Decoherence in superconducting qubits emerges from the interplay of multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion (HEOM) under $1/f$ non-Markovian pure dephasing. In the resulting non-perturbative regime -- where filter-function predictions become quantitatively uninformative -- CPMG scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown -- non-monotonic decoherence, partial coherence revival, and pronounced X--Y population asymmetry ($0.204$ vs ${<}\,0.01$) -- driven by third-level anharmonicity amplified by bath memory; X-CPMG maintains well-behaved power-law scaling with a finite-$n$ transient excess consistent with non-Markovian bath-memory effects. The structural null is equally informative: waveform-level differences -- Standard versus VPPU realizations -- remain undetectable across all coupling strengths, establishing that rotating-frame pure-dephasing coupling renders control-layer detail invisible to scaling observables. These findings define testable predictions, the most experimentally accessible requiring only qualitative verification.
Comments
28 pages, 5 figures, 43 pages SI, comments/suggestions are welcomed
Decoherence in superconducting qubits emerges from the interplay of multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion (HEOM) under 1/f non-Markovian pure dephasing. In the resulting non-perturbative regime -- where filter-function predictions become quantitatively uninformative -- CPMG scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown -- non-monotonic decoherence, partial coherence revival, and pronounced X--Y population asymmetry (0.204 vs <0.01) -- driven by third-level anharmonicity amplified by bath memory; X-CPMG maintains well-behaved power-law scaling with a finite-n transient excess consistent with non-Markovian bath-memory effects. The structural null is equally informative: waveform-level differences -- Standard versus VPPU realizations -- remain undetectable across all coupling strengths, establishing that rotating-frame pure-dephasing coupling renders control-layer detail invisible to scaling observables. These findings define testable predictions, the most experimentally accessible requiring only qualitative verification.
Abstract Decoherence in superconducting qubits arises from both multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion under 1 / f non-Markovian pure dephasing. In the resulting non-perturbative regime—where filter-function predictions become quantitatively uninformative—Carr–Purcell–Meiboom–Gill (CPMG) scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown—non-monotonic decoherence, partial coherence revival, and pronounced X – Y population asymmetry ( 0.204 vs < 0.01 )—driven by third-level anharmonicity amplified by bath memory; X-CPMG maintains well-behaved power-law scaling with a finite- n transient excess consistent n-Markovian bath-memory effects. This null result is equally informative: waveform-level differences—Standard versus virtual pulse processing unit (VPPU) realizations—remain undetectable across all coupling strengths. This shows that rotating-frame pure-dephasing coupling renders control-layer detail invisible to scaling observables. These findings define testable predictions, the most experimentally accessible requiring only qualitative verification.
Simulation of one and two qubit superconducting quantum gates under the non-Markovian 1/f noise
Non-Markovian 1/f noise consists a dominant source of decoherence in superconducting qubits, yet its slow nature poses a significant challenge for accurate simulation. Here we develop a hierarchical equations of motion (HEOM) framework that enables efficient and reliable modeling of qubit dynamics and gate operations under 1/f noise. By using the approach, it is first shown that perturbative quantum master equations may fail to reproduce the correct dephasing dynamics of a qubit coupled to slow baths. We then analyze dynamical decoupling sequences by including effects of finite pulse duration. It is found that different pulse sequences results in different behavior in error accumulation: all X-CPMG sequences exhibit linear scaling with parity effects, Y-CPMG follows quadratic growth, and alternating XY-type sequences can suppress the error accumulation significantly. Finally, we extend the framework to two-qubit cross-resonance (CR) gates, reconstructing the full Choi matrix and Pauli Transfer Matrix (PTM) to identify the incoherent error induced by 1/f noise. Together, these results establish HEOM as a robust methodology for simulating the environmental noise in superconducting circuits and provide new insights into error mechanisms in both single- and two-qubit gates.
