相关论文: Operator algebra and algorithmic construction of b…
We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing…
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of $\mathcal{A}$-free operators and for a singularly perturbed $T_3$-structure for the divergence…
An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated…
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
In this paper, we give a generalization of Kitaev's stabilizer code based on chain complex theory of bicommutative Hopf algebras. Due to the bicommutativity, the Kitaev's stabilizer code extends to a broader class of spaces, e.g. finite…
I present a fault-tolerant quantum computing method for 2D architectures that is particularly appealing for photonic qubits. It relies on a crossover of techniques from topological stabilizer codes and measurement based quantum computation.…
We discuss a method to adapt the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. We focus on the corresponding Pauli error models for amplitude damping noise and phase damping noise. In…
We apply the recent graphical framework of "Quantum Lego" to XP stabilizer codes where the stabilizer group is generally non-Abelian. We show that the idea of operator matching continues to hold for such codes and is sufficient for…
We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule.…
We introduce a set of axioms for locally topologically ordered quantum spin systems in terms of nets of local ground state projections, and we show they are satisfied by Kitaev's Toric Code and Levin-Wen type models. For a locally…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
We study the fundamental limits on the reliable storage of quantum information in lattices of qubits by deriving tradeoff bounds for approximate quantum error correcting codes. We introduce a notion of local approximate correctability and…
Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions…
We elaborate an algebraic framework for describing internal topological symmetries of gapped boundaries of (2+1)D topological orders. We present a categorical obstruction to the coherence of bulk group symmetry and boundary symmetries in…
Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…