Related papers: Quantum Statistics and Spacetime Topology: Quantum…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…
Open topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling conjecture which connects topological recursion and topological string…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
Quantum resources such as entanglement, information redundancy, and coherence enable revolutionary advantages but obey fundamental tradeoffs. We present a unified geometric constraint governing three core operational tasks: teleportation…
In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is directly related to global transformations of…
We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of $d=4$, $\mathcal{N}=2$ supersymmetric field theories of class…
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…
Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally…
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between…
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…
Topological quantum computing holding global anti-interference ability is realized by braiding some anyons, such as well-known Fibonacci anyons. Here, based on $SO(3)_2 $ theory we obtain a total of 6 anyon models utilizing…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
This is a review article on the quantum toroidal algebras, focusing on their roles in various solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string theory. Using $\mathcal{W}$-algebras as our starting…