Related papers: Presheaf models of quantum computation: an outline
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order…
This paper makes contributions to ``pure'' sheaf model theory, the part of model theory in which the models are sheaves over a complete Heyting algebra. We start by outlining the theory in a way we hope is readable for the non-specialist.…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient…
This is the first of a series of papers on enriched infinity categories, seeking to reduce enriched higher category theory to the higher algebra of presentable infinity categories, which is better understood and can be approached via…
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore,…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
We study presheaves on semicategories enriched in a quantaloid: this gives rise to the notion of regular presheaf. A semicategory is regular when its representable presheaves are regular, and its regular presheaves then constitute an…
This work presents a comprehensive overview of variational quantum computing and their key role in advancing quantum simulation. This work explores the simulation of quantum systems and sets itself apart from approaches centered on…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Building on work of Marta Bunge in the one-categorical case, we characterize when a given model category is Quillen equivalent to a presheaf category with the projective model structure. This involves introducing a notion of homotopy atoms,…
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this…
This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…