Related papers: Towards a Theory of Conservative Computing
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
This letter presents an approach to guarantee online safety of a cyber-physical system under multiple state and input constraints. Our proposed framework, called gatekeeper, recursively guarantees the existence of an infinite-horizon…
Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
The recent debate on hypercomputation has arisen new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of "effective physical process" as the essentially…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We introduce "representative generation," extending the theoretical framework for generation proposed by Kleinberg et al. (2024) and formalized by Li et al. (2024), to additionally address diversity and bias concerns in generative models.…
We propose a duality between thermodynamics and computational complexity, elevating the difficulty of a computational task to the status of a thermodynamic variable. By introducing a complexity measure C as a novel coordinate, we formulate…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics…
Recently, the author and collaborators proposed a method to construct a new conserved charge different from the Noether one for general relativistic field theory on curved space-time with energy-momentum tensor covariantly conserved, and…
The scalar-tensor representation of $f(R,T)$ gravity is extended to incorporate the Herglotz variational principle. The field equations are derived in both the geometric and scalar-tensor frameworks. Although the divergence of the…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery's more egregious…