Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide an integrated open-source tool set for control, calibration, and characterization ( ${\mathbb{C}}^{3}$ ), capable of open-loop pulse optimization, model-free calibration, model fitting, and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates, and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than $1\mathrm{%}$ error and derive a coherence-limited cross-resonance gate that achieves $99.6\mathrm{%}$ fidelity without the need for calibration.Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide an integrated open-source tool set for control, calibration, and characterization (${\mathbb{C}}^{3}$), capable of open-loop pulse optimization, model-free calibration, model fitting, and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates, and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than $1\mathrm{%}$ error and derive a coherence-limited cross-resonance gate that achieves $99.6\mathrm{%}$ fidelity without the need for calibration.

arXiv:2009.09866Physical Review AppliedMar 29, 202185 citations

Gate error models for superconducting qubit architectures

Devin Underwood, J. Stehlik, Timothy Phung +3 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

Quantum gates for superconducting qubits

Chad T. Rigetti

Jan 1, 200910 citations

Optimizing Superconducting Qubit Performance: A Theoretical Framework for Design, Analysis, and Calibration

Ram, Sirshi S, Muralikrishna Molli, Vamshi M. Katukuri +1 more

Designing a qubit architecture is one of the most critical challenges in achieving scalable and fault-tolerant quantum computing as the performance of a quantum computer is heavily dependent on the coherence times, connectivity and low noise environments. Superconducting qubits have emerged as a frontrunner among many competing technologies, primarily because of their speed of operations, relatively well-developed and offer a promising path toward scalability. Here, we address the challenges of optimizing superconducting qubit hardware through the development of a comprehensive theoretical framework that spans the entire process - from design to the calibration of hardware through quantum gate execution. We develop this framework in four key steps: circuit design, electromagnetic analysis, spectral analysis, and pulse sequencing with calibration. We first refine the qubit's core components - such as capacitance, Josephson junctions, and resonators - to set the foundation for strong performance. The electromagnetic analysis, using the Lumped Oscillator model, allows us to map out the capacitance matrix, ensuring that we minimize spectral dispersion while maximizing coherence times. Following this, we conduct spectral analysis to fine-tune the qubit's frequency spectrum and coherence properties, ensuring that the qubit parameters are optimized. Finally, we focus on pulse sequencing, including pulse-width optimization, DRAG optimization, and randomized benchmarking, to achieve high gate fidelity. We applied this framework to both Transmon and Fluxonium qubits, obtaining results that closely match those found in experimental studies. This work provides a detailed and practical approach to the design, optimization, and calibration of superconducting qubits, contributing to the broader effort to develop scalable quantum computing technologies.Designing a qubit architecture is one of the most critical challenges in achieving scalable and fault-tolerant quantum computing as the performance of a quantum computer is heavily dependent on the coherence times, connectivity and low noise environments. Superconducting qubits have emerged as a frontrunner among many competing technologies, primarily because of their speed of operations, relatively well-developed and offer a promising path toward scalability. Here, we address the challenges of optimizing superconducting qubit hardware through the development of a comprehensive theoretical framework that spans the entire process - from design to the calibration of hardware through quantum gate execution. We develop this framework in four key steps: circuit design, electromagnetic analysis, spectral analysis, and pulse sequencing with calibration. We first refine the qubit's core components - such as capacitance, Josephson junctions, and resonators - to set the foundation for strong performance. The electromagnetic analysis, using the Lumped Oscillator model, allows us to map out the capacitance matrix, ensuring that we minimize spectral dispersion while maximizing coherence times. Following this, we conduct spectral analysis to fine-tune the qubit's frequency spectrum and coherence properties, ensuring that the qubit parameters are optimized. Finally, we focus on pulse sequencing, including pulse-width optimization, DRAG optimization, and randomized benchmarking, to achieve high gate fidelity. We applied this framework to both Transmon and Fluxonium qubits, obtaining results that closely match those found in experimental studies. This work provides a detailed and practical approach to the design, optimization, and calibration of superconducting qubits, contributing to the broader effort to develop scalable quantum computing technologies.

arXiv:2501.17825Jan 29, 20250 citations

Graybox characterization and calibration with finite-shot estimation on superconducting-qubit experiments

Poramet Pathumsoot, Areeya Chantasri, Michal Hajdušek +1 more

Abstract Characterization and calibration of quantum devices are necessary steps to achieve fault-tolerant quantum computing. As quantum devices become more sophisticated, it is increasingly essential to rely not only on physics-based models but also on machine learning models with open-loop optimization. The Graybox approach is a recently proposed platform-agnostic method offering flexibility in modeling the implicit noise. Despite promising results in photonic qubits, its suitability for other platforms is still unknown. We investigate its performance and limitations under realistic conditions, both numerically and experimentally, for the characterization and calibration of gates on superconducting-qubit devices. We find that the Graybox approach performs well on the devices’ pulse-level controls and is able to search for pulse shapes of high-fidelity gates. However, an important limiting factor of the model’s ability to reduce the training errors is the finite number of measurement shots. We therefore derive analytical bounds to explain this limitation, and use them to indicate users whether the characterization performance is optimized. Furthermore, the model’s predictability also depends on other factors such as parameter drift that may occur between the characterization and calibration processes. Our results provide insights into quantum device characterization and gate optimization on superconducting qubits under realistic scenarios using the Graybox approach.Abstract Characterization and calibration of quantum devices are necessary steps to achieve fault-tolerant quantum computing. As quantum devices become more sophisticated, it is increasingly essential to rely not only on physics-based models but also on machine learning models with open-loop optimization. The Graybox approach is a recently proposed platform-agnostic method offering flexibility in modeling the implicit noise. Despite promising results in photonic qubits, its suitability for other platforms is still unknown. We investigate its performance and limitations under realistic conditions, both numerically and experimentally, for the characterization and calibration of gates on superconducting-qubit devices. We find that the Graybox approach performs well on the devices’ pulse-level controls and is able to search for pulse shapes of high-fidelity gates. However, an important limiting factor of the model’s ability to reduce the training errors is the finite number of measurement shots. We therefore derive analytical bounds to explain this limitation, and use them to indicate users whether the characterization performance is optimized. Furthermore, the model’s predictability also depends on other factors such as parameter drift that may occur between the characterization and calibration processes. Our results provide insights into quantum device characterization and gate optimization on superconducting qubits under realistic scenarios using the Graybox approach.

arXiv:2508.12822New Journal of PhysicsMay 1, 20260 citations

Detecting and Reducing Gate Leakage in Superconducting Qubits

Benchmarking Z. Chen, J. Kelly, B. Campbell +14 more

Jan 1, 20140 citations

{\mathbb{C}}^{3}

), capable of open-loop pulse optimization, model-free calibration, model fitting, and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates, and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than $1\mathrm{%}$ error and derive a coherence-limited cross-resonance gate that achieves $99.6\mathrm{%}$ fidelity without the need for calibration.