Related papers: On the Cleaning Lemma of Quantum Coding Theory
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
The multivariate covering lemma states that given a collection of $k$ codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
The performance of a quantum error-correction process is determined by the likelihood that a random configuration of errors introduced to the system will lead to the corruption of encoded logical information. In this work we compare two…
This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…
Based on the concept of many-letter theory, an observable is defined measuring the raw quantum information content of single messages. A general characterization of quantum codes using the Kraus representation is given. Compression codes…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Determining the largest size, or equivalently finding the lowest redundancy, of q-ary codes for given length and minimum distance is one of the central and fundamental problems in coding theory. Inspired by the construction of…
We study the distance between symmetry-violating quantum field theories and the surface of symmetric theories. We use this notion to quantify how precise Lorentz symmetry is today, according to experimental data. The metric in parameter…
Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We first give simple arguments in favor of the "Zero Constants Party", i.e. that quantum theory should not contain fundamental dimensionful constants at all. Then we argue that quantum theory should proceed not from a space-time background…
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower…