Two-qubit gate error budgets in superconducting qubits

Short answer: An error budget splits the infidelity of a two-qubit gate into physical causes. In published superconducting-qubit studies, the main contributors are relaxation and dephasing, leakage out of the computational states, and calibration errors. One experimental study of a parametric CZ gate finds incoherent errors limit fidelity, with leakage second. These are research results on small devices.

Decomposing Intrinsic Infidelity

The core objective of error budgeting is to attribute gate infidelity to distinct physical mechanisms rather than treating it as a monolithic failure. For cross-resonance (CR) gates in superconducting transmons, researchers have shown that a simple semianalytical method accurately predicts gate duration and compensating single-qubit rotations. However, full numerical simulations are required to calculate the intrinsic fidelity. By decomposing numerical infidelity, studies reveal that at small drive amplitudes, fidelity is limited by imperfections in target-qubit rotations. Conversely, at large amplitudes, the dominant limitation shifts to leakage. This amplitude-dependent transition shows that no single error source dominates across all operating regimes.

Coherent vs. Incoherent Error Channels

Experimental analyses of parametric resonance gates distinguish between incoherent and coherent error sources. In the incoherent domain, errors arise from qubit relaxation, Markovian noise-induced dephasing, and non-Markovian 1/f flux noise. Measurements of coherence times under gate operating conditions indicate that these incoherent errors, primarily from relaxation and dephasing, limit the fidelity of two-qubit gates. On the coherent front, errors include amplitude errors, deviations in conditional phase rotations, and leakage. Leakage to noncomputational states is characterized as the second largest contributor to infidelity. This distinction is critical because coherent errors often stem from imperfect calibration, where population remains outside the computational subspace due to transfer dynamics.

Methodological Approaches to Error Estimation

Accurate error budgeting requires methodologies that can isolate specific noise contributions with limited experimental overhead. One proposed learning-based framework extracts the contribution of each physical noise source to gate infidelity using a small number of experimental measurements. This approach is particularly relevant for superconducting transmon architectures implementing diabatic controlled-Z (CZ) gates with tunable couplers. The framework accounts for non-Markovian noise, electronics imperfections, and the specific effects of tunable couplers. While modeling provides a first approach to predicting performance, realistic circuit execution often violates simplifying assumptions. For instance, experiments report longer spin echo dephasing times compared to Ramsey decay times, demonstrating the presence of time-correlated noise that simple models may miss.

Impact of Gate Dynamics and Calibration

The dynamics of errors are strongly dependent on the two-qubit gate time and pulse shape parameters. Numerical analyses of CR gates examine how fidelity varies with detuning between qubits, coupling strength, drive frequency, and the relative duration of pulse ramps. Microwave crosstalk and the effect of echo sequences are also analyzed numerically. Calibration imperfections are a significant factor; many two-qubit gate implementations rely on transferring population outside the computational subspace. If calibration is imperfect, part of the population remains outside this subspace, contributing to leakage errors. Since state-of-the-art architectures employ non-computational elements like tunable couplers, these calibration-dependent leakage channels are a major infidelity contributor.

FAQ

What limits CR gate fidelity at high drive amplitudes?

At large drive amplitudes, cross-resonance gate fidelity is primarily limited by leakage. Numerical simulations decomposing infidelity show that while small amplitudes are limited by rotation imperfections, high amplitudes shift the dominant error source to leakage into non-computational states.

How do researchers estimate error contributions with limited measurements?

A learning-based framework allows the extraction of each physical noise source's contribution to gate infidelity using a small number of experimental measurements. This method is designed for superconducting transmon architectures and accounts for non-Markovian noise and electronics imperfections.

What is the second largest error contributor in parametric resonance gates?

Leakage to noncomputational states is the second largest contributor to two-qubit gate infidelity in parametric resonance architectures. This is characterized using leakage-randomized benchmarking, following incoherent errors from relaxation and dephasing as the primary limitation.

Why is non-Markovian noise significant in error budgeting?

Non-Markovian noise, such as 1/f flux noise, is significant because it causes time-correlated dephasing not captured by simple models. Experiments show longer spin echo times than Ramsey decay, indicating this noise directly impacts gate performance and must be included in realistic error budgets.

Does calibration error affect two-qubit gate fidelity?

Yes, imperfect calibration often results in population remaining outside the computational subspace. Since many gate implementations rely on transferring population to non-computational states, calibration deviations directly contribute to leakage errors and reduce overall gate fidelity.