This work presents an empirical characterization of long-time coherence decay in a trapped-ion qubit on the IonQ Forte-1 quantum processor using high-depth CPMG dynamical-decoupling sequences. Across 97 independent runs, the measured coherence envelope exhibits a shallow long-time curvature that a standard single-exponential model cannot capture. To summarize the behavior over a wide time range, we introduce an extended empirical envelope of the formC(t) = A exp(−t/τ) t⁻ᵅ,which significantly improves fit quality (AIC/BIC, RMSE, and residual autocorrelation) relative to a pure exponential decay. The extracted power-law exponents fall in the range 0.1 ≤ α ≤ 0.3, indicating persistent long-time structure in the coherence decay. This extended envelope provides a compact descriptive model for benchmarking trapped-ion systems, evaluating dynamical-decoupling performance, and informing hardware-aware noise characterization. The empirical crossover timescale tₚ = ατ offers a simple indicator of when the power-law component becomes relevant within the experimental window. The methods include AWS Braket execution, IonQ device calibration reporting, nonlinear least-squares fitting, and statistical diagnostics. This dataset and analysis serve as a practical reference for long-time coherence studies in trapped-ion quantum hardware.
This work presents an empirical characterization of long-time coherence decay in a trapped-ion qubit on the IonQ Forte-1 quantum processor using high-depth CPMG dynamical-decoupling sequences. Across 97 independent runs, the measured coherence envelope exhibits a shallow long-time curvature that a standard single-exponential model cannot capture. To summarize the behavior over a wide time range, we introduce an extended empirical envelope of the formC(t) = A exp(−t/τ) t⁻ᵅ,which significantly improves fit quality (AIC/BIC, RMSE, and residual autocorrelation) relative to a pure exponential decay. The extracted power-law exponents fall in the range 0.1 ≤ α ≤ 0.3, indicating persistent long-time structure in the coherence decay. This extended envelope provides a compact descriptive model for benchmarking trapped-ion systems, evaluating dynamical-decoupling performance, and informing hardware-aware noise characterization. The empirical crossover timescale tₚ = ατ offers a simple indicator of when the power-law component becomes relevant within the experimental window. The methods include AWS Braket execution, IonQ device calibration reporting, nonlinear least-squares fitting, and statistical diagnostics. This dataset and analysis serve as a practical reference for long-time coherence studies in trapped-ion quantum hardware.
Abstract This work presents an empirical characterization of long-time coherence decay in a trapped-ion qubit on the IonQ Forte-1 quantum processor using high-depth CPMG dynamical-decoupling sequences. Across 97 independent runs, the measured coherence envelope exhibits a shallow long-time curvature that a standard single-exponential model cannot capture. To summarize the behavior over a wide time range, we introduce an extended empirical envelope of the form C(t) = A exp(−t/τ) t⁻ᵅ , which significantly improves fit quality (AIC/BIC, RMSE, and residual autocorrelation) relative to a pure exponential decay. The extracted power-law exponents fall in the range 0.1 ≤ α ≤ 0.3 , indicating persistent long-time structure in the coherence decay. This extended envelope provides a compact descriptive model for benchmarking trapped-ion systems, evaluating dynamical-decoupling performance, and informing hardware-aware noise characterization. The empirical crossover timescale tₚ = ατ offers a simple indicator of when the power-law component becomes relevant within the experimental window. The methods include AWS Braket execution, IonQ device calibration reporting, nonlinear least-squares fitting, and statistical diagnostics. This dataset and analysis serve as a practical reference for long-time coherence studies in trapped-ion quantum hardware.
Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical ε∝N−1/2 sampling law with the Heisenberg-limited ε∝N−1 scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report a systematic experimental benchmark of a Maximum-Likelihood Amplitude Estimation QMC pipeline on IonQ trapped-ion processors, comprising 60 hardware trials on IonQ Forte-1 across five settings(5 & 9 qubits, 100-200 shots per depth, linear & exponential amplification schedules, ~113 device-hours), together with 100 trials on IonQ Aria-1 & Forte-1 noise models at 5, 9 & 19 qubits. The pipeline combines controlled-Ry rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against bmax−1∫0bmaxsin2xdx with bmax=π/5 ,given results emerge. First, the noiseless limit it attains ε∝N−0.88, close to the Heisenberg-scaling reference, reducing the error 54-74x over a 133x increase in oracle calls. Second, scaling does not survive on hardware. Every noisy backend saturates at an error floor of (2-5)x 10^{-2}, with fitted exponents of 0.04-0.15 on Forte-1 linear schedules and α≤0 on the vendor noise models: beyond the optimal shallow depth, however, deeper amplification provides no sustained accuracy gain and instead returns to the noise floor. Forte-1 hardware also outperformed IonQ's own Aria-1 noise model at every depth m≥2, indicating that vendor noise models are bad predictors of MLAE accuracy. The practical implication for UQ is that on current devices the useful operating point is a shallow, schedule-tuned amplification depth chosen so that the deepest circuit lands near p~1/2 not the deepest schedule the coherence budget allows.
Quantum computers are rapidly becoming more capable, with dramatic increases in both qubit count \cite{kim2023evidence} and quality \cite{moses2023race}. Among different hardware approaches, trapped-ion quantum processors are a leading technology for quantum computing, with established high-fidelity operations and architectures with promising scaling. Here, we demonstrate and thoroughly benchmark the IonQ Forte system: configured as a single-chain 30-qubit trapped-ion quantum computer with all-to-all operations. We assess the performance of our quantum computer operation at the component level via direct randomized benchmarking (DRB) across all 30 choose 2 = 435 gate pairs. We then show the results of application-oriented \cite{IonQ_AQ20_2022}\cite{qedcPeerReviewed} benchmarks and show that the system passes the suite of algorithmic qubit (AQ) benchmarks up to #AQ 29. Finally, we use our component-level benchmarking to build a system-level model to predict the application benchmarking data through direct simulation. While we find that the system-level model correlates with the experiment in predicting application circuit performance, we note quantitative discrepancies indicating significant out-of-model errors, leading to higher predicted performance than what is observed. This highlights that as quantum computers move toward larger and higher-quality devices, characterization becomes more challenging, suggesting future work required to push performance further.
Quantum computing testbeds exhibit high-fidelity quantum control over small collections of qubits, enabling performance of precise, repeatable operations followed by measurements. Currently, these noisy intermediate-scale devices can support a sufficient number of sequential operations prior to decoherence such that near term algorithms can be performed with proximate accuracy (like chemical accuracy for quantum chemistry problems). While the results of these algorithms are imperfect, these imperfections can help bootstrap quantum computer testbed development. Demonstrations of these algorithms over the past few years, coupled with the idea that imperfect algorithm performance can be caused by several dominant noise sources in the quantum processor, which can be measured and calibrated during algorithm execution or in post-processing, has led to the use of noise mitigation to improve typical computational results. Conversely, benchmark algorithms coupled with noise mitigation can help diagnose the nature of the noise, whether systematic or purely random. Here, we outline the use of coherent noise mitigation techniques as a characterization tool in trapped-ion testbeds. We perform model-fitting of the noisy data to determine the noise source based on realistic physics focused noise models and demonstrate that systematic noise amplification coupled with error mitigation schemes provides useful data for noise model deduction. Further, in order to connect lower level noise model details with application specific performance of near term algorithms, we experimentally construct the loss landscape of a variational algorithm under various injected noise sources coupled with error mitigation techniques. This type of connection enables application-aware hardware codesign, in which the most important noise sources in specific applications, like quantum chemistry, become foci of improvement in subsequent hardware generations.
We study a deterministic modulation protocol, Q-Loop, that replaces multi-axis, measurementdependent control with a single scalar waveform and is implementable as an open-loop schedule on current NISQ hardware. Building on earlier work where Q-Loop was shown to reduce both the dephasing functional χ(τ ) and the minimum control amplitude required to stabilize few-qubit GHZ states under classical 1/f noise, we revisit the protocol with a more conservative analytic treatment and a quantitative comparison to alternative empirical scaling forms for modest system sizes (n = 2–8 qubits). In a pure-dephasing (or effectively commuting) regime we derive the filter-function structure of an idealized Q-Loop waveform and show that it produces a discrete comb of sidebands with tunable low-frequency suppression relative to free evolution and standard Carr–Purcell (CP) sequences. For more general noise channels the scalar filter-function picture is used as a qualitative guide, and quantitative statements are obtained from stochastic-Hamiltonian simulations with classical 1/f γ noise. Using QuTiP-based simulations of Schrödinger dynamics with time-dependent Hamiltonians and classical 1/f γ local and correlated noise, we compute the minimum control amplitude β ∗ (n) needed to maintain a fixed target fidelity as a function of system size n for n = 2–8 qubits. Over this range the ensemble-averaged β ∗ (n) data are empirically well described by β ∗ (n) ≈ Aeαn with α ≃ 0.23–0.25, while quadratic and power-law forms yield systematically higher residuals and poorer goodness-of-fit metrics (including R2 , RMSE, and Bayesian information criterion), with BIC values for the exponential model typically 10–15 units lower than for polynomial alternatives. We emphasize that this exponential behaviour is an empirical description over a finite range, not an asymptotic law. We further map the Q-Loop-induced reduction in decoherence onto a toy physical error rate p and propagate this into a repetition-code capacity model. For a fixed phenomenological mapping, Q-Loop preprocessing yields an apparent 5–6× elevation of toy thresholds relative to an amplitudematched CP baseline, although these numbers are not intended as accurate thresholds for any specific fault-tolerant architecture. Finally, we discuss deployment on superconducting, trapped-ion, and photonic platforms using a Python-based waveform generator with PyVISA AWG integration, and outline how platform-specific noise spectra could be used to tune Q-Loop parameters in situ
Coherence measurements as high as 0.9995 on IBM hardware and 0.975 on Rigetti—persisting even at extreme single-qubit depths up to 2048 H–S–H blocks—define an empirical outlier far beyond anything predicted by standard decoherence models. This stability emerges precisely where contemporary theory expects rapid collapse toward mixed states, yet the circuits remain sharply ordered and depth-insensitive. This behavior is empirically and mathematically congruent with the two-parameter unified Kālīon Field, a scalar–tensor framework shown to resolve the Hubble tension, reproduce the MOND acceleration law, unify dark-sector phenomenology, reduce quantum entropy, preserve coherence under non-unital evolution, constrain vacuum curvature, and organize gravitational–informational dynamics within a single coupled structure. The paper presents the anomaly independently of interpretation: fidelities and entropies are reconstructed directly from raw IBM and Rigetti outputs; the full dataset shows no monotonic decay toward the p₀ = 0.5 baseline; and the significance relative to a mixed-state null is extreme. The alignment with the Kālīon predictions is documented but not presupposed. All raw data, circuit reconstructions, and analysis scripts accompany this Zenodo deposit for full replication and scrutiny.