Related papers: TQFTs and quantum computing
qPCF is a paradigmatic quantum programming language that ex- tends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a…
Quantum computing (QC) offers a new computing paradigm that has the potential to provide significant speedups over classical computing. Each additional qubit doubles the size of the computational state space available to a quantum…
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
Quantum circuit execution is the central task in quantum computation. Due to inherent quantum-mechanical constraints, quantum computing workflows often involve a considerable number of independent measurements over a large set of slightly…
We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes…
Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in…
Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed $d$-manifolds endowed with extra structure in the form of homotopy classes of maps…
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or…
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
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…
Quantum two-level systems, i.e. qubits, form the basis for most quantum machine learning approaches that have been proposed throughout the years. However, higher dimensional quantum systems constitute a promising alternative and are…
Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits…