Undecidability of the spectral gap
The spectral gap—the energy difference between the ground state and first excited state of a
system—is central to quantum many-body physics. Many challenging open problems, such …
system—is central to quantum many-body physics. Many challenging open problems, such …
Undecidability in quantum thermalization
N Shiraishi, K Matsumoto - Nature communications, 2021 - nature.com
The investigation of thermalization in isolated quantum many-body systems has a long
history, dating back to the time of developing statistical mechanics. Most quantum many …
history, dating back to the time of developing statistical mechanics. Most quantum many …
The undecidability of conditional affine information inequalities and conditional independence implication with a binary constraint
CT Li - IEEE Transactions on Information Theory, 2022 - ieeexplore.ieee.org
We establish the undecidability of conditional affine information inequalities, the
undecidability of the conditional independence implication problem with a constraint that …
undecidability of the conditional independence implication problem with a constraint that …
Undecidable problems in quantum field theory
Y Tachikawa - International Journal of Theoretical Physics, 2023 - Springer
We point out that some questions in quantum field theory are undecidable in a precise
mathematical sense. More concretely, it will be demonstrated that there is no algorithm …
mathematical sense. More concretely, it will be demonstrated that there is no algorithm …
The busy beaver frontier
S Aaronson - ACM SIGACT News, 2020 - dl.acm.org
The Busy Beaver function, with its incomprehensibly rapid growth, has captivated
generations of computer scientists, mathematicians, and hobbyists. In this survey, I o er a …
generations of computer scientists, mathematicians, and hobbyists. In this survey, I o er a …
Undecidability of the spectral gap
We construct families of translationally invariant, nearest-neighbour Hamiltonians on a 2D
square lattice of d-level quantum systems (d constant), for which determining whether the …
square lattice of d-level quantum systems (d constant), for which determining whether the …
On some algebraic ways to calculate zeros of the Riemann zeta function
Y Matiyasevich - International Conference on Algebraic Informatics, 2022 - Springer
The Riemann zeta function is an important number-theoretical tool for studying prime
numbers. The first part of the paper is a short survey of some known results about this …
numbers. The first part of the paper is a short survey of some known results about this …
Undecidability of the Spectral Gap (full version)
We show that the spectral gap problem is undecidable. Specifically, we construct families of
translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level …
translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level …
A Pair of Bayesian Network Structures has Undecidable Conditional Independencies
CT Li - arXiv preprint arXiv:2405.07107, 2024 - arxiv.org
Given a Bayesian network structure (directed acyclic graph), the celebrated d-separation
algorithm efficiently determines whether the network structure implies a given conditional …
algorithm efficiently determines whether the network structure implies a given conditional …
The busy beaver competition: a historical survey
P Michel - arXiv preprint arXiv:0906.3749, 2009 - arxiv.org
Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give
explicit definitions for some functions that are not computable and grow faster than any …
explicit definitions for some functions that are not computable and grow faster than any …