Low-cost algorithm-to-execution framework for surface-code quantum computing

Abstract

Fault-tolerant quantum computing is progressing from demonstrations of individual logical components toward the execution of useful quantum algorithms on large-scale error-corrected processors. Realizing this transition requires co-design across algorithms, fault-tolerant implementations, and hardware resources. Here we develop an algorithm-to-execution framework for low-cost surface-code quantum computing that carries the structure of a computation from hierarchical logical descriptions to circuit-specific spatial organization, non-Clifford resource planning, and physical resource evaluation. We apply the framework to twenty benchmark circuits spanning seven algorithm families and to a hierarchically reconstructed application-scale elliptic-curve discrete-logarithm workload. Under the stated error and resource-supply models, combining circuit-specific layouts with hybrid non-Clifford implementation reduces space--time volume by up to 12.70x relative to an all-synthesis Litinski fast-block baseline. Circuit-specific layouts reduce both modeled runtime and space--time volume in eighteen benchmarks, while the remaining two retain the fast layout. These results show that the physical cost of fault-tolerant computation emerges from the interaction between algorithm structure, error-corrected implementation, and hardware organization rather than from aggregate logical resource counts alone.

arXiv comment36 pages, 7 figures, updated on resource estimation results and relative discussions