arXiv subjects

Isabel Nha Minh Le

Publications and source records attributed to Isabel Nha Minh Le.

8 recordsLinked to original sources

arXiv2026

A Quantum Algorithm with Polylogarithmic Depth per Trotter Step for the Extended Hubbard Model

The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but its simulation remains challenging because long-range interactions give rise to a large number of interaction terms. Here we present Q2FMM, an efficient quantum algorithm for simulating this model within the Trotter product formula. Inspired by the fast multipole method, Q2FMM replaces site-site interactions with interactions between hierarchical coarse-grained boxes across multiple length scales. In addition, the multipole expansions of boxes are reused for their parent boxes, further enhancing the efficiency. To enable this hierarchical reuse coherently, we design a reversible quantum circuit that removes garbage information through uncomputing. The resulting circuit depth for a single Trotter step scales polylogarithmically with system size.

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arXiv2026

Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression

Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior. In this work, we provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit with near-optimal gate complexity $\mathcal{O}\left( N \, t \, \text{polylog}(N \, t/ε) \right)$ for all local and translationally invariant Hamiltonians. We demonstrate our method by encoding the globally controlled time evolution of a Heisenberg antiferromagnet on a Kagome lattice. For $N = 48$ sites, evolution time $t=0.1$ and infidelity $ε\approx1\%$, the controlled time-evolution circuit requires 960 two-qubit B gates, for which we propose a straightforward implementation scheme for ion-trap setups. Thereby, our recipe extends digital quantum simulators toward system sizes and geometries that are challenging for classical computation.

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arXiv2026

Hessian-vector products for tensor networks via recursive tangent-state propagation

Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is computationally prohibitive for large-scale systems. In this work, we bypass this bottleneck by introducing an analytical Hessian-vector product kernel designed for arbitrary compositions of linear maps. This two-pass algorithm leverages recursive tangent-state propagation with a bounded virtual bond dimension to guarantee scalability. We demonstrate the practical utility of this kernel by integrating it into a Riemannian trust-region framework for quantum circuit compression. Evaluated on time-evolution circuits for various spin chains, our second-order approach achieves up to a four-order-of-magnitude improvement in fidelity over naive Trotterization, while delivering significantly smoother, faster convergence than conventional first-order methods such as Riemannian ADAM.

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arXiv2025

Improved Ising Meson Spectroscopy Simulation on a Noisy Digital Quantum Device

The transverse-field Ising model serves as a paradigm for studying confinement and excitation spectra, particularly the emergence of $E_8$ symmetry near criticality. However, experimentally resolving the Ising meson spectroscopy required to verify these symmetries is challenging on near-term quantum hardware due to the depth of circuits required for real-time evolution. Here, we demonstrate improved spectroscopy of confined excitations using two distinct error-resilient circuit construction techniques on the IBM Torino device: first-order Trotter decomposition utilizing native fractional gates, and a tensor-network-based circuit compression via Riemannian optimization. By analyzing the Fourier spectrum of error-mitigated time-series data, we successfully identify key signatures of $E_8$ symmetry despite hardware noise. These results validate the viability of both circuit compression and hardware-efficient compilation for probing complex topological phenomena on NISQ devices.

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arXiv2025

Riemannian quantum circuit optimization based on matrix product operators

We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our method imposes no symmetry assumptions, such as translational invariance, on the quantum systems. This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator. Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian. In these cases, our approach achieves a relative error improvement of up to four orders of magnitude for systems of 50 qubits, although our method is also applicable to larger systems. Furthermore, we demonstrate the versatility of our method by applying it to molecular systems, specifically lithium hydride, achieving an error improvement of up to eight orders of magnitude. This proof of concept highlights the potential of our approach for broader applications in quantum simulations.

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arXiv2025

High-Performance Contraction of Quantum Circuits for Riemannian Optimization

This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian optimization methods -- specifically the Riemannian trust-region algorithm -- which involves second derivative calculations with respect to the gates. Our key technical contribution is a matrix-free algorithmic framework that avoids the explicit construction and storage of large unitary matrices acting on the whole Hilbert space. Instead, we evaluate all quantities as sums over state vectors, assuming that these vectors can be stored in memory. We develop HPC-optimized kernels for applying gates to state vectors and for the gradient and Hessian computation. Further improvements are achieved by exploiting sparsity structures due to Hamiltonian conservation laws, such as parity conservation, and lattice translation invariance. We benchmark our implementation on the Fermi-Hubbard model with up to 16 sites, demonstrating a nearly linear parallelization speed-up with up to 112 CPU threads. Finally, we compare our implementation with an alternative matrix product operator-based approach.

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arXiv2023

Symmetry-invariant quantum machine learning force fields

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

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arXiv2021

Analytic Filter Function Derivatives for Quantum Optimal Control

Auto-correlated noise appears in many solid state qubit systems and hence needs to be taken into account when developing gate operations for quantum information processing. However, explicitly simulating this kind of noise is often less efficient than approximate methods. Here, we focus on the filter function formalism, which allows the computation of gate fidelities in the presence of auto-correlated classical noise. Hence, this formalism can be combined with optimal control algorithms to design control pulses, which optimally implement quantum gates. To enable the use of gradient-based algorithms with fast convergence, we present analytically derived filter function gradients with respect to control pulse amplitudes, and analyze the computational complexity of our results. When comparing pulse optimization using our derivatives to a gradient-free approach, we find that the gradient-based method is roughly two orders of magnitude faster for our test cases. We also provide a modular computational implementation compatible with quantum optimal control packages.

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