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Engineering Non-Linear Decay Dynamics: Pulse-Level Control and Software-Defined Qubit Rescue on Superconducting Processors

K S, Unnikuttan

Published Dec 27, 2025• 736 citations
Publisher

Abstract

The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices is currently constrained by material defects, specifically Two-Level Systems (TLS) that induce resonant decoherence in superconducting qubits. This study presents a comprehensive experimental analysis using the IBM Quantum ibm_fez processor to demonstrate "Software-Defined Hardware" optimization. By employing a novel "Instruction-Level Calibration Injection" technique, we bypass standard compiler constraints to inject continuous off-resonant AC Stark drives ($N_{shots} = 4096$). Methodology The experiment utilizes a Floquet engineering approach to perform pulse-level Hamiltonian engineering. We implement custom instruction-level calibrations to apply continuous off-resonant AC Stark drives, effectively modifying the qubit frequency to avoid resonant interactions with defect states. Key Findings The application of this protocol yielded three primary results: Spectral Decoupling: Successfully restored Ramsey fringes in a defect-limited qubit (Q150), achieving a coherence time of $T_2^* \approx 6.36 \: \mu\text{s}$. Protocol Benchmarking: The "Stark Rescue" protocol demonstrated a statistical advantage over standard CPMG dynamical decoupling. It extended coherence time by 11.3% ($T_2^{Stark} = 8.17 \: \mu\text{s}$ vs. $T_2^{CPMG} = 7.34 \: \mu\text{s}$; $p = 0.042$, Bootstrap t-test). Topological Simulation: Digital simulation of a topological domain wall under engineered correlated noise revealed a sigmoidal stability threshold ($SSE \approx 0.0008$), significantly outperforming standard exponential models ($SSE \approx 0.0085$). Conclusion These results confirm that pulse-level Hamiltonian engineering can effectively reclaim compromised hardware resources on current NISQ platforms. Keywords NISQ, Superconducting Qubits, Two-Level Systems (TLS), Floquet Engineering, AC Stark Effect, IBM Quantum, Dynamical Decoupling, Quantum Control.

