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Multi-Dimensional Quantum-like Resources from Complex Synchronized Networks.

Debadrita Saha1, Gregory D Scholes1

  • 1Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.

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Summary
This summary is machine-generated.

This study introduces quantum-like (QL) dits, higher-dimensional analogs of QL bits, emerging from synchronized networks. These QL dits offer potential computational advantages and improved classical resource efficiency for quantum-like information processing.

Keywords:
k-regular graphsquantum resourcequantum-likequdits

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Area of Science:

  • Theoretical Computer Science
  • Quantum Information Theory
  • Network Science

Background:

  • Recent work introduced quantum-like (QL) bits derived from synchronized network dynamics.
  • QL bits encompass QL states and QL gate operations.

Purpose of the Study:

  • To extend the concept of QL bits to higher-dimensional quantum-like (QL) resources, termed QL dits.
  • To explore the construction and properties of these QL dits using k-regular graphs.
  • To investigate the potential computational advantages of d-nary QL systems.

Main Methods:

  • Construction of QL dits using k-regular graphs for arbitrary dimensions.
  • Definition of the QL state space via the eigenspectrum of adjacency matrices.
  • Realization of tensor product structure using the Cartesian product of graphs.

Main Results:

  • QL dits are proposed as higher-dimensional analogs of QL bits.
  • The eigenspectrum of adjacency matrices in k-regular graphs defines the QL state space.
  • The Cartesian product of graphs facilitates the tensor product structure for multi-QL dit systems.

Conclusions:

  • This work generalizes the paradigm of QL information processing to higher dimensions.
  • QL dits offer potential advantages in classical resource efficiency compared to QL bits.
  • Synchronized network dynamics provide a foundation for advanced QL information processing.