Quantum Simulations and Computing
Understanding correlated many-body systems is crucial across a wide range of scientific and technological domains. Their intrinsic complexity makes them difficult to treat with classical computers when the system becomes sufficiently large, prompting growing interest in quantum simulation and quantum computing as promising alternatives, a direction that directly motivates our work.
Analog Quantum Simulation with Ultracold Atoms
Ultracold-atom quantum simulators confine neutral atoms in optical lattices, effectively mimicking electrons or spins in crystals or molecules. These systems provide a promising platform for exploring quantum many-body physics through analog simulations. A key model implemented in such simulators is the Fermi-Hubbard model, which uses fermionic atoms. By leveraging two hyperfine states and the Feshbach resonance, the on-site interaction U can be finely tuned. Quantum gas microscopes facilitate site-resolved, statistical measurements, enabling the evaluation of instantaneous spin and charge distributions as well as multi-point correlations that encode entanglement and topological orders.
Our group investigates many-body phenomena driven by strong correlations at the wavefunction level, collaborating closely with cold-atom experiments to uncover physics inaccessible to reductive theories. Examples include high-order correlations and multipartite entanglement in models relevant to real materials. Additionally, we develop algorithmic methods that utilize the observables accessible in ultracold-atom simulators, enabling analog simulations of condensed matter problems that exceed the capabilities of classical computation.
Relevant papers:
- Ding et al. “Sampling Electronic Fock States using Determinant Quantum Monte Carlo“, Commun. Phys. 8, 48 (2025)
- Koepsell et al. “Microscopic Evolution of Doped Mott Insulators from Polaronic Metal to Fermi Liquid“, Science 374, 82 (2021)
- Wang et al. “Higher-Order Spin-Hole Correlations around a Localized Charge Impurity“, Phys. Rev. Research 3, 033204 (2021)
- Bohrdt et al. “Dominant Fifth-Order Correlations in Doped Quantum Anti-Ferromagnets“, Phys. Rev. Lett. 126, 026401 (2021)
Quantum Dots and Material-Based Quantum Simulations
Recent advances in nanotechnologies and low-dimensional materials have enabled material-based quantum simulation. In contrast to ultracold atom platforms, which use neutral atoms to emulate electrons in quantum many-body models, these material-based systems confine actual electrons within mesoscopic lattice structures. Although they are generally less clean than cold-atom simulators, they naturally retain long-range Coulomb interactions, multi-orbital physics, band topology, and electron-phonon coupling that are critical for materials and difficult to mimic in ultracold atom experiments.
Gate-defined quantum dots in semiconductors represent a leading platform in this area. These systems can host multiple electronic orbitals within a single dot and maintain entanglement across coupled dots. The tunnel barriers between dots can be individually tuned, allowing precise control over the geometry and topology of the simulated system. In addition, single-snapshot measurements, combined with adiabatic or diabatic tuning, enable direct access to spin configurations, making this platform ideal for studying magnetic phenomena. Another promising platform is provided by moiré superlattices in two-dimensional heterostructures, where low-energy electronic states are governed by the superlattice potential rather than the underlying atomic lattice. Our group is interested in modeling and simulations based on these material-based mesoscopic simulators.
Relevant papers:
- Zheng et al. “Electronic Ratchet Effect in a Moiré System: Signatures of Excitonic Ferroelectricity“, arXiv:2306.03922 (2023)
- Dehollain et al. “Nagaoka Ferromagnetism Observed in a Quantum Dot Plaquette“, Nature 579, 528 (2020)
- Wang et al. “Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots“, Phys. Rev. B 100, 155133 (2019)
Hybrid Quantum-Classical Algorithms
While classical-computer-based quantum many-body algorithms are leading the theoretical discoveries in this field, future study is likely to be hindered by the difficulty of accurate simulation of large-scale many-body systems on classical computers, which stems from the exponential growth of their Hilbert space sizes with the number of particles. Quantum computing technologies, including hybrid quantum-classical algorithms, constitute a promising new direction for theoretical investigations of strongly correlated many-body systems.
Our group is interested in designing efficient quantum-classical algorithms and ansatzs to solve material- or molecule-relevant simulation problems. We are particularly interested in systems with intrinsically unbounded Hilbert space, such as models with fermion-boson coupling. We design efficient hybrid quantum-classical algorithm applicable to overcome the Hilbert-space issues through variational many-body transformations. Our group is also interested in the optimization of variational ansatz through entanglement depth and basis selection.
Relevant papers:
- Denner et al. “A Hybrid Quantum-Classical Method for Electron-Phonon Systems“, Commun. Phys. 6, 233 (2023)
- Salek et al. “A Novel Hybrid Quantum-Classical Framework for an In-vehicle Controller Area Network Intrusion Detection“, IEEE Access 11, 96081 (2023)
- Wang et al. “Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study“, Phys. Rev. Research 2, 043258 (2020)
Quantum Machine Learning
The foundational principles of quantum mechanics offer computational advantages for solving specific classes of problems, motivating the development of quantum-enhanced algorithms. In our group, one active area of research focuses on quantum acceleration for machine learning, including techniques that can be implemented on classical platforms. We are particularly interested in hybrid quantum-classical algorithms that employ quantum annealing to optimize complex, highly nonlinear functions found in deep learning architectures such as multilayer perceptrons. Beyond hardware integration, we also explore the incorporation of quantum-inspired structures within traditional machine learning models. An extension of this effort is applying these methods to real-world engineering problems where classical optimization approaches often face scalability limits.
Relevant papers:
- Li et al. “Quantum-Inspired Weight-Constrained Neural Network: Reducing Variable Numbers by 100x Compared to Standard Neural Networks“, arXiv:2412.19355 (2024)
- Li et al. “Quantum-Inspired Activation Functions in the Convolutional Neural Network“, arXiv:2404.05901 (2024)
- Salek et al. “A Novel Hybrid Quantum-Classical Framework for an In-vehicle Controller Area Network Intrusion Detection“, IEEE Access 11, 96081 (2023)