HOMOTOPICAL QUANTUM COMPUTATION- THEORY AND APPLICATIONS OF SIMPLICIAL DISTRIBUTIONS
Abstract
The predictive power of physical theories is based on the measurement statistics they produce. Quantum theory stands out by enabling non-local correlations that surpass those achievable in any classical theory. However, current computational devices are built on principles that do not harness the potential of these quantum correlations. To tap into this vast potential for information processing, a deeper understanding of non-locality and its generalization, known as quantum contextuality, is crucial, among other non-classical features such as superposition and entanglement. Quantum contextuality refers to how the result of a quantum measurement is influenced by the set of other properties measured alongside it, essentially its measurement context. Quantum probabilities over measurement contexts satisfy the non-signaling condition prohibiting superluminal signaling. Our innovative proposal is that the contextual behavior of quantum probabilities is concealed within the topological structure of the measurements and their outcomes. The theory of simplicial distributions, developed by the principal investigator (PI) and his team at Bilkent University, encapsulates this new concept. Simplicial distributions are combinatorial models of probability distributions on spaces of measurements and outcomes extending the theory of non-signaling distributions in quantum foundations. In our framework, spaces are modeled by simplicial sets - combinatorial models used in modern homotopy theory. This way, quantum contextuality can be expressed as a topological phenomenon amenable to the methods of algebraic topology, displaying a new way quantum and topology interact at a fundamental level. Advancing the theory of simplicial distributions into a comprehensive framework for studying the foundational puzzles responsible for quantum advantage will deepen our understanding of quantum resources, allowing us to design more robust and efficient quantum algorithms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410257
Entities
People
- Cihan Okay
Organizations
- Air Force Office of Scientific Research
- United States Air Force