DOI
10.5281/zenodo.18067974

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Quantum information processing holds the promise of a paradigm shift in computational power for specific problem classes. While contemporary quantum processors operate in the Noisy Intermediate-Scale Quantum (NISQ) regime and remain highly susceptible to errors, ongoing experimental efforts on these near-term devices are crucial for advancing the underlying technology. Among the various hardware implementations, superconducting quantum circuits stand out as one of the most robust architectures for scalable quantum technologies. Nevertheless, the primary bottleneck in these systems is the fragility of quantum information: interactions with the environment inevitably perturb the quantum states, a phenomenon known as decoherence. This rapid loss of stored information imposes a fundamental limit on the time available to reliably execute computations on these devices. Within this context, this thesis focuses on the comprehensive experimental characterization of a planar chip featuring isolated, fixed-frequency superconducting transmon qubits. The measurements were conducted in a cryogenic environment, relying on a dilution refrigerator to maintain the device at millikelvin temperatures. To probe the quantum system under these conditions, custom measurement scripts were developed to operate state-of-the-art microwave control electronics (Keysight Quantum Control System), establishing full control over pulse generation, signal acquisition, and digital demodulation. The experimental workflow systematically mapped the physical properties of the device through a progressive series of characterization steps. Initial spectroscopic techniques probed the coupled resonator-qubit system, identifying its fundamental transition frequencies and relevant energy scales. Building upon these frequency-domain measurements, coherent control was achieved by calibrating resonant microwave pulses to drive single-qubit rotations, enabling the reliable preparation of the qubit in excited or coherent superposition states. Finally, specific time-domain protocols were implemented to evaluate the operational limits of the device. By executing standard pulse sequences, the characteristic decoherence metrics of the system, namely the longitudinal energy relaxation time (T1) and the inhomogeneous dephasing time (T2*), were successfully extracted, providing a quantitative assessment of the qubit's overall performance and establishing a baseline for future implementations of more advanced quantum control protocols.
Decoherence is a primary barrier to practical quantum computation, causing quantum states to degrade through phase randomization and irreversible energy relaxation. This study presents a simulation-based evaluation of echo-based dynamical decoupling (DD) pulse sequences as a software-level mitigation strategy in single-qubit systems. Using the Qiskit Aer density matrix simulator, four strategies—baseline, Hahn Echo, Carr-Purcell-Meiboom-Gill (CPMG), and Mixed Synchronization—were evaluated across low-frequency phase noise, high-frequency phase noise, and combined T₁ + T₂ noise regimes. Hahn Echo restored mean fidelity to 100.00% under low-frequency noise (baseline: 57.90%), while CPMG achieved 97.62% under high-frequency noise (baseline: 2.45%). Under combined noise, all strategies showed limited improvement, with Mixed-Sync reaching 65.34% versus 60.95%. Coefficient of variation (CV) analysis across 500 Monte Carlo trials showed that CPMG reduced purity-decay variance threefold under high-frequency noise, with bootstrap confidence intervals confirming statistical significance. Time-resolved analysis showed that CPMG suppressed variance growth throughout evolution, reducing variance growth from +267% (baseline) to +89%, while baseline and Hahn Echo exhibited progressive amplification of variance. These results show that dynamical decoupling influences the temporal structure of noise, not just mean fidelity. In T₂-dominated regimes, pulse sequences constrain variability; in mixed regimes, they partially shape it; and in T₁-dominated regimes, both mean performance and variability converge to hardware-limited behavior. DD effectively corrects reversible phase errors but cannot overcome irreversible T₁ loss, with implications for NISQ circuit design.
Precise control of multi-qubit architectures remains a critical bottleneck in superconducting quantum processors. In this work, we investigate the synthesis of high-fidelity quantum operations and state transfer protocols within an extended superconducting linear chain, scaling from three to seven sites. Using Floquet theory, we model the periodic drive as a train of delta-like pulses, mapping the quantum control problem onto quasi-energy resonance conditions. Combining the Baker-Campbell-Hausdorff expansion with Floquet spectral decomposition, we analytically identify optimal driving parameters, refined via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the three-qubit architecture, this enables high-fidelity synthesis of the iSWAP gate. Extending to a seven-site chain, we implement periodic trains of finite-width Gaussian pulses to activate distinct double-excitation transport channels with ultra-short gate durations t_gate (~170 ns). This achieves a clear scale separation from energy-relaxation times (T1) typical of fixed-frequency transmon devices with tunable couplers, such as IBM Quantum hardware. Finally, we benchmark stability under realistic imperfections, revealing a heightened sensitivity to static parameter disorder at the sub-percent level (eta ~ 10^-3) driven by spectral crowding, and discuss how closed-loop topologies could mitigate this constraint. This framework bridges time-periodic control theory and practical quantum gate engineering.
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency 1/f1/f1/f charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over time, fluctuating the qubit lifetime. Here, we propose to mitigate those harmful effects by engineering the relevant TLS noise spectral densities. Specifically, our protocols smooth the high-frequency noise spectrum and suppress the low-frequency noise amplitude via depolarizing and dephasing the TLSs, respectively. As a result, we predict a drastic stabilization in qubit lifetime and an increase in qubit pure dephasing time. Our detailed analysis of feasible experimental implementations shows that the improvement is not compromised by spurious coupling from the applied noise to the qubit.
The effective use of current Noisy Intermediate-Scale Quantum (NISQ) devices is often limited by the noise which is caused by interaction with the environment and affects the fidelity of quantum gates. In transmon qubit systems, the quantum gate fidelity can be improved by applying control pulses that can minimize the effects of the environmental noise. In this work, we employ physics-guided quantum optimal control strategies to design optimal pulses driving quantum gates on superconducting qubit systems. We test our results by conducting experiments on the IBM quantum hardware using their OpenPulse API. We compare the performance of our pulse-optimized quantum gates against the default quantum gates and show that the optimized pulses improve the fidelity of the quantum gates, in particular the single-qubit gates. We discuss the challenges we encountered in our work and point to possible future improvements.
Pulse-level calibration metrics — coherence times T₁ and T₂ measured through single-qubit Rabi and Ramsey sequences — are the standard by which quantum hardware providers certify device health. We demonstrate, through 191 circuit executions on three 156-qubit IBM Heron r2 processors (ibm_kingston, ibm_fez, and ibm_marrakesh), that these pulse-level metrics can give opposite conclusions to circuit-level diagnostics on the same device at the same time. Specifically, between experimental sessions on July 3 and July 5, 2026, IBM reported ibm_marrakesh T₂ improved from 303 μs to 340 μs (a 12% improvement), while the K–R scaling exponent α measured from GHZ circuit scaling increased from 1.406 to 3.811 (a 171% increase in coherent error dominance) and GHZ n=2 infidelity rose from 0.018 to 0.204 — a 920% increase in circuit error. We further demonstrate that Ramsey circuit-context T₂ on qubit 0 is approximately 9–30 μs, compared to IBM-reported pulse-level T₂ of 32–340 μs — a discrepancy of 3–11×. We introduce five experimental demonstrations showing K–R circuit-level diagnostics detect degradation invisible to T₁/T₂, provide higher temporal sensitivity, enable algorithm failure prediction, and confirm the theoretical prediction αₜᵥₜᶜʰ + αₑₜₕₒ = 2 within 7% on real hardware. These findings establish circuit-level K–R diagnostics as a necessary complement to pulse-level calibration for operational quantum computing.