A formally certified end-to-end implementation of Shor’s factorization algorithm

Author:

Peng Yuxiang12ORCID,Hietala Kesha1ORCID,Tao Runzhou3,Li Liyi12,Rand Robert4ORCID,Hicks Michael12ORCID,Wu Xiaodi12

Affiliation:

1. Department of Computer Science, University of Maryland, College Park, MD 20740

2. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20740

3. Department of Computer Science, Columbia University, New York, NY 10027

4. Department of Computer Science, University of Chicago, Chicago, IL 60637

Abstract

Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors—“bugs.” Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof’s validity is automatically confirmed—certified—by a “proof assistant.” Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor’s prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way.

Funder

DOE | Office of Science

DOD | USAF | AMC | Air Force Office of Scientific Research

National Science Foundation

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

Reference39 articles.

1. Roads towards fault-tolerant universal quantum computation

2. Quantum error correction for quantum memories

3. Functionality in Combinatory Logic

4. W. A. Howard “The formulæ-as-types notion of construction” in The Curry-Howard Isomorphism P. D. Groote Ed. (Academia 1995).

5. The verifying compiler

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