Quantum Computing without the Linear Algebra

Aws Albarghouthi

Paper 2025/1091

Quantum Computing without the Linear Algebra

Aws Albarghouthi

, University of Wisconsin-Madison

Abstract

Quantum computing is often introduced through the lens of linear algebra with notation that is inherited from quantum mechanics. In this paper, we take an operational view of quantum computing that is easy to demonstrate programmatically. The hope is that this viewpoint will (1) demystify quantum computing and make it more accessible to a wider audience, particularly computer science students and software engineers, and (2) possibly serve as the basis of a formal foundation for automatically reasoning about quantum programs. We treat the state of a quantum computer as a set and present the operations of a quantum computer—quantum gates and measurements—using familiar functional set transformations (think map, filter, fold, etc.). By the end of the paper, we will have implemented a simple quantum circuit simulator that can be used to simulate small quantum circuits. The code is available at https://github.com/qqq-wisc/qwla.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Contact author(s): aws @ cs wisc edu
History: 2025-06-13: last of 4 revisions; 2025-06-10: received; See all versions
Short URL: https://ia.cr/2025/1091
License: CC BY-NC-SA

BibTeX

@misc{cryptoeprint:2025/1091,
      author = {Aws Albarghouthi},
      title = {Quantum Computing without the Linear Algebra},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1091},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1091}
}