Related papers: Noisy Machines
It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most…
To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure "inference devices". I present a set of existence and impossibility results…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have…
In the present paper, we construct what we call a pedagogical universal Turing machine. We try to understand which comparisons with biological phenomena can be deduced from its encoding and from its working.
In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the…
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the…
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…