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arXiv:2606.20501

Fidelity bounds for adiabatic gates and other quantum operations with time-dependent dissipation

Simon Pettersson Fors, Aniket Patel, Anton Frisk Kockum, Tahereh Abad

quant-phSubmitted Jun 18, 2026• Announced Jun 19, 2026• 0 citations
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Abstract

As quantum-computing platforms are susceptible to noise, the fidelity of quantum operations is limited by decoherence. Understanding this limitation is crucial for building utility-scale quantum processors. In previous works [Phys. Rev. Lett. 129, 150504 (2022); Quantum 9, 1684 (2025)], we presented analytical formulae for the average gate fidelity of multi-qubit operations under static Markovian noise processes, including operations that temporarily leave the computational subspace. However, some quantum-computing architectures dynamically modulate qubit or coupler frequencies to implement two-qubit gates, e.g., baseband flux gates; such modulation can lead to dissipation rates varying in time. In this Letter, we therefore generalize the fidelity-reduction formulae to encompass time-dependent dissipation. Applying our generalized formula, we obtain a fidelity bound for adiabatic operations and demonstrate that flux-dependent noise sensitivity, combined with qubit-coupler hybridization, significantly reduces the fidelity of adiabatic controlled-Z (CZ) gates in superconducting quantum computers. Our work thus provides essential theoretical tools for evaluating error budgets and optimizing the design of quantum operations in tunable quantum-computing architectures, and may also find applications in quantum-sensing and quantum-communication protocols that are affected by time-dependent dissipation.

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As quantum-computing platforms are susceptible to noise, the fidelity of quantum operations is limited by decoherence. Understanding this limitation is crucial for building utility-scale quantum processors. In previous works [Phys. Rev. Lett. 129, 150504 (2022); Quantum 9, 1684 (2025)], we presented analytical formulae for the average gate fidelity of multi-qubit operations under static Markovian noise processes, including operations that temporarily leave the computational subspace. However, some quantum-computing architectures dynamically modulate qubit or coupler frequencies to implement two-qubit gates, e.g., baseband flux gates; such modulation can lead to dissipation rates varying in time. In this Letter, we therefore generalize the fidelity-reduction formulae to encompass time-dependent dissipation. Applying our generalized formula, we obtain a fidelity bound for adiabatic operations and demonstrate that flux-dependent noise sensitivity, combined with qubit-coupler hybridization, significantly reduces the fidelity of adiabatic controlled-Z (CZ) gates in superconducting quantum computers. Our work thus provides essential theoretical tools for evaluating error budgets and optimizing the design of quantum operations in tunable quantum-computing architectures, and may also find applications in quantum-sensing and quantum-communication protocols that are affected by time-dependent dissipation.
The fidelity of quantum operations is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In Phys. Rev. Lett. 129, 150504 (2022), we presented an analytical result for the average gate fidelity of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators, provided that the operation remains in the computational subspace throughout the time evolution. Here we generalize this expression for the average gate fidelity to include the cases where the system state temporarily leaves the computational subspace during the gate. Such gate mechanisms are integral to several quantum-computing platforms, and our formula is applicable to all of them; as examples, we employ it for the two-qubit controlled-Z gate in both superconducting qubits and neutral atoms. We also obtain the average gate fidelity for simultaneous operations applied in multiqubit systems. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.
Fault-tolerant quantum computing requires quantum gates that combine short duration, high fidelity, and robustness to noise. As quantum processors scale, robustness becomes increasingly important because exhaustive characterization and frequent recalibration of individual gates become impractical. We present a comprehensive optimal-control framework for controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons that systematically accounts for intrinsic Hamiltonian errors and realistic decoherence mechanisms, including energy relaxation and dephasing. Using smooth, single-shot flux pulses, we obtain 12-ns CZ gates---close to the theoretical speed limit of 11.6 ns---with intrinsic errors suppressed to the 2×10−52\times10^{-5}2×10−5 level. We construct dephasing noise models, calibrated against published experimental measurements, that capture fast dephasing from room-temperature control electronics and slow dephasing from 1/f1/f1/f flux noise. Using these models, we identify dephasing sweet spots that suppress sensitivity to dephasing noise. We further exploit transmon asymmetry as a design parameter to access distinct noise-resilient operating regimes. These results establish an experimentally applicable framework for balancing gate speed, fidelity, and noise robustness while reducing characterization and recalibration overhead.
High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502 (2020); Phys. Rev. Lett. 125, 240503 (2020)] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast ZZZZZZ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near ${10}^{\ensuremath{-}5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.
High fidelity two-qubit gates are fundamental for scaling up the superconducting qubit number. We use two qubits coupled via a frequency-tunable coupler which can adjust the coupling strength, and demonstrate the CZ gate using two different schemes, adiabatic and diabatic methods. The Clifford based randomized benchmarking (RB) method is used to assess and optimize the CZ gate fidelity. The fidelities of adiabatic and diabatic CZ gates are 99.53(8)% and 98.72(2)%, respectively. We also analyze the errors induced by the decoherence. Comparing to 30 ns duration time of adiabatic CZ gate, the duration time of diabatic CZ gate is 19 ns, revealing lower incoherence error rate r ′ incoherent , int = 0.0197 ( 5 ) compared to r incoherent, int = 0.0223(3).
Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we use the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope pulse parametrizations and are able to reach 99.9% controlled- Z -gate fidelity using a 64-ns-long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization, we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.
Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing.For superconducting quantum processors, though isolated one-or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance.Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling.An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk.Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus.Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions.During CZ gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points.To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits.Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.