arXiv subjects

Maxine Luo

Publications and source records attributed to Maxine Luo.

5 recordsLinked to original sources

arXiv2026

Efficient Auxiliary-Field Quantum Monte Carlo using Isometric Tensor Hypercontraction

Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious fermionic modes. Our method shows reduced theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear $\ce{H10}$-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wavefunction methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.

physics.chem-ph↗

arXiv2025

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.

quant-ph↗

arXiv2024

Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction

We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov subspace methods, which can find low-lying eigenstates and simulate quantum time evolution while avoiding local minima and maintaining high accuracy. In our approach, the molecular Hamiltonian is represented as a sum of products of four MPOs, each with a bond dimension of only 2. Iteratively applying the MPOs to the current quantum state in MPS form, summing and re-compressing the MPS leads to a scheme with the same asymptotic memory cost as the bare MPS and reduces the computational cost scaling compared to the Krylov method using a conventional MPO construction. We provide a detailed theoretical derivation of these statements and conduct supporting numerical experiments to demonstrate the advantage. Our algorithm is highly parallelizable and thus lends itself to large-scale HPC simulations.

cond-mat.str-el↗

arXiv2024

Efficient simulation of quantum chemistry problems in an enlarged basis set

We propose a quantum algorithm to simulate the dynamics in quantum chemistry problems. It is based on adding fresh qubits at each Trotter step, which enables a simpler implementation of the dynamics in the extended system. After each step, the extra qubits are recycled, so that the whole process accurately approximates the correct unitary evolution. A key ingredient of the approach is an isometry that maps a simple, diagonal Hamiltonian in the extended system to the original one, and we give a procedure to compute this isometry. We estimate the error at each time step, as well as the number of gates, which scales as $O(N^2)$, where $N$ is the number of orbitals. We illustrate our results with three examples: the Hydrogen chain, small molecules, and the FeMoco molecule. In the Hydrogen chain and the Hydrogen molecule we observe that the error scales in the same way as the Trotter error. For FeMoco, we estimate the number of gates in a fault-tolerant setup.

quant-ph↗

arXiv2023

Probing Off-diagonal Eigenstate Thermalization with Tensor Networks

Energy filter methods in combination with quantum simulation can efficiently access the properties of quantum many-body systems at finite energy densities [Lu et al. PRX Quantum 2, 020321 (2021)]. Classically simulating this algorithm with tensor networks can be used to investigate the microcanonical properties of large spin chains, as recently shown in [Yang et al. Phys. Rev. B 106, 024307 (2022)]. Here we extend this strategy to explore the properties of off-diagonal matrix elements of observables in the energy eigenbasis, fundamentally connected to the thermalization behavior and the eigenstate thermalization hypothesis. We test the method on integrable and non-integrable spin chains of up to 60 sites, much larger than accessible with exact diagonalization. Our results allow us to explore the scaling of the off-diagonal functions with the size and energy difference, and to establish quantitative differences between integrable and non-integrable cases.

quant-ph↗