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Shuchen Zhu

Shuchen Zhu appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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quant-ph cond-mat.str-el Data Structures and Algorithms hep-lat Machine Learning math.NA math.OC Numerical Analysis physics.chem-ph Populations and Evolution

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preprint2026arXiv

Learning Hamiltonians in the Heisenberg limit with static single-qubit fields

Learning the Hamiltonian governing a quantum system is a central task in quantum metrology, sensing, and device characterization. Existing Heisenberg-limited Hamiltonian learning protocols either require multi-qubit operations that are prone to noise, or single-qubit operations whose frequency or strength increases with the desired precision. These two requirements limit the applicability of Hamiltonian learning on near-term quantum platforms. We present a protocol that learns a quantum Hamiltonian with the optimal Heisenberg-limited scaling using only single-qubit control in the form of static fields with strengths that are independent of the target precision. Our protocol is robust against the state preparation and measurement (SPAM) error. By overcoming these limitations, our protocol provides new tools for device characterization and quantum sensing. We demonstrate that our method achieves the Heisenberg-limited scaling through rigorous mathematical proof and numerical experiments. We also prove an information-theoretic lower bound showing that a non-vanishing static field strength is necessary for achieving the Heisenberg limit unless one employs an extensive number of discrete control operations.

preprint2026arXiv

Subspace Optimization for Efficient Federated Learning under Heterogeneous Data

Federated learning increasingly operates in a large-model regime where communication, memory, and computation are all scarce. Typically, non-IID client data induce drift that degrades the stability and performance of local training. Existing remedies such as SCAFFOLD introduce heterogeneity-correction mechanisms to address this challenge, but they incur substantial extra communication and memory overhead. This paper proposes a subspace optimization method for federated learning (SSF), which performs heterogeneity-corrected optimization in a low-dimensional subspace using only projected quantities, while preserving full-dimensional control information through a backfill-style update that retains residual components whenever the active subspace changes. Under standard smoothness and bounded-variance assumptions, SSF attains a non-asymptotic rate of order $\widetilde{\mathcal{O}}(1/T+1/\sqrt{NKT})$. Experiments show favorable accuracy--efficiency trade-offs under heterogeneous data.

preprint2021arXiv

A Theory of Trotter Error

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of $5$, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

preprint2020arXiv

Gluon Field Digitization via Group Space Decimation for Quantum Computers

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.

preprint2011arXiv

Short and Long Range Population Dynamics of the Monarch

The monarch butterfly annually migrates from central Mexico to southern Canada. During recent decades, its population has been reduced due to human interaction with their habitat. We examine the effect of herbicide usage on the monarch butterfly's population by creating a system of linear and non-linear ordinary differential equations that describe the interaction between the monarch's population and its environment at various stages of migration: spring migration, summer loitering, and fall migration. The model has various stages that are used to describe the dynamics of the monarch butterfly population over multiple generations. In Stage 1, we propose a system of coupled ordinary differential equations that model the populations of the monarch butterflies and larvae during spring migration. In Stage 2, we propose a predator-prey model with age structure to model the population dynamics at the summer breeding site. In Stages 3 and 4, we propose exponential decay functions to model the monarch butterfly's fall migration to central Mexico and their time at the overwintering site. The model is used to analyze the long-term behavior of the monarch butterflies through numerical analysis, given data available in the research literature.