Related papers: Uncountable classical and quantum complexity class…
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…
Particle-style token machines are a way to interpret proofs and programs, when the latter are defined according to the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are…
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
Human language and logic abilities are computationally quantified within the well-studied grammar-automata hierarchy. We identify three hierarchical tiers and two corresponding transitions and show their correspondence to specific abilities…
Although recent quantized Large Language Models (LLMs), such as BitNet, have paved the way for significant reduction in memory usage during deployment with binary or ternary weights, training these models still demands substantial memory…
Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the ground-state energy of the +/-J Ising spin glass model on the…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Quantum Mechanics (QM) has already shown its effectiveness in many fields and…
Large language models (LLMs) are demonstrably capable of cross-lingual transfer, but can produce inconsistent output when prompted with the same queries written in different languages. To understand how language models are able to…
Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially…
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…
We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (BMS) learner is considered successful in…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on read-out. By transforming the system into a 1D transverse Ising model undergoing…
While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum…
Large language models fail at counting repeated tokens despite strong performance on broader reasoning benchmarks. These failures are commonly attributed to limitations in internal count tracking. We show this attribution is wrong. Linear…
We study a model of one-way quantum automaton where only measurement operations are allowed ($\mon$). We give an algebraic characterization of $\lmo(\Sigma)$, showing that the syntactic monoids of the languages in $\lmo(\Sigma)$ are exactly…
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis…