Triangulated relativistic quantum computation

We are happy to announce the publication of our latest paper, Triangulated relativistic quantum computation: A curvature modulated unification of quantum and relativistic computing.

This paper introduces Triangulated Relativistic Quantum Computation (TRQC), a mathematically rigorous framework that unifies relativistic causal structure with quantum channel dynamics. The work advances quantum information theory by elevating intrinsic spacetime curvature to an explicit operational parameter governing quantum evolution.

At the core of TRQC is a discrete, geometry-aware model of spacetime. Events are organized as an oriented simplicial complex equipped with a time labeling that induces a causal partial order. Finite-dimensional quantum systems are associated with vertices, while local evolution proceeds along edges via completely positive trace-preserving maps generated by Lindbladian dynamics whose generators are modulated by curvature. This construction ensures compatibility with both relativistic causality and open quantum system dynamics.

Curvature is treated intrinsically rather than as an external background. On spacelike slices, it is inferred from angle deficits of a latent triangulation corresponding to a piecewise-Euclidean metric. The resulting curvature estimator is invariant under global orthogonal transformations of the latent embedding and is defined with an explicit scale convention per slice. This allows curvature to act as a well-defined, controllable input to quantum dynamics rather than a passive geometric feature.

The paper establishes a range of theoretical guarantees underpinning the framework. These include gauge invariance of curvature quantities, well-posedness and norm-continuity of curvature-modulated quantum dynamical semigroups, and causal factorization ensuring no-signaling between spacelike-separated subcomputations. The authors further demonstrate robustness with respect to triangulation choice, including invariance under commuting-local refinements and convergence in a Lie–Trotter limit. Additional results include a discrete Gauss–Bonnet identity on closed slices, as well as curvature-dependent quantum speed limits and perturbation bounds for Lindbladian evolution.

TRQC recovers familiar models in appropriate limits: it reduces to standard quantum circuits in flat spacetime, and to classical relativistic computation when quantum channels become entanglement-breaking. Beyond its foundational contributions, the framework is designed with implementation in mind. The paper outlines algorithms for curvature estimation on dynamically evolving meshes, causal scheduling of quantum operations, and remeshing-robust Trotterization schemes.

Potential applications span relativistic quantum networking, analog simulation on curved or hyperbolic lattices, geometry-aware quantum error correction, and quantum transport on curved or fractal nanostructures. By providing both conceptual clarity and operational tools, TRQC offers a practical semantics for designing and simulating quantum information processing in settings where geometry, causality, and time dilation play an essential role.