Related papers: Geometrically Local Quantum and Classical Codes fr…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…
Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication.…
We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
Several new constructions of 3-dimensional optical orthogonal codes are presented here. In each case the codes have ideal autocorrelation $\mathbf{ \lambda_a=0} $, and in all but one case a cross correlation of $ \mathbf{\lambda_c=1} $. All…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
The purpose of this article is to present a short review of local conformal symmetry in curved 4d space-time. Furthermore we discuss the conformal anomaly and anomaly-induced effective actions. Despite the conformal symmetry is always…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…
We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…
Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and…
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.…