An extension of the Variational Quantum Eigensolver (VQE) method is presented where a quantum computer generates an accurate exchange-correlation potential for a Density Functional Theory (DFT) simulation on classical hardware. The method enables efficient simulations of quantum systems by interweaving calculations on classical and quantum resources. DFT is implemented on classical hardware, which enables the efficient representation of and operation on quantum systems while being formally exact. The portion of the simulation operating on quantum hardware produces an accurate exchange-correlation potential but only requires relatively short depth quantum circuits.
An extension of the Variational Quantum Eigensolver (VQE) method is presented where a quantum computer generates an accurate exchange-correlation potential for a Density Functional Theory (DFT) simulation on classical hardware. The method enables efficient simulations of quantum systems by interweaving calculations on classical and quantum resources. DFT is implemented on classical hardware, which enables the efficient representation of and operation on quantum systems while being formally exact. The portion of the simulation operating on quantum hardware produces an accurate exchange-correlation potential but only requires relatively short depth quantum circuits.
Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations of the unknown universal functional, limiting its general applicability for many fundamental and technologically relevant systems. In this work we develop a hybrid quantum/classical algorithm called quantum enhanced DFT (QEDFT) that systematically constructs quantum approximations of the universal functional using data obtained from a quantum computer. We benchmark the QEDFT algorithm on the Fermi-Hubbard model, both numerically and on data from experiments on real quantum hardware. We find that QEDFT surpasses the quality of groundstate results obtained from Hartree-Fock DFT, as well as from direct application of conventional quantum algorithms such as VQE. Furthermore, we demonstrate that QEDFT works even when only noisy, low-depth quantum computation is available, by benchmarking the algorithm on data obtained from Google's quantum computer. We further show how QEDFT also captures quintessential properties of strongly correlated Mott physics for large Fermi-Hubbard systems using functionals generated on much smaller system sizes. Our results indicate that QEDFT can be applied to realistic materials and molecular systems, and has the potential to outperform the direct application of either DFT or VQE alone, without the requirement of large scale or fully fault-tolerant quantum computers.
Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.
Scientific simulations demand methods combining scalability with predictive accuracy. Density Functional Theory (DFT) on High-Performance Computing (HPC) enables large-scale electronic-structure simulations but is limited by approximations affecting strongly correlated systems and band-gap predictions. Quantum computing offers a pathway to address this, though current Noisy Intermediate-Scale Quantum (NISQ) hardware remains constrained by qubit resources, noise, and execution cost.
This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver. Large systems are partitioned to isolate a chemically relevant active space, treated via the Variational Quantum Eigensolver (VQE), while the remaining degrees of freedom are described by DFT. The framework incorporates active-space selection, embedded Hamiltonian construction, symmetry preservation, operator mapping, self-consistent density updating, and modular classical-quantum coupling.
We focus on noiseless quantum simulation to systematically evaluate accuracy, convergence, active-space dependence, computational cost, and HPC scalability without hardware noise. Detailed profiling identifies computational bottlenecks and highlights limitations of CPU-based quantum simulation. A QPU runtime-estimation methodology is additionally developed to assess execution requirements on actual quantum hardware.
Results demonstrate quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability. Noisy quantum simulation and QPU execution remain key future directions, providing a pathway toward practical, scalable HPC-quantum hybrid simulations as hardware matures.
Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parametrized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parametrization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground-state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground-state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by contemporary quantum computers are still limited, restricting the simulations to very simple molecules. In order to rapidly scale up to more interesting molecular systems, we propose the embedding of the quantum electronic structure calculation into a classically computed environment obtained at the Hartree-Fock (HF) or density functional theory (DFT) level of theory. This result is achieved by constructing an effective Hamiltonian that incorporates a mean field potential describing the action of the inactive electrons on a selected Active Space (AS). The ground state of the AS Hamiltonian is then determined by means of the variational quantum eigensolver algorithm. We show that with the proposed HF and DFT embedding schemes, we can obtain significant energy corrections to the reference HF and DFT calculations for a number of simple molecules in their strongly correlated limit (the dissociation regime) as well as for systems of the size of the oxirane molecule.
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization etc. Although quantum computing offers paths forward, including variational techniques, embedding strategies, and quantum linear solvers, the discussion remains scattered. Without shared terms or structure, evaluating progress in hybrid quantum-classical DFT efforts becomes challenging. To bring order, we introduce a three-axis scheme based on where the method connects into DFT, whether the quantum part boosts precision or cuts time, alongside intended device type: current noisy machines or future error-corrected ones. Sorting known approaches in this way shows why embedding frameworks fit modern tools better, while faster linear algebra waits for more advanced systems.