Computational spin networks and quantum paths in space–time

Louis Hirsch Kauffman, Samuel J. Lomonaco

Jincheng Zhang

This paper introduces a novel quantum path search algorithm based on string quantum computation, aiming to significantly enhance the efficiency of path exploration within quantum systems. Traditional pathfinding methods often rely on classical physics models, limiting the potential for optimal traversal. We propose a framework that leverages the unique properties of string quantum computation, specifically quantum entanglement and spin, to construct a "quantum network" to facilitate more accurate path discovery. The core mechanism involves mapping the search space to a string representation, allowing for parallel processing and enhanced connectivity. This research explores the design of this quantum network and its impact on pathfinding accuracy, offering a promising alternative to existing classical algorithms.

David Peter Divincenzo

Yuanbo Zhang, Lin Chen

Surface codes have emerged as a promising approach for protecting quantum information against decoherence in quantum computation and communication. In this paper, we investigate the fundamental problem of path computation in quantum networks where surface codes are systematically employed in quantum information transmission. Specifically, we formulate the problem of finding a min-cost path subject to end-to-end fidelity constraint. The problem is non-trivial as only a subset of nodes in the network can perform coding and decoding operations due to its high cost, adding a combinatorial flavor to it. Our problem being NP-hard, we design an approximation path optimization algorithm by technically employing a discretization scheme allowing to bound the time and space complexity of the algorithm to be polynomial. We also demonstrate the effectiveness of our algorithm via extensive numerical analysis.

Antoon Hendrik Hams

Ilija Srpak, Michael J. Willatt, Stuart C. Althorpe +1 more

We build on the framework for studying systems containing spin-phonon coupling using molecular dynamics as the method for sampling the positions of atoms carrying spins, whose interaction is described by the Heisenberg model, and which we presented in a previous paper Srpak et al. [Phys. Rev. B 112, 205132 (2025)]. In applying the real-space path integral framework to the spin-phonon problem, neighboring imaginary time slices become coupled via overlap of eigenvector matrices propagating along the path integral, leading to interactions that go beyond the pure harmonic interactions between neighboring beads of the ring-polymers in Born-Oppenheimer-based path integral molecular dynamics (PIMD) simulations of quantum nuclei. We show how the use of a spin-force, defined as the negative gradient of the spin free energy, accounts for this type of coupling, valid for systems in thermal equilibrium. The spin force is computed using either ring-polymer exact diagonalization (for small systems) or stochastic series expansion (for large systems). We provide the technical details for these implementations. We present a neural network approach for this type of PIMD simulation, where we compute the spin force based on training data obtained from the ring-polymer stochastic series expansion method. Utilizing these methods, we compare them with the literature and demonstrate how one can obtain phase diagrams clearly showing how the thermal and nuclear quantum effects influence the stability of the spin-Peierls dimerized phase. We also show how machine learning makes it possible to apply the method to two dimensional systems.