Methods toward large-scale and highly-accurate quantum mechanics simulations of materials

Hiroto Imachi, 39454, 39455

Numerical methods for large-scale quantum material simulations

Hiroto Imachi

Reza Haghshenas, Eli Chertkov, Matthew P. DeCross +11 more

Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws emerge entirely due to quantum correlations over a diverging length scale. The accurate description of such transitions is challenging for classical simulation methods of quantum systems, and is a natural application space for quantum simulation. These quantum simulations are, however, not without their own challenges-representing quantum critical states on a quantum computer requires encoding entanglement of a large number of degrees of freedom, placing strict demands on the coherence and fidelity of the computer's operations. Using Quantinuum's H1-1 quantum computer, we address these challenges by employing hierarchical quantum tensor-network techniques, creating the ground state of the critical transverse-field Ising chain on 128-sites with sufficient fidelity to extract accurate critical properties of the model. Our results suggest a viable path to quantum-assisted tensor-network contraction beyond the limits of classical methods.

T. C. Schulthess

Ayberk Demir Bakırcı

Multi-scale modeling of coupled thermal, mechanical, and electromagnetic phenomena presents one of the most computationally demanding challenges in scientific simulation. These interactions often span quantum-level processes, mesoscopic transport behavior, and macroscopic material responses, requiring integrated frameworks capable of resolving complex nonlinearity, strong coupling, and multi-physics feedback loops. Quantum computing offers a transformative pathway toward more accurate and scalable simulations of such systems. This study investigates quantum-enhanced approaches for modeling heat transfer, stress evolution, electromagnetic field propagation, and their mutual interactions across scales. By integrating quantum algorithms for partial differential equations, quantum linear solvers, and quantum-accelerated spectral and tensor representations, the research explores how quantum models can capture high-dimensional dependencies and strong correlations that classical methods struggle to resolve. The analysis highlights the potential of hybrid quantum–classical workflows to accelerate multi-physics simulation, improve predictive fidelity, and support the design of advanced materials, energy devices, and engineering systems that rely on thermal–mechanical–electromagnetic coupling.

Jincheng Zhang

This paper presents a novel multi-scale quantum phase transition calculation framework designed to simulate and predict the behavior of quantum materials. The core mechanism involves decomposing the phase transition process into multiple scales, represented by a "quantum phase transition map" which includes multiple evolution pathways. This approach offers a fundamentally new method for analyzing and predicting complex material behavior, addressing limitations of existing computational techniques. The framework's primary goal is to provide a robust and accurate tool for investigating and understanding the intricate dynamics of quantum phase transitions. We demonstrate the framework's effectiveness through the simulation of a specific quantum material, highlighting its ability to capture the essential features of the transition. The study underscores the potential of this approach to significantly advance the field of quantum materials science.