arXiv subjects

Daniel T. Chen

Publications and source records attributed to Daniel T. Chen.

7 recordsLinked to original sources

arXiv2025

ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms

Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a major bottleneck. Although large language models can generate isolated code fragments, they lack the structured reasoning required to design, verify, and iteratively refine complete scientific pipelines. Here we introduce ATHENA, an agentic framework explicitly designed to emulate scientific research modeled as a knowledge-driven contextual bandit process. Its core loop separates conceptual policy from numerical realization through expert-derived conceptual scaffolding, enabling principled diagnosis, reformulation, and repair of computational strategies. Across scientific computing and scientific machine learning tasks, ATHENA autonomously derives and correctly applies exact analytical solutions, constructs stable numerical solvers, diagnoses ill-posed formulations, and orchestrates hybrid symbolic-numeric workflows. Quantitatively, ATHENA matches and frequently surpasses the accuracy of expert-authored reference solutions reported in the literature on canonical benchmarks. By reframing computation as an object of agentic reasoning, our framework enables autonomous orchestration of heterogeneous algorithms across scientific domains.

cs.LG↗

arXiv2025

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning

Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the residual. Different transformations correspond to distinct objective functionals: exponential weights target the minimization of uniform error, while linear weights recover the minimization of quadratic error. Within this perspective, adaptive weighting is equivalent to selecting sampling distributions that optimize the primal objective, thereby linking discretization choices directly to error metrics. This principled approach yields three benefits: (1) it enables systematic design of adaptive schemes across norms, (2) reduces discretization error through variance reduction of the loss estimator, and (3) enhances learning dynamics by improving the gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across optimizers and architectures. Our results provide a theoretical justification of residual-based adaptivity and establish a foundation for principled discretization and training strategies.

cs.LG↗

arXiv2024

Efficient Circuit Wire Cutting Based on Commuting Groups

Current quantum devices face challenges when dealing with large circuits due to error rates as circuit size and the number of qubits increase. The circuit wire-cutting technique addresses this issue by breaking down a large circuit into smaller, more manageable subcircuits. However, the exponential increase in the number of subcircuits and the complexity of reconstruction as more cuts are made poses a great practical challenge. Inspired by ancilla-assisted quantum process tomography and the MUBs-based grouping technique for simultaneous measurement, we propose a new approach that can reduce subcircuit running overhead. The approach first uses ancillary qubits to transform all quantum input initializations into quantum output measurements. These output measurements are then organized into commuting groups for the purpose of simultaneous measurement, based on MUBs-based grouping. This approach significantly reduces the number of necessary subcircuits as well as the total number of shots. Lastly, we provide numerical experiments to demonstrate the complexity reduction.

quant-ph↗

arXiv2024

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits, and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits, and discuss the mechanisms for this advantage.

quant-ph↗

arXiv2023

Inferring Quantum Network Topology using Local Measurements

Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities -- namely, the von Neumann entropy and the measured mutual information -- as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.

quant-ph↗

arXiv2023

Online Detection of Golden Circuit Cutting Points

Quantum circuit cutting has emerged as a promising method for simulating large quantum circuits using a collection of small quantum machines. Running low-qubit "circuit fragments" not only overcomes the size limitation of near-term hardware, but it also increases the fidelity of the simulation. However, reconstructing measurement statistics requires computational resources - both classical and quantum - that grow exponentially with the number of cuts. In this manuscript, we introduce the concept of a golden cutting point, which identifies unnecessary basis components during reconstruction and avoids related down-stream computation. We propose a hypothesis-testing scheme for identifying golden cutting points, and provide robustness results in the case of the test failing with low probability. Lastly, we demonstrate the applicability of our method on Qiskit's Aer simulator and observe a reduced wall time from identifying and avoiding obsolete measurements.

quant-ph↗

arXiv2023

Efficient Quantum Circuit Cutting by Neglecting Basis Elements

Quantum circuit cutting has been proposed to help execute large quantum circuits using only small and noisy machines. Intuitively, cutting a qubit wire can be thought of as classically passing information of a quantum state along each element in a basis set. As the number of cuts increase, the number of quantum degrees of freedom needed to be passed through scales exponentially. We propose a simple reduction scheme to lower the classical and quantum resources required to perform a cut. Particularly, we recognize that for some cuts, certain basis element might pass "no information" through the qubit wire and can effectively be neglected. We empirically demonstrate our method on circuit simulators as well as IBM quantum hardware, and we observed up to 33 percent reduction in wall time without loss of accuracy.

quant-ph↗