Regular language quantum states
- URL: http://arxiv.org/abs/2407.17641v1
- Date: Wed, 24 Jul 2024 21:09:22 GMT
- Title: Regular language quantum states
- Authors: Marta Florido-Llinàs, Álvaro M. Alhambra, David Pérez-García, J. Ignacio Cirac,
- Abstract summary: We introduce regular language states, a family of quantum many-body states.
They are built from a special class of formal languages, called regular.
We exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant.
- Score: 0.5499796332553706
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood as the superposition of all the words in a regular language and encompass physically relevant states such as the GHZ-, W- or Dicke-states. By leveraging the theory of regular languages, we develop a theoretical framework to describe them. First, we express them in terms of matrix product states, providing efficient criteria to recognize them. We then develop a canonical form which allows us to formulate a fundamental theorem for the equivalence of regular language states, including under local unitary operations. We also exploit the theory of tensor networks to find an efficient criterion to determine when regular languages are shift-invariant.
Related papers
- How Proficient Are Large Language Models in Formal Languages? An In-Depth Insight for Knowledge Base Question Answering [52.86931192259096]
Knowledge Base Question Answering (KBQA) aims to answer natural language questions based on facts in knowledge bases.
Recent works leverage the capabilities of large language models (LLMs) for logical form generation to improve performance.
arXiv Detail & Related papers (2024-01-11T09:27:50Z) - Quantum and Reality [0.0]
We describe a natural emergence of Hermiticity which is rooted in principles of equivariant homotopy theory.
This construction of Hermitian forms requires of the ambient linear type theory nothing further than a negative unit term of tensor unit type.
We show how this allows for encoding (and verifying) the unitarity of quantum gates and of quantum channels in quantum languages embedded into LHoTT.
arXiv Detail & Related papers (2023-11-18T11:00:12Z) - Formal Specifications from Natural Language [3.1806743741013657]
We study the ability of language models to translate natural language into formal specifications with complex semantics.
In particular, we fine-tune off-the-shelf language models on three datasets consisting of structured English sentences.
arXiv Detail & Related papers (2022-06-04T10:49:30Z) - Universality-of-clock-rates test using atom interferometry with $T^{3}$
scaling [63.08516384181491]
Atomic clocks generate delocalized quantum clocks.
Tests of universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks proposed.
Results extend our notion of time, detached from classical and localized philosophies.
arXiv Detail & Related papers (2022-04-05T12:26:56Z) - Learning Symbolic Rules for Reasoning in Quasi-Natural Language [74.96601852906328]
We build a rule-based system that can reason with natural language input but without the manual construction of rules.
We propose MetaQNL, a "Quasi-Natural" language that can express both formal logic and natural language sentences.
Our approach achieves state-of-the-art accuracy on multiple reasoning benchmarks.
arXiv Detail & Related papers (2021-11-23T17:49:00Z) - Language learnability in the limit for general metrics: a Gold-Angluin
result [91.3755431537592]
We use Niyogi's extended version of a theorem by Blum and Blum (1975) on the existence of locking data sets to prove a necessary condition for learnability in the limit of any family of languages in any given metric.
When the language family is further assumed to contain all finite languages, the same condition also becomes sufficient for learnability in the limit.
arXiv Detail & Related papers (2021-03-24T13:11:09Z) - Generalization of group-theoretic coherent states for variational
calculations [1.2599533416395767]
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states.
We generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties.
arXiv Detail & Related papers (2020-12-22T16:50:25Z) - Computational linguistic assessment of textbook and online learning
media by means of threshold concepts in business education [59.003956312175795]
From a linguistic perspective, threshold concepts are instances of specialized vocabularies, exhibiting particular linguistic features.
The profiles of 63 threshold concepts from business education have been investigated in textbooks, newspapers, and Wikipedia.
The three kinds of resources can indeed be distinguished in terms of their threshold concepts' profiles.
arXiv Detail & Related papers (2020-08-05T12:56:16Z) - Linear Dependent Type Theory for Quantum Programming Languages [1.7166794984161973]
Modern quantum programming languages integrate quantum resources and classical control.
They must be linearly typed to reflect the no-cloning property of quantum resources.
High-level and practical languages should also support quantum circuits as first-class citizens.
arXiv Detail & Related papers (2020-04-28T13:11:06Z) - PBS-Calculus: A Graphical Language for Coherent Control of Quantum
Computations [77.34726150561087]
We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations.
We equip the language with an equational theory, which is proved to be sound and complete.
We consider applications like the implementation of controlled permutations and the unrolling of loops.
arXiv Detail & Related papers (2020-02-21T16:15:58Z) - Model-theoretic Characterizations of Existential Rule Languages [9.845164265154832]
Existential rules, a.k.a. dependencies in databases, are a family of important logical languages widely used in computer science and artificial intelligence.
We establish model-theoretic characterizations for a number of existential rule languages such as (disjunctive) embedded dependencies,generating dependencies (TGDs), (frontier-)guarded TGDs and linear TGDs.
As a natural application of these characterizations, complexity bounds for the rewritability of above languages are also identified.
arXiv Detail & Related papers (2020-01-23T17:29:18Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.