A formally certified end-to-end implementation of Shor’s factorization algorithm
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 15, 2023
- Source ID
- 10.1073/pnas.2218775120
Entities
People
- Kesha Hietala
- Liyi Li
- Michael Hicks
- Robert Rand
- Runzhou Tao
- Xiaodi Wu
- Yuxiang Peng
Organizations
- Air Force Office of Scientific Research
- Columbia University
- National Science Foundation
- Office of Science
- University of Chicago
- University of Maryland