Quantum algorithms are often represented in terms of quantum circuits operating on ideal (logical) qubits. However, the practical implementation of these algorithms poses significant challenges. Many quantum algorithms require a substantial number of logical qubits, and the inherent susceptibility to errors of quantum computers require quantum error correction. The integration of error correction introduces overhead in terms of both space (physical qubits required) and runtime (how long the algorithm needs to be run for). This paper addresses the complexity of comparing classical and quantum algorithms, primarily stemming from the additional quantum error correction overhead. We propose a comprehensive framework that facilitates a direct and meaningful comparison between classical and quantum algorithms. By acknowledging and addressing the challenges introduced by quantum error correction, our framework aims to provide a clearer understanding of the comparative performance of classical and quantum computing approaches. This work contributes to understanding the practical viability and potential advantages of quantum algorithms in real-world applications.

中文翻译：

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大规模量子算法的量子资源估计


量子算法通常用在理想（逻辑）量子位上运行的量子电路来表示。然而，这些算法的实际实现提出了重大挑战。许多量子算法需要大量的逻辑量子位，而量子计算机固有的对错误的敏感性需要量子纠错。纠错的集成会带来空间（所需的物理量子位）和运行时间（算法需要运行多长时间）方面的开销。本文讨论了比较经典算法和量子算法的复杂性，主要源于额外的量子纠错开销。我们提出了一个全面的框架，有助于对经典算法和量子算法进行直接且有意义的比较。通过承认和解决量子纠错带来的挑战，我们的框架旨在提供对经典计算方法和量子计算方法的比较性能的更清晰的理解。这项工作有助于理解量子算法在现实应用中的实际可行性和潜在优势。