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arXiv:2604.06322

Probing the Planck scale with quantum computation

Boaz Katz, Shlomi Kotler

quant-phgr-qchep-thSubmitted Apr 7, 2026• Announced Apr 9, 2026• 0 citations
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Abstract

General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or equivalently $2^{491}$ m$^{-3}$ s$^{-1}$. Here we quantify the relation between the logical qubit count and the extent to which classicality is challenged. We argue that 500 logical qubits are sufficient to reject theories confined to a laboratory. We account for the operational cost of computation and communication at all scales up to and including the observable universe, ultimately constrained by a 1600-logical-qubit computer. Remarkably, current plans for commercial quantum computers are projected to surpass this limit, thereby putting the quantum-gravity standoff to the test.

Comments
10 pages, 4 figures, 3 supplementary pages

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General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or equivalently 24912^{491}2491 m−3^{-3}−3 s−1^{-1}−1. Here we quantify the relation between the logical qubit count and the extent to which classicality is challenged. We argue that 500 logical qubits are sufficient to reject theories confined to a laboratory. We account for the operational cost of computation and communication at all scales up to and including the observable universe, ultimately constrained by a 1600-logical-qubit computer. Remarkably, current plans for commercial quantum computers are projected to surpass this limit, thereby putting the quantum-gravity standoff to the test.
We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational model for quantum gravity. In this domain, all computable functions are the laws of physics in their most primordial form, and non computable mathematics finds no room in the physical world. Moreover, we show that a theorem that classically was considered true but non computable, at the Planck scale becomes computable but non decidable. This fact is due to the change of logic for observers in a quantum-computing universe: from standard quantum logic and classical logic, to paraconsistent logic.
Lloyd has considered the ultimate limitations physics places on quantum computers. He concludes in particular that for an ``ultimate laptop'' (a computer of one liter of volume and one kilogram of mass) the maximum number of operations per second is bounded by 105110^{51}1051. The limit is derived considering ordinary quantum mechanics. Here we consider additional limits that are placed by quantum gravity ideas, namely the use of a relational notion of time and fundamental gravitational limits that exist on time measurements. We then particularize for the case of an ultimate laptop and show that the maximum number of operations is further constrained to 104710^{47}1047 per second.
This essay aims at emphasizing the potential of a synergy between quantum gravity and the quantum computing technologies. Such a combination would be beneficial for both understanding the Planck scale physics and the stimulation of development of the quantum technologies. This is especially important in the present early days of commercial quantum computers, when challenges originating from the basic research may catalyze the technological progress. Our attention is focused on simulations of a Planck scale system with the use of existing adiabatic quantum computers. Current possibilities, technological challenges and prospects for the future are outlined.
In quantum gravity interpretations, the role of space- and time-related concepts is debated. Some argue that these concepts are not needed to describe physical reality at the Planck scale. Others object that an operational definition of magnitudes cannot get rid of spatiotemporal notions. We propose a “conceptual test” to assess if the mathematical content of a quantum gravity theory refers to some possibly verifiable empirical model. Given that any physical model describes the evolution of a set of measurables, these must be detectable in any empirical interpretation of a physical theory, including quantum gravity ones. Our test ultimately relies on considerations and studies concerning human cognitive limits in the discrimination of magnitudes.
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.
The Margolus-Levitin (ML) bound establishes a fundamental limit on the speed of quantum evolution, stating that a system with mean energy ⟨H⟩\langle H \rangle⟨H⟩ above its ground state requires a minimum time τ≥πℏ/(2⟨H⟩)\tau \ge \pi\hbar/(2\langle H\rangle)τ≥πℏ/(2⟨H⟩) to evolve between orthogonal states. This preprint rigorously derives the ML bound and critically examines its applicability as a universal per-operation energy-time limit for quantum computation at the Landauer-relevant energy scale. We show that while the ML bound constrains the intrinsic dynamics of the qubit register, it does not account for the dominant energy dissipation from cryogenic control hardware. Consequently, the ML bound alone is insufficient to characterize the energy cost of a logical operation. To address this, we connect the theoretical limit to the QNFO joules-per-compute (JPCUB) benchmark program and propose a concrete normalization of computational cost. This normalization quantifies energy per logical qubit operation by incorporating both the intrinsic qubit energy and the overhead of cryogenic controllers, providing a practical metric for quantum computation efficiency. ## 1. Introduction Quantum speed limits (QSLs) bound the minimum time required for a quantum state to evolve to an orthogonal state. The Margolus-Levitin (ML) bound is a prominent QSL, relating this minimum time to the mean energy of the system. As quantum computing hardware matures, understanding the fundamental energy limits of computation becomes critical. The Landauer limit sets a lower bound on the energy dissipated by irreversible operations, while the ML bound sets a lower bound on the time required for state evolution. This preprint derives the ML bound and assesses its role as a universal per-operation energy-time bound for quantum computation. We then connect this theoretical limit to the QNFO joules-per-compute (JPCUB) benchmark program, proposing a concrete normalization for the energy cost of logical qubit operations in cr