Related papers: A Symplectic Proof of the Quantum Singleton Bound
We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model…
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…
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
In this work, we analyze a framework for constructing fault-tolerant measurement schedules of varying lengths by combining stabilizer generators, and prove results about the distance of such schedules by combining according to classical…
In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
The stabilizer formalism is a scheme, generalizing well-known techniques developed by Gottesman [quant-ph/9705052] in the case of qubits, to efficiently simulate a class of transformations ("stabilizer circuits", which include the quantum…
In this paper we present some quantitative results concerning symplectic barriers. In particular, we answer a question raised by Sackel, Song, Varolgunes, and Zhu regarding the symplectic size of the $2n$-dimensional Euclidean ball with a…
We develop a symplectic method of quantization of lightcone QCD. We find that boundary gauge fields are crucial for a consistent and complete quantization. By applying the symplectic Faddeev-Jackiw method, we very carefully remove…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We show quantum lower bounds for two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. It has been known that, for any $k$,…
We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such…
The problem of finding a constant bound on a term given a set of assumptions has wide applications in optimization as well as program analysis. However, in many contexts the objective term may be unbounded. Still, some sort of symbolic…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
The existence of $k$-uniform states has been a widely studied problem due to their applications in several quantum information tasks and their close relation to combinatorial objects like Latin squares and orthogonal arrays. With the…
We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have…