubit implementation. Our results show that qudits provide a framework for spectral analysis and thermodynamic characterization of multi-level quantum systems.
Abstract Qudits, the multi-level generalization of qubits, provide a natural extension of the binary paradigm in quantum computation and offer new opportunities to enhance algorithmic performance. Beyond their direct applicability to the simulation of multi-level quantum systems, higher-dimensional ancillae can improve sampling efficiency in quantum algorithms by enabling the simultaneous implementation of multiple control operations, thereby reducing circuit complexity. In this work, we pursue three main objectives. First, we present a formulation of the Rodeo algorithm employing a general d-level ancilla qudit. Second, we introduce the concept of the Rodeo kernel, defined as a two-frequency interferometer, which acts as a spectral filter in the energy domain. Finally, we propose a microcanonical protocol for the Rodeo algorithm. This protocol enables the estimation of entropic quantities through a single energy sweep and admits a natural interpretation as a Gaussian convolution of the density of states. To support the theoretical analysis, we perform numerical evaluations of the corresponding quantum circuit using ancilla qudits of dimensions three, four, and five. The simulations are performed for the one-dimensional Ising model, considering both spin-1/2 and spin-1 particles. The ancilla qutrit implementation exhibits an 18% reduction in fluctuations compared to the qubit implementation. Our results show that the qudits provide a framework for spectral analysis and thermodynamic characterization of multi-level quantum systems.
We extend sample-based quantum diagonalization (SQD) to anharmonic vibrational spectra and use it to benchmark how vibrational ansätze scale on present-day hardware under a direct one-hot encoding (up to 72 qubits). Five particle-conserving circuits are warm-started through vibrational coupled-cluster (VCC) t1, t2 amplitudes: UVCCSD, the compact heuristic circuit (CHC), and three unitary-cluster-Jastrow ansätze introduced here, VLUCJ, Vg-uCJ, and VIm-uCJ. A self-consistent configuration-recovery loop reconstructs correlated states from hardware samples in the low-retention regime where naïve post-selection breaks down, enabling the calculation of ground-state energies for H2O, CH2O, and CH2ClF (3-9 modes). We compare harmonic-oscillator and vibrational self-consistent-field (VSCF, "modal") reference bases. In the small-modal-basis regime relevant for near-term devices, the modal basis is typically more accurate than the harmonic-oscillator representation; empirically, it also yields substantially better-converged hardware sampling for deep circuits at these qubit counts. Across ansätze, we find a clear retention/accuracy tradeoff when scaling: the new VLUCJ circuit is the most hardware-robust, retaining the largest fraction of physically valid one-hot outcomes, whereas the more expressive uCJ variants and UVCCSD can recover more correlation when retention is sufficient. Finally, we extend the recovery protocol to excited states by targeting a chosen per-mode VSCF occupation and warm-starting it with a state-specific VCC calculation, and we demonstrate the calculation of one representative fundamental vibrational frequency per molecule on IBM QPUs.
Validating quantum processors at scale increasingly relies on approximate classical simulation, which adds truncation error to the comparison between ideal and observed behavior. We describe a 15-qubit dynamic-circuit benchmark that stays within exact state-vector simulation, so the ideal reference value is computed without approximation. The circuit scrambles a 6-qubit system, couples it to a 5-qubit engineered environment, reads out four weakly coupled probe qubits mid-circuit, and then applies the inverse of the scrambling and system–environment coupling to restore the system's coherence. Exact summation over the 16 probe outcomes gives an ideal recovery fidelity F_max = 0.9889 on the 11-qubit system–environment register; the shortfall from unity reflects information carried away by the probes, whose coupling is not inverted and which are discarded after readout. We demonstrate the pipeline with a single 400-shot run on the Quantinuum H2-1 emulator (quantinuum.sim.h2-1e) via Azure Quantum. A local surrogate built from three published H2-1 headline error rates predicted F_exp = 0.8353 ± 0.0054; the emulator returned a readout-mitigated F_rec = 0.7836 ± 0.0212, 2.36 nominal standard errors lower. Because the surrogate's quoted uncertainty reflects sampling error only, we interpret the shortfall as evidence of surrogate-model mismatch—expected, given the emulator's richer noise model—rather than as a statistically calibrated anomaly. No physical-hardware data are reported. Changes in v50: Retitled (formerly "A 15-Qubit Decoherence-Reversal Protocol for Benchmarking Mid-Circuit Measurements and Environmental Imprinting"). Corrected the echo formulation (v49 Eq. 4 was identically 1) and the reported raw frequency (77.5%, not 76.0%). Result reframed as a nominal surrogate-model mismatch on the H2-1 emulator rather than anomalous decoherence; SWAP-routing explanation withdrawn. References corrected; limitations and data/code availability added. Analysis code unchanged from v48. Code and data: https://github.com/dkahng/15-qubit-mcm-protocol
Hardware noise and finite sampling perturb the fidelity estimates forming a quantum-kernel Gram matrix. We measured how far three hardware-reconstructed Gram matrices depart from an exact statevector reference for one frozen four-qubit ZZ feature map on N=24 indoor air-quality windows, executed on ibm_fez at 1024 shots per circuit in three single, non-interleaved jobs: baseline, dynamical decoupling alone, and gate twirling alone. All were complete, finite, and positive-semidefinite. Off-diagonal root-mean-squared error (RMSE) against the reference was 0.0878, 0.0864, and 0.0427; full-matrix centered kernel alignment (CKA) ranged 0.933-0.989 and the post hoc diagonal-excluded (U-centered) CKA 0.816-0.986. The gate-twirled job deviated least on every reported geometry axis; its baseline contrasts are deletion-stable for the Spearman, mean-absolute-error, RMSE, and full-matrix CKA diagnostics, while the Pearson and diagonal-excluded contrasts fall just below that convention. Dynamical decoupling was not separated from the baseline. The observed error exceeded both finite-shot reference scales, so, under those sampling-only models, sampling does not explain it. Centered kernel-target alignment did not track reconstruction fidelity and stayed at or below each label-permutation reference: implementation fidelity and task relevance are distinct diagnostic axes. All configuration-level statements describe three realized jobs on one backend; no mitigation-efficacy, classifier-superiority, forecasting, or quantum-advantage claim is made.