Harmonic flow-field representations of quantum bits and gates

Patil, Vishal P. (author), Kos, Žiga (author), Dunkel, Jörn (author)

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector f ield configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural f ield representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor’s algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation.

• Language: English
• Keywords: hydrodynamics, vector fields, qubits
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 043039-1-043039-16
• Numbering: Vol. 6, iss. 4
• PID: 20.500.12556/RUL-165072
• UDC: 53
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.6.043039
• COBISS.SI-ID: 216088067
• Publication date in RUL: 22.11.2024

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: hidrodinamika, vektorska polja, kubiti