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arXiv:2605.29774

Quantum algorithms for density functional theory with minimal readout

Yuansheng Zhao, Hirofumi Nishi, Taichi Kosugi, Satoshi Hirose, Hiroki Sakagami, Tatsuki Oikawa, Tatsuya Okayama, Yu-ichiro Matsushita

quant-phSubmitted May 28, 2026• Announced May 29, 2026• 0 citations
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Abstract

While quantum computers have shown significant promise for electronic structure calculations, their potential to accelerate density functional theory (DFT) calculations remains unclear. In this work, we present a qubit-efficient encoding scheme for wavefunctions in Kohn--Sham (KS) DFT, together with a quantum algorithm that computes all occupied orbitals simultaneously. We further show that our algorithm is particularly well suited to the Harris functional, enabling the total energy to be evaluated with a potential exponential speedup over classical approaches by entirely avoiding the costly readout of the electronic density. In addition, we propose a second method for achieving self-consistent DFT calculations using multiple copies of the wavefunction, which likewise circumvents density readout. The applicability of our algorithms is demonstrated through several numerical examples, and their efficiency is compared with that of existing approaches.

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Ground-State Energy and Related Properties Estimation in Quantum Chemistry with Linear Dependence on the Number of Atoms

Taehee Ko, Xiantao Li, Chunhao Wang

At the heart of quantum chemistry and materials science lies the critical task of estimating ground-state properties. We present a quantum algorithm for this task by quantizing the density-functional theory (DFT). A key aspect of imple-menting DFT faithfully is the requirement for self-consistent calculations, which involve repeated di-agonalizations of the Hamiltonian. This procedure, however, creates a significant bottleneck, as a classical algorithm generally demands a computational complexity that grows cubically with the number of electrons, restricting the scalability of DFT for tackling large-scale problems that involve complex chemical environments and microstructures. This article presents the first quantum algorithm that has provided substantial speedup for the ground state computation, by improving the complexity to one with a linear scaling with the number of atoms. The algorithm leverages the exponential speedup by the quantum singular value transformation to generate a quantum circuit to encode the density-matrix, followed by an efficient estimation method for the output electron density, which constitutes a simple hybrid approach for achieving self-consistency. Moreover, the algorithm produces the ground state Hamiltonian, from which the ground state energy and band structures can be efficiently computed. The proposed framework is accompanied by a rigorous error analysis that establishes the convergence and quantifies various sources of error and the overall computational complexity. The combination of effi-ciency and precision opens new avenues for exploring large-scale physical systems.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•1 citation

Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms

Taehee Ko, Xiantao Li, Chunhao Wang

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.

arXiv:2307.07067•Jul 13, 2023•3 citations

Quantum-Computing Self-Consistent Kohn-Sham DFT: Plane-Wave-Orthonormalized Orbitals with a Dual-Basis Quantum Eigensolver

Lazaro Calderin

We present a first-quantization, all-electron, full-potential Kohn-Sham density functional theory method for quantum computers, based on a classically optimized quantum-circuit eigensolver for the self-consistent field (SCF) eigenproblems in any orthonormal basis. The plane-wave-orthonormalized-orbital (PWOO) basis combines plane waves with atomic orbitals (AOs) orthonormalized against them and one another. The eigensolver has a dual-basis form: after full-basis bootstrap steps, it solves each SCF step in a contracted basis of $K$ functions ($\lceil\log_2 K\rceil$ qubits), updated in the full basis when the residual outside it exceeds a threshold. For an H$_8$ chain (SVWN, $K=8$), the state-vector-emulated SCF agrees with classical calculations within 0.02 mHa for 32768 plane waves and PWOO bases up to cc-pVTZ; contraction changes these PWOO energies by at most 5.7 $μ$Ha. With emulated shot noise, the STO-3G PWOO SCF converges near the noise-free fixed point. On IonQ Forte-1, three-qubit-register readout reproduces the noise-free PWOO-AO energy difference within one standard deviation.

quant-pharXiv:2609.33934•Sep 29, 2026•0 citations

A Tensor-product approach for large scale electronic structure calculations using Kohn–Sham density functional theory

Phani Motamarri, Vikram Gavini, Thomas Blesgen

Quantum-mechanical calculations based on Kohn–Sham density functional theory (DFT) played a significant role in accurately predicting various aspects of materials behavior over the past decade. The Kohn–Sham approach to DFT reduces the many-body Schrodinger (eigen value) problem of interacting electrons into an equivalent problem of noninteracting electrons in an effective mean field that is governed by electron-density. Despite the reduced computational complexity of Kohn–Sham DFT, large-scale DFT calculations are still computationally very demanding with the resulting computational complexity scaling cubically with number of atoms in a given materials system. Numerical algorithms with reduced scaling behavior which are robust, computationally efficient and scalable on parallel computing architectures are always desirable to enable simulations at larger scales and on more complex systems. Following this line of thought, this study explores the use of tensor structured methods for ab-initio numerical solution of Kohn–Sham equations arising in DFT calculations. Earlier studies on tensor-structured methods have been quite successful in the accurate calculation of Hartree and the nonlocal exchange operators arising in the Hartree–Fock equations. A recent investigation of low-rank Tucker-type decomposition of the electron-density of large aluminum clusters (obtained from the finite-element discretization of orbital free DFT) shows the exponential decay of approximation error with respect to Tucