Related papers: A HoTT Quantum Equational Theory (Extended Version…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. Of particular practical relevance…
In this note we point out the fact that the proper conceptual setting of quantum computation is the theory of Linear Time Invariant systems. To convince readers of the utility of the approach, we introduce a new model of computation based…
In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent's uncertainty about the input signal. We show how…
Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a…
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
Large language models (LLMs) have rapidly improved text embeddings for a growing array of natural-language processing tasks. However, their opaqueness and proliferation into scientific domains such as neuroscience have created a growing…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum…
We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for…
Interest in quantum machine learning is increasingly growing due to its potential to offer more efficient solutions for problems that are difficult to tackle with classical methods. In this context, the research work presented here focuses…
The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
Despite significant advances in quantum computing across various domains, research on applying quantum approaches to language compositionality - such as modeling linguistic structures and interactions - remains limited. This gap extends to…