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.
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.
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.
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.
Version 3.1: Extended cross-platform validation of structural coherence protection in GHZ entangled states. KEY FINDINGS:- GHZ states show 2.4-13.8× slower decay (IBM Heron) and +5-9% fidelity advantage (IonQ Forte) vs product states- Structural protection is GHZ-specific: W-states (-12%) and Cluster states (-38%) underperform product states on IonQ- Non-Markovian memory (N1) detected in trapped ions: Dynamical decoupling with Z-pulses improves GHZ protection by +2.99%, 5× stronger than IBM's +0.6%- Scaling confirmed from 3 to 7 qubits with 100% consistency across all measurements PLATFORMS:- IBM Heron: ibm_torino (r1), ibm_fez (r2), ibm_boston (r3)- IonQ Forte 1 (trapped ions, 36 qubits) EXPERIMENT DATES: January 15-18, 2026TOTAL INVESTMENT: ~$2,350 USD (IBM + AWS/IonQ) This version extends v2.1 (DOI: 10.5281/zenodo.18284373) with IonQ cross-platform validation, entanglement-type dependence analysis, and non-Markovian memory detection via dynamical decoupling.
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
Abstract We report the experimental implementation of dynamical decoupling on a small, non-interacting ensemble of up to 25 optically trapped, neutral Cs atoms. The qubit consists of the two magnetic-insensitive Cs clock states | F = 3 , m F = 0 ⟩ and | F = 4 , m F = 0 ⟩ , which are coupled by microwave radiation. We observe a significant enhancement of the coherence time when employing Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. A CPMG sequence with ten refocusing pulses increases the coherence time of 16.2(9) ms by more than one order of magnitude to 178(2) ms. In addition, we make use of the filter function formalism and utilise the CPMG sequence to measure the background noise floor affecting the qubit coherence, finding a power-law noise spectrum 1 / ω α with α = 0.89 ( 2 ) . This finding is in very good agreement with an independent measurement of the noise in the intensity of the trapping laser. Moreover, the measured coherence evolutions also exhibit signatures of low-frequency noise originating at distinct frequencies. Our findings point toward noise spectroscopy of engineered atomic baths through single-atom dynamical decoupling in a system of individual Cs impurities immersed in an ultracold 87Rb bath.