Related papers: Topological Quantum Computing and 3-Manifolds
A single qubit may be represented on the Bloch sphere or similarly on the $3$-sphere $S^3$. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of $3$-manifolds. A magic state and…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
Quantum invariants in low dimensional topology offer a wide variety of valuable invariants of knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is…
To each local field (including the real or complex numbers) we associate a quantum dilogarithm and show that it satisfies a pentagon identity and some symmetries. Using an angled version of these quantum dilogarithms, we construct three…
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum…
Topological phases of matter is a natural place for encoding robust qubits for quantum computation. In this work we extend the newly introduced class of qubits based on valence-bond solid models with SPT (symmetry-protected topological)…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…
Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the…
The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
Measurement-based quantum computation is a model for quantum information processing utilizing local measurements on suitably entangled resource states for the implementation of quantum gates. A complete characterization for universal…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…
In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…