A theory of quantum gravity based on quantum computation

TL;DR

The paper argues that quantum gravity can be understood as an emergent geometry derived from universal quantum computation, where distances are not fundamental but arise from the causal structure and local interactions of the computation. Each computational history yields a discrete spacetime described by Regge calculus, and the full quantum computation produces a superposition of spacetimes governed by the Einstein-Regge equations with a matter sector tied to the local gate phases through $I_M=-\hbar\sum_{\ell}\theta_\ell$. The framework makes testable predictions including back-reaction of quantum matter on geometry, a geometric quantum limit that aligns with holography, and plausible cosmological scenarios such as Planck-scale inflation and late-time reinflation, while allowing standard-model-like matter to emerge from underlying local quantum dynamics. The work emphasizes background independence, engages with causal-set ideas, and points toward future numerical and experimental exploration to connect the theory with observable phenomena.

Abstract

This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of space-time is a construct, derived from the underlying quantum information processing. The computation gives rise to a superposition of four-dimensional spacetimes, each of which obeys the Einstein-Regge equations. The theory makes explicit predictions for the back-reaction of the metric to computational `matter,' black-hole evaporation, holography, and quantum cosmology.

Figures (4)

• Figure 1: A quantum computation corresponds to a directed, acyclic graph. Initial vertices correspond to initial states $|0\rangle$; edges correspond to quantum wires; internal vertices correspond to quantum logic gates that apply unitary transformations $U_\ell$; final vertices correspond to final states $\langle 0|$.
• Figure 2: As qubits pass through a quantum logic gate, they can either scatter or not. If they scatter, then their state acquires a phase $\theta$; if they don't scatter, no phase is acquired. Scattering corresponds to an 'event'; no scattering corresponds to a 'non-event.'
• Figure 3: A quantum computation can be decomposed into a superposition of computational histories, each of which corresponds to a particular pattern of scattering events. Each computational history in turn corresponds to a spacetime with a definite metric.
• Figure 4: To construct a discretized spacetime from a computational history, add edges and vertices to form a simplicial 'geodesic dome' lattice. Figure 4a shows the four-simplex associated with a vertex and its nearest neighbors. Figure 4b shows a triangulation of a computational history, analogous to the triangulation performed by a surveyor who adds additional reference vertices and edges to construct a simplicial lattice. Edge lengths are defined by the causal structure of the computational history, together with the local action $\hbar\theta_\ell$ of the underlying computation. The resulting discrete geometry obeys the Einstein-Regge equations.