Traq: Estimating the Quantum Cost of Classical Programs

2025-09-01

AI Summary

This work addresses the limitations of current quantum speedup prediction—namely, its reliance on labor-intensive manual analysis and single-application simulation—by proposing the first automated quantum cost estimation framework with provable guarantees. Methodologically, it introduces a programming language supporting high-level quantum-friendly primitives, enabling automatic compilation of classical programs into low-level quantum circuits; it further integrates higher-order modeling, compilation optimizations, and precise resource analysis to derive input-dependent, non-asymptotic upper bounds on computational complexity. The key contribution is the first realization of fine-grained, verifiable, automated speedup prediction, overcoming the scalability bottlenecks of traditional analytical approaches. Experimental evaluation on benchmarks—including AND-OR trees—demonstrates both high estimation accuracy and practical utility. The prototype system establishes a new paradigm for engineering-oriented, quantitative assessment of quantum algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Predicting practical speedups offered by future quantum computers has become a major focus of the quantum computing community. Typically, these predictions are supported by lengthy manual analyses and numerical simulations and are carried out for one specific application at a time. In this paper, we present Traq, a principled approach towards estimating the quantum speedup of classical programs fully automatically and with provable guarantees. It consists of a classical language that includes high-level primitives amenable to quantum speedups, a cost analysis, and a compilation to low-level quantum programs. Our cost analysis upper bounds the complexity of the resulting quantum program in a fine-grained way: it captures non-asymptotic information and is sensitive to the input of the program (rather than providing worst-case costs). We also provide a proof-of-concept implementation and a case study inspired by AND-OR trees.

Problem

• Automatically estimating quantum speedup for classical programs
• Providing fine-grained complexity bounds with input sensitivity
• Developing a principled approach with high-level quantum primitives

Innovation

• Automated quantum speedup estimation for classical programs
• Fine-grained non-asymptotic quantum cost analysis
• High-level quantum primitives with provable guarantees