Consequences of Computational Limits

Feng Xu

Abstract We show that certain singular limits of relative entropy of vacuum states in two dimensional massive free fermion theory exist and compute these limits. As an application we show that the c function computed by Casini and Huerta based on heuristic arguments arise naturally as a consequence of our results.

Najera Olivas, Sebastian

Recent proposals regarding Closed Timelike Curves (CTCs) suggest they could efficiently solve NP-complete problems. However, we have previously demonstrated that physical CTCs must be dissipative to satisfy the Novikov Self-Consistency Principle. In this work, we derive the computational consequences of this thermodynamic stability. We introduce Geometric Causal Complexity (GCC), a measure based on the accessible volume of the Hilbert space under the Fubini-Study metric. We prove a Universal Causal Complexity Bound: the computational advantage ΔC of a retrocausal channel is strictly limited by the ratio of non-linearity to dissipation, ΔC ≤ (K/γ) C_max. This implies that the "Arrow of Time" acts as a computational resource constraint: the same mechanism that prevents logical paradoxes also prevents the violation of the Church-Turing thesis. We analyze the implications for Rydberg atoms, superconducting circuits, and photonic networks, classifying them by their potential for non-Markovian quantum advantage.

Ashley M. Aitken

Materov

Since Turing, it's been generally accepted that computing systems have two types of limitations: algorithmic (some problems are fundamentally unsolvable) and engineering (the hardware is imperfect, noisy, and breaks). Quantum computing has added a third type— complexity : some problems are solvable, but require resources that grow faster than any polynomial. This supplement introduces a fourth type of restriction, previously not described in the literature: The fundamental limit of quantum computing (FQC) is a limit on the precision of any quantum computing device, which arises not from imperfections in the implementation, but from the discrete structure of spacetime at the Planck scale. This limit cannot be overcome by any technological advancement. It is not a consequence of decoherence , thermal noise, or imperfect gates. It is built into the geometry of reality—just as the speed of light is built into the structure of spacetime and cannot be overcome by any acceleration.Unlike collapse-model-based limits on quantum hardware, the Fundamental Limit of Quantum Computation is proposed as an ontological bound arising from the discrete structure of spacetime itself.