Topology-aware Block Coordinate Descent Achieves Faster Qubit Frequency Calibration for Superconducting Quantum Processors

Accurate calibration of qubit frequencies represents a significant hurdle in the operation of superconducting quantum processors, particularly when addressing the complexities introduced by qubit interactions. Zheng Zhao, Weifeng Zhuang, and colleagues from Tsinghua University and the Beijing Academy of Quantum Information Sciences, alongside Yanwu Gu, Peng Qian, Xiao Xiao, and Dong E. Liu, demonstrate a theoretical equivalence between the commonly used Snake optimizer and Block Coordinate Descent (BCD). This work establishes a rigorous foundation for calibration strategies and introduces a novel topology-aware block ordering, formulated as a Sequence-Dependent Traveling Salesman Problem and solved using a nearest-neighbor heuristic. By minimising per-epoch evaluation time and achieving linear complexity with qubit count, the researchers present a scalable workflow that demonstrably improves calibration speed and robustness against noise, paving the way for more efficient operation of large-scale quantum computers. Simulations confirm this method outperforms existing graph-based approaches, offering a practical solution for frequency calibration in the current era of quantum processing.

This breakthrough allows for the application of established classical optimization theory to the complex problem of quantum processor calibration, offering a new framework for understanding and improving performance. The SD-TSP cost function directly reflects the size of the reduced-circuit footprint needed to accurately evaluate each block’s objective, enabling the selection of orders that minimise per-epoch evaluation time. Under assumptions of local crosstalk and bounded-degree interactions, this method achieves linear complexity in qubit count per epoch, maintaining calibration quality while dramatically reducing computational demands. Researchers rigorously formalised the calibration objective, clarifying the conditions under which reduced experiments accurately reflect the full objective function, and analysed the convergence of the resulting inexact BCD algorithm even with noisy measurements.

Experiments conducted on multi-qubit models demonstrate that the proposed BCD-NNA ordering attains equivalent optimization accuracy to graph-based heuristics like Breadth-First Search (BFS) and Depth-First Search (DFS), and random orders, but at a markedly lower runtime. Crucially, the method proves robust to measurement noise and tolerant to moderate levels of non-local crosstalk, expanding its applicability to a wider range of quantum processor architectures. Simulations reveal a significant performance advantage, showcasing the ability to achieve the same level of optimisation with substantially reduced computational effort. This work establishes a scalable, implementation-ready workflow for frequency calibration on NISQ-era processors, addressing a critical need for efficient optimisation techniques as qubit counts increase. The team’s approach systematically reduces complexity compared to previous methods, offering a principled way to navigate the exponential search space inherent in quantum calibration. The SD-TSP cost function directly correlates to the reduced-circuit footprint needed to evaluate each block, facilitating orders that minimise evaluation time per epoch.

The team engineered a method achieving linear complexity in qubit count per epoch, while simultaneously maintaining calibration quality, under assumptions of local crosstalk and bounded-degree connectivity. Researchers rigorously formalised the calibration objective, clarifying conditions where reduced experiments accurately reflect the full objective, and subsequently analysed the convergence of the resulting inexact BCD algorithm when subject to noisy measurements. This analytical work enabled the development of a scalable approach to frequency calibration. Experiments employed multi-qubit models to demonstrate that the proposed BCD-Nearest Neighbor Algorithm (NNA) ordering achieves comparable optimisation accuracy to graph-based heuristics like Breadth-First Search (BFS) and Depth-First Search (DFS), and random orders, but at a markedly lower runtime.

The system delivers robust performance even in the presence of measurement noise and demonstrates tolerance to moderate levels of non-local crosstalk. Simulations consistently showed the BCD-NNA ordering outperformed existing methods in terms of speed and reliability. These results provide an implementation-ready workflow for frequency calibration on near-term quantum processors, addressing a critical bottleneck in the field and paving the way for more complex quantum computations. This formalization provides a rigorous theoretical foundation for existing calibration strategies and allows application of classical optimization theory to quantum systems. This innovative approach minimizes per-epoch evaluation time by strategically ordering blocks to reduce the reduced-circuit footprint required for objective evaluation.

Experiments reveal that under local crosstalk and bounded-degree assumptions, the proposed method achieves linear complexity in qubit count per epoch, representing a significant advancement in scalability. The team formalized the calibration objective, clarifying conditions where reduced experiments accurately reflect the full objective, and analyzed the convergence of the resulting inexact BCD algorithm even with noisy measurements. Simulations on multi-qubit models demonstrate that the BCD-Nearest Neighbor Algorithm (NNA) ordering attains equivalent optimization accuracy to graph-based heuristics like Breadth-First Search (BFS) and Depth-First Search (DFS), and random orders, but with markedly lower runtime. Data shows the BCD-NNA ordering is robust to measurement noise and tolerant to moderate non-local crosstalk, critical factors in real-world quantum processors.

The team’s work demonstrates a scalable, implementation-ready workflow for frequency calibration, offering a substantial improvement over existing methods. Measurements confirm that the proposed algorithm maintains calibration quality while drastically reducing computational demands, paving the way for more efficient calibration of increasingly complex quantum systems. This research delivers a new perspective on calibration strategies for Noisy Intermediate-Scale Quantum (NISQ)-era processors. By systematically optimizing block traversal order, the team has unlocked a pathway to enhance quantum system performance and address the critical bottleneck of pre-execution calibration. The resulting BCD-based approach achieves linear complexity with qubit count per epoch, assuming local crosstalk conditions, and demonstrates robustness to measurement noise. The findings represent a scalable workflow for frequency calibration applicable to current quantum processors, offering improvements over existing graph-based heuristics. Simulations confirm the method’s ability to attain equivalent optimization accuracy with reduced runtime, a significant advancement for the field. The authors acknowledge limitations related to strong nonlocal crosstalk, which can degrade performance, and outline future research focused on adaptive crosstalk detection and parallel optimization strategies to address this challenge and further enhance scalability for larger quantum systems.