Related papers: Quantum simulation beyond Hamiltonian paradigm: ca…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology.…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
Quantum simulations are designed to model quantum systems, and many compilation frameworks have been developed for executing such simulations on quantum computers. Most compilers leverage the capabilities of digital and analog quantum…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…