A Quantum-Walk Representation of Color-Ordered MHV Scattering Amplitudes

• URL: http://arxiv.org/abs/2607.02456v1
• Date: Thu, 02 Jul 2026 17:24:01 GMT
• Title: A Quantum-Walk Representation of Color-Ordered MHV Scattering Amplitudes
• Abstract summary: We introduce a graph-theoretic framework for representing color-ordered maximally helicity violating (MHV) scattering amplitudes in quantum chromodynamics.<n>Each root-to-terminal path corresponds to a distinct color ordering of the external gluons.<n>Local transition amplitudes are assigned according to the spinor-product structure of the Parke--Taylor amplitudes.
• Score: 6.4812669809987975
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a graph-theoretic framework for representing color-ordered maximally helicity violating (MHV) scattering amplitudes in quantum chromodynamics using coined quantum walks on permutation trees. Each root-to-terminal path corresponds to a distinct color ordering of the external gluons, while local transition amplitudes are assigned according to the spinor-product structure of the Parke--Taylor amplitudes. The walk evolves in coherent superpositions over permutation sectors, giving a dynamical picture of the underlying combinatorics. A quantum-channel formulation based on Kraus operators is also introduced to describe sector-resolved contributions, while a weighted collection operator coherently combines the terminal sectors at a common reference node. A quantum Fourier transform on the coin space is then employed to combine the encoded contributions into the corresponding color-decomposed amplitude. Together, these constructions establish a unified graph-based framework connecting permutation trees, quantum walks, and open quantum systems providing a framework for quantum algorithms to simulate scattering processes in quantum field theory. As an example, numerical results for low-point gluon amplitudes demonstrate that the proposed representation faithfully captures the characteristic Parke--Taylor structure and is consistent with analytical results.

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