Understanding the benefits of quantum computing for solving combinatorial optimization problems (COPs) remains an open research question. In this work, we extend and analyze algorithms that solve COPs by recursively shrinking them. The algorithms leverage correlations between variables extracted from quantum or classical subroutines to recursively simplify the problem. We compare the performance of the algorithms equipped with correlations from the quantum approximate optimization algorithm (QAOA) as well as the classical linear programming (LP) and semi-definite programming (SDP) relaxations. This allows us to benchmark the utility of QAOA correlations against established classical relaxation algorithms. We apply the recursive algorithm to MaxCut problem instances with up to a hundred vertices at different graph densities. Our results indicate that LP outperforms all other approaches for low-density instances, while SDP excels for high-density problems. Moreover, the shrinking algorithm proves to be a viable alternative to established methods of rounding LP and SDP relaxations. In addition, the recursive shrinking algorithm outperforms its bare counterparts for all three types of correlations, i.e., LP with spanning tree rounding, the Goemans-Williamson algorithm, and conventional QAOA. While the lowest depth QAOA consistently yields worse results than the SDP, our tensor network experiments show that the performance increases significantly for deeper QAOA circuits.

Retrieval-augmented generation (RAG) systems trained using reinforcement learning (RL) with reasoning are hampered by inefficient context management, where long, noisy retrieved documents increase costs and degrade performance. We introduce RECON (REasoning with CONdensation), a framework that integrates an explicit summarization module to compress evidence within the reasoning loop. Our summarizer is trained via a two-stage process: relevance pretraining on QA datasets, followed by multi-aspect distillation from proprietary LLMs to ensure factuality and clarity. Integrated into the Search-R1 pipeline, RECON reduces total context length by 35\%, leading to improved training speed and inference latency, while simultaneously improving RAG performance on downstream QA benchmarks. Notably, it boosts the average EM score of the 3B model by 14.5\% and the 7B model by 3.0\%, showing particular strength in multi-hop QA. RECON demonstrates that learned context compression is essential for building practical, scalable, and performant RAG systems. Our code implementation is made available at this https URL.

Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These simulators, primarily based on neutral atoms, trapped ions, and superconducting circuits, hold the potential to address long-standing questions in nuclear, high-energy, and condensed-matter physics, and may ultimately allow first-principles studies of matter evolution in settings ranging from the early universe to high-energy collisions. Research in this rapidly growing field is also driving the convergence of concepts across disciplines and uncovering new phenomena. In this Review, we highlight recent experimental and theoretical developments, focusing on phenomena accessible in current and near-term quantum simulators, including particle production and string breaking, collision dynamics, thermalization, ergodicity breaking, and dynamical quantum phase transitions. We conclude by outlining promising directions for future research and opportunities enabled by available quantum hardware.

We present a quantum simulation framework universally applicable to a wide class of quantum systems, including quantum field theories such as quantum chromodynamics (QCD). Specifically, we generalize an efficient quantum simulation protocol developed for bosonic theories in [Halimeh et al., arXiv:2411.13161] which, when applied to Yang-Mills theory, demonstrated an exponential resource advantage with respect to the truncation level of the bosonic modes, to systems with both bosons and fermions using the Jordan-Wigner transform and also the Verstraete-Cirac transform. We apply this framework to QCD using the orbifold lattice formulation and achieve an exponential speedup compared to previous proposals. As a by-product, exponential speedup is achieved in the quantum simulation of the Kogut-Susskind Hamiltonian, the latter being a special limit of the orbifold lattice Hamiltonian. In the case of Hamiltonian time evolution of a theory on an $L^d$ spatial lattice via Trotterization, one Trotter step can be realized using $\mathcal{O}(L^d)$ numbers of CNOT gates, Hadamard gates, phase gates, and one-qubit rotations. We show this analytically for any matter content and $\mathrm{SU}(N)$ gauge group with any $N$. Even when we use the Jordan-Wigner transform, we can utilize the cancellation of quantum gates to significantly simplify the quantum circuit. We also discuss a block encoding of the Hamiltonian as a linear combination of unitaries using the Verstraete-Cirac transform. Our protocols do not assume oracles, but rather present explicit constructions with rigorous resource estimations without a hidden cost, and are thus readily implementable on a quantum computer.

Visual instruction tuning adapts pre-trained Multimodal Large Language Models (MLLMs) to follow human instructions for real-world applications. However, the rapid growth of these datasets introduces significant redundancy, leading to increased computational costs. Existing methods for selecting instruction data aim to prune this redundancy, but predominantly rely on computationally demanding techniques such as proxy-based inference or training-based metrics. Consequently, the substantial computational costs incurred by these selection processes often exacerbate the very efficiency bottlenecks they are intended to resolve, posing a significant challenge to the scalable and effective tuning of MLLMs. To address this challenge, we first identify a critical, yet previously overlooked, factor: the anisotropy inherent in visual feature distributions. We find that this anisotropy induces a \textit{Global Semantic Drift}, and overlooking this phenomenon is a key factor limiting the efficiency of current data selection methods. Motivated by this insight, we devise \textbf{PRISM}, the first training-free framework for efficient visual instruction selection. PRISM surgically removes the corrupting influence of global background features by modeling the intrinsic visual semantics via implicit re-centering. Empirically, PRISM reduces the end-to-end time for data selection and model tuning to just 30\% of conventional pipelines. More remarkably, it achieves this efficiency while simultaneously enhancing performance, surpassing models fine-tuned on the full dataset across eight multimodal and three language understanding benchmarks, culminating in a 101.7\% relative improvement over the baseline. The code is available for access via \href{this https URL}{this repository}.