3 citations · 5 across the 21 of their papers we have counts for
13 papers · 1 filter
Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time
William Gay, Fernando Granha Jeronimo, Abhi Shukul
In classical coding theory, the quest for explicit codes achieving list decoding capacity has been an important driving force. While random codes are easily shown to achieve capaci…
Quantum List Recovery and Decoding: Achievability and Limitations
Fernando Granha Jeronimo, Xiaojuan Ma
Quantum list recovery (QLR) and quantum list decoding (QLD) seek short lists of logically distinct Pauli corrections consistent with a syndrome and prescribed error constraints. Fo…
From Random Quantum Codes to Explicit qLDPC Codes via Local Properties
Fernando Granha Jeronimo, Xiaojuan Ma, Nikhil Shagrithaya
Constructing explicit codes matching the parameters of random codes has been a central and largely elusive question in coding theory. The quantum setting is even more challenging s…
Stable Regularity Lemmas: Efficient Algorithms and Essentially Tight Littlestone Bounds
Leonardo N. Coregliano, Fernando G. Jeronimo
In this paper, we determine the precise asymptotics of the number of parts of stable regularity equipartitions in terms of the Littlestone dimension: every graph of Littlestone…
Asymptotically Good Quantum Locally Testable Codes
William Gay, Fernando Granha Jeronimo
We construct explicit families of asymptotically good quantum locally testable codes over qubits. More precseily, we construct explicit quantum LDPC CSS codes over qubits having co…
PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax
William Gay, Fernando Granha Jeronimo, Lenny Liu +3
Pure-state consistency problems naturally lead to quantum proof systems in which a single pure witness must satisfy many acceptance constraints. The corresponding class $\mathsf{Pu…
Algorithmic List Decoding at Capacity and Optimal Proximity Gaps for Reed-Solomon Codes
Fernando Granha Jeronimo
We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluatio…
The Honeycomb Framework for Code Bounds
William Gay, Fernando Granha Jeronimo, Lenny Liu
We introduce the honeycomb hierarchy, a representation-theoretic framework that gives new asymptotic upper bounds on . Its first level is the two-row hyperoctahedral repres…
Dimension-Free Polylogarithmic Quantum Shadow Tomography
Fernando Granha Jeronimo, Qizhao Huang, Lenny Liu
Shadow Tomography is a fundamental problem in quantum information theory. Given multiple copies of an unknown -dimensional quantum state and a known collection of observable…
Optimal Quantum de Finetti Theorems via Argmax Rounding
Fernando Granha Jeronimo, Pei Wu, Haochen Xu
We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state , there is a probability measure on the unit sphere such t…
An Optimal Analysis of the Product Test
Jacob Beckey, Fernando Granha Jeronimo, Pei Wu
Product testing, i.e., deciding whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition, serves as a bridge between quantum property…
The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
William Gay, Fernando Granha Jeronimo
Interference and entanglement are among the most fundamental properties of quantum mechanics. In this work, we investigate the power of interference in the role of detecting entang…
Optimal Proximity Gap for Folded Reed--Solomon Codes via Subspace Designs
Fernando Granha Jeronimo, Lenny Liu, Pranav Rajpal
A collection of sets satisfies a -proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are -close t…