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 (Nshots=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 T2∗≈6.36μs. Protocol Benchmarking: The "Stark Rescue" protocol demonstrated a statistical advantage over standard CPMG dynamical decoupling. It extended coherence time by 11.3% (T2Stark=8.17μs vs. T2CPMG=7.34μs; 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≈0.0008), significantly outperforming standard exponential models (SSE≈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.
Logic gates in superconducting quantum processors are implemented through precisely shaped microwave pulses, whose durations are constrained by both device coherence and the multilevel structure of artificial atoms. While single-qubit fidelities above 0.999 are routinely achieved, the physical execution time of these gates remains a major bottleneck for deep quantum circuits. Here we examine single-qubit control across adiabatic [where the rotating-wave approximation (RWA) is valid], intermediate, and diabatic driving regimes using both an ideal two-level model and a realistic weakly anharmonic transmon Hamiltonian. By sweeping pulse durations and drive strengths over experimentally relevant ranges, we compare performance trade-offs and identify the conditions under which ultrashort gates remain viable. Our simulations uncover a quantitative speed-limit mechanism intrinsic to weakly anharmonic superconducting qubits: leakage to higher levels rises sharply once the peak Rabi rate exceeds a fixed fraction of the anharmonicity. Across all pulse shapes and driving regimes studied, we find a consistent numerical threshold at Ω max /|Δ|≈0.15−0.20, where Ω max denotes the peak drive (Rabi) amplitude and Δ is the transmon anharmonicity. Beyond this ratio, gate fidelity deteriorates regardless of waveform engineering. This boundary, obtained from full multilevel time-domain simulations spanning adiabatic, intermediate, and diabatic regimes, constitutes a previously unreported characterization of the fundamental leakage barrier in transmon devices. Our results, therefore, provide the first unified quantitative map linking pulse duration, driving strength, and anharmonicity, establishing why realistic superconducting qubits cannot sustain picosecond-scale gates despite ideal two-level predictions, and offering a practical benchmark for next-generation architectures seeking shorter, high-fidelity control.
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.
We report phase-resolved measurements of amplitude-phase coupling (APC) in strongly driven superconducting transmon qubits, a symmetry-based mechanism analysis, and follow-up experiments on a second device. On a Rigetti Ankaa-3 transmon (1000 shots per point, five drive amplitudes, matched root-mean-square drive), the fitted optimal control phase ϕ∗(A) drifts by more than 3 rad across the explored amplitude range for both a rectangular reference pulse and a self-intersecting Figure-8 trajectory, and the phase contrast of the two waveform families exhibits a reproducible low-/high-amplitude crossover. Theoretically, we prove that in the resonant rotating frame of the three-level Duffing model a constant-phase rectangular drive cannot produce any phase-dependent population response: CRect=0 exactly. Any measured rectangular phase contrast is therefore a probe of physics outside this model (beyond-rotating-wave carrier-phase dependence, control-chain distortion, readout imperfections). The Figure-8 waveform breaks the symmetry intrinsically through its 2:1 Fourier content; a third-order resonance ω+ω−2ω=0 mediated by the anharmonic level ∣2⟩ predicts CF8∝A6N2 at weak drive, confirmed by direct numerical propagation (fitted log-log slope 5.97±0.02; loop-number ratio 2434 vs. predicted 2500). On the successor device Cepheus-1-108Q, the predicted phase contrast lies below the binomial shot-noise floor at the accessible amplitudes, but the same dataset reveals a stronger signature of the underlying first-order average-Hamiltonian cancellation: the phase-averaged survival probability of the Figure-8 train remains pinned at ⟨P(∣0⟩)⟩ϕ≈0.985 across all tested conditions, while the isenergetic rectangular reference sweeps the full range 0.24-0.93—an approximately 70-fold suppression of the Rabi-drive response. Together these results identify APC as a measurable control-landscape feature with distinct intrinsic and extrinsic components, and demonstrate a calibration-free, amplitude-insensitive idling property of Figure-8 pulse trains.