Topology-Aware Block Coordinate Descent for Qubit Frequency Calibration of Superconducting Quantum Processors

Pre-execution calibration is a major bottleneck for operating superconducting quantum processors, and qubit frequency allocation is especially challenging due to crosstalk-coupled objectives. We establish that the widely-used Snake optimizer is mathematically equivalent to Block Coordinate Descent (BCD), providing a rigorous theoretical foundation for this calibration strategy. Building on this formalization, we present a topology-aware block ordering obtained by casting order selection as a Sequence-Dependent Traveling Salesman Problem (SD-TSP) and solving it efficiently with a nearest-neighbor heuristic. The SD-TSP cost reflects how a given block choice expands the reduced-circuit footprint required to evaluate the block-local objective, enabling orders that minimize per-epoch evaluation time. Under local crosstalk/bounded-degree assumptions, the method achieves linear complexity in qubit count per epoch, while retaining calibration quality. We formalize the calibration objective, clarify when reduced experiments are equivalent or approximate to the full objective, and analyze convergence of the resulting inexact BCD with noisy measurements. Simulations on multi-qubit models show that the proposed BCD-NNA ordering attains the same optimization accuracy at markedly lower runtime than graph-based heuristics (BFS, DFS) and random orders, and is robust to measurement noise and tolerant to moderate non-local crosstalk. These results provide a scalable, implementation-ready workflow for frequency calibration on NISQ-era processors.