arXiv subjects

Jason Luo

Publications and source records attributed to Jason Luo.

6 recordsLinked to original sources

arXiv2026

Subexponential Approximation of the Permanent in Deterministic Polynomial Time

We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor. For a matrix of order $n$, the approximation factor is \[ \exp\!\left(O\!\left(\frac{n(\log\log n)^2}{\log n}\right)\right)=\exp(o(n)). \] All previously known deterministic polynomial time guarantees for unrestricted inputs had approximation factors $\exp(\Omega(n))$. Our proof uses convex optimization to tighten an upper bound on the permanent. The bound is based on weighted sums over all matchings in a bipartite graph representing the matrix, and correlations between unmatched vertices control its error. We approximate these sums deterministically using correlation decay and a bound on the effect of vertex deletion.

cs.DS↗

arXiv2026

Beyond halfway to Hadwiger's conjecture

Hadwiger conjectured in 1943 that every graph with no $K_t$ minor has chromatic number at most $t-1$. Delcourt and Postle proved that every graph with no $K_t$ minor has chromatic number $O(t\log\log t)$. We build on their result to improve this bound to $O(t\log\log\log t)$.

math.CO↗

arXiv2026

Tight Lower Bounds for State Tomography with Limited Entanglement

We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $\epsilon$ is, up to absolute constant factors, $\max\{d^3/(\sqrt{k}\epsilon^2),d^2/\epsilon^2\}$ for every $k$ and all sufficiently small $\epsilon$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigenvalue is of order $1/d$, even when the center is known. The main ingredient is a uniform Fisher information bound for one measurement block that depends only on the smallest eigenvalue of the state. The proof avoids the perturbative expansion responsible for the restriction in [arXiv:2402.16353]. Fano's inequality for metric balls and a log-Sobolev comparison between mutual and Fisher information then reduce the adaptive protocol to this block bound [arXiv:1607.00550, arXiv:1902.08582].

quant-ph↗

arXiv2026

MUDDLE: Measuring Understanding of Documents under Distractor and Length Effects

Document question-answering systems increasingly answer questions over collections of retrieved documents rather than one clean source, so robustness to distracting context matters as much as reading ability. When such systems fail, it is often unclear whether the context was too long or the distractors were too close to the topic, because prior work tends to conflate these two effects. We present MUDDLE, a controlled benchmark that separates them. MUDDLE uses 270 human-annotated questions, each tied to a single source document, and instantiates every question in five conditions: the source alone, the source with two or four topically similar hard negatives, and the source with two or four random distractors. The random distractors are matched to the hard negatives in length and provenance, so an accuracy gap between the two arms reflects topical similarity rather than length. All five conditions are rendered in markdown, page images, and raw PDF, but the distractor sweep reported here is run in markdown, since a source plus its distractors exceeds current image and PDF input limits. We score answers with an LLM judge across three model families. In the complete markdown sweep, hard negatives lower accuracy more than length-matched random documents at both context sizes for gpt-5-mini, while random documents stay near the no-distractor baseline. The effect is small but directionally consistent, and for gpt-5-mini hard negatives significantly underperform length-matched random distractors when pooled across context sizes. We release the data and evaluation code for a reproducible study of context degradation.

cs.CL↗

arXiv2021

A Structured Method for Compilation of QAOA Circuits in Quantum Computing

Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of two-qubit operators that commute. The flexibility in reordering the two-qubit gates allows compiler optimizations to generate circuits with better depths, gate count, and fidelity. However, it also imposes significant challenges due to additional freedom exposed in the compilation. Prior studies lack the following: (1) Performance guarantee, (2) Scalability, and (3) Awareness of regularity in scalable hardware. We propose a structured method that ensures linear depth for any compiled QAOA circuit on multi-dimensional quantum architectures. We also demonstrate how our method runs on Google Sycamore and IBM Non-linear architectures in a scalable manner and in linear time. Overall, we can compile a circuit with up to 1024 qubits in 10 seconds with a 3.8X speedup in depth, 17% reduction in gate count, and 18X improvement for circuit ESP.

quant-ph↗

arXiv2019

Uncovering Political Promotion in China: A Network Analysis of Patronage Relationship in Autocracy

Understanding patronage networks in Chinese Bureaucracy helps us quantify the promotion mechanism underlying autocratic political systems. Although there are qualitative studies analyzing political promotions, few use quantitative methods to model promotions and make inferences on the fitted mathematical model. Using publicly available datasets, we implement network analysis techniques to advance scholarly understanding of patronage networks in autocratic regimes, using the Chinese bureaucracy as an example. Using graph-based and non-graph-based features, we design three studies to examine drivers of political promotions. We find that careers of politicians are closely associated with their genders, home origins, and positions in the patronage networks.

cs.SI↗