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Quantum Simulations of Material Properties on Quantum Computers

Nan Sheng, Christian Vorwerk, Marco Govoni, Giulia Galli

Published May 11, 2021• 2 citations
OpenAlex

Abstract

Quantum computers hold promise to greatly improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories and effective many-body Hamiltonians. We focus on a specific class of materials, i.e., spin defects in solids, which are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear within reach.

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•Aug 31, 2026•0 citations
Quantum computers hold promise to greatly improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories and effective many-body Hamiltonians. We focus on a specific class of materials, i.e., spin defects in solids, which are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear within reach.
Abstract Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here, we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.
Abstract Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin polarized states of a hydrogen chain (1D-H), the equation of state of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices.
Quantum computing introduces a revolutionary approach to solving problems that are computationally beyond the reach of classical systems. Among its most promising applications is the simulation of many-body systems, where strong particle interactions lead to complex quantum behaviors. Traditional computational techniques often fail due to exponential resource requirements, but quantum simulators can efficiently model these interactions through entanglement and superposition. Recent advances in superconducting qubits, trapped ions, and photonic quantum devices have enabled small- scale experimental demonstrations of spin models, Hubbard systems, and correlated electron dynamics. These developments offer new insights into condensed matter physics and quantum phase transitions. As quantum technologies continue to evolve, they hold the potential to transform the study of materials, superconductivity, and other many-body phenomena with remarkable precision and scalability.
Abstract There has been a good deal of work on algorithms to simulate quantum many-body systems with fault-tolerant quantum computers- those with full error correction. Fault-tolerant quantum computers of scale requisite to achieve computational advantage for these problems are likely over a decade away. Moreover, devices that we can build in the near term, called Noisy Intermediate Scale Quantum computers (NISQ), have too much noise to implement the long circuits required by these algorithms. We review heuristic, short-depth quantum algorithms more suited to NISQ computers; specifically, their scaling properties when applied to electronic and nuclear structure calculations, including Hamiltonian complexity with particle number, ansatz state preparation, convergence, and noise. We will present examples of actual quantum structure calculations with NISQ computers, as well as a newly-developed error mitigation technique that significantly improves accuracy. We end with an outlook for “advantage” – when NISQ systems might excel conventional HPC approaches for comparable problems.
We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol.We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies.We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation.We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation.We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.
This paper explores the application of quantum simulation to predict material properties. Traditional methods for predicting material properties often rely on computationally intensive density functional theory (DFT) calculations or experimental techniques, which can be limited by computational resources and the difficulty of accurately modeling complex quantum systems. Quantum simulation offers a fundamentally different approach by leveraging the principles of quantum mechanics to directly simulate the behavior of materials at the quantum level. This work outlines the core concept, mechanism, and potential advantages of utilizing quantum computers to compute electronic structure, energies, and wavefunctions, ultimately leading to accurate predictions of material properties. The focus is on demonstrating the transformative potential of this technology and its ability to surpass the limitations of conventional approaches. The theoretical framework presented provides a roadmap for future research and development in this emerging field. ---