相关论文: A Sparse $Z_2$ Chain Complex Without a Sparse Lift

The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this…

We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…

We demonstrate a strategy for implementation a quantum full adder in a spin chain quantum computer. As an example, we simulate a quantum full adder in a chain containing 201 spins. Our simulations also demonstrate how one can minimize…

This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…

The $Q$-system is an efficient method for finding complete physical solutions of Bethe ansatz equations, but so far its application has been confined to systems possessing $U(1)$ symmetry. We extend the rational $Q$-system framework to…

In the paper is considered stairway-like design of quantum computer, i.e., array of double quantum dots or wells. The model is quite general to include wide variety of physical systems from coupled quantum dots in experiments with solid…

In this paper we consider the use of variable length non prefix-free codes for coding constrained sequences of symbols. We suppose to have a Markov source where some state transitions are impossible, i.e. the stochastic matrix associated…

We present a detailed description of an architecture for fault-tolerant quantum computation, which is based on the cluster model of encoded qubits. In this cluster-based architecture, concatenated computation is implemented in a quite…

In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of…

It is generally unclear whether smaller codes can be "concatenated" to systematically create quantum LDPC codes or their sparse subsystem code cousins where the degree of the Tanner graph remains bounded while increasing the code distance.…

The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the…

Semiconductor spin qubits are an attractive quantum computing platform that offers long qubit coherence times and compatibility with existing semiconductor fabrication technology for scale up. Here, we propose a spin-qubit architecture…

We consider three kinds of quotients of the curve complex which are obtained by coning off uniformly quasi-convex subspaces: symmetric curve sets, non-maximal train track sets, and compression body disc sets. We show that the actions of the…

We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a…

In this work we explore a correspondence between quantum circuits and low-degree polynomials over the finite field F_2. Any quantum circuit made up of Hadamard, Z, controlled-Z and controlled-controlled-Z gates gives rise to a degree-3…

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…

We give a procedure for "reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over $\mathbb{Z}$. Applying this procedure to chain complexes obtained by "lifting"…

It is widely believed that integer quantum Hall systems do not have fractional excitations. Here we show the converse to be true for a class of systems where integer quantum Hall effect emerges spontaneously due to the interplay of…

We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…