Related papers: Two paradigms for topological quantum computation
We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion.…
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the…
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial statistical transformations as one excitation is moved (braided) around another. Topological…
We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum…
On basis of generalized 6j-symbols we give a formulation of topological quantum field theories for 3-manifolds including observables in the form of coloured graphs. It is shown that the 6j-symbols associated with deformations of the…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes -- high-dimensional extensions of combinatorial graphs. We show that meaningful invariants of such…
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…
We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The fusion rules induce an association scheme with Krein…
We investigate the computational power and unified resource use of hybrid quantum-classical computations, such as teleportation and measurement-based computing. We introduce a physically causal and local graphical calculus for quantum…
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
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…
In recent years, Quantum Computing witnessed massive improvements in terms of available resources and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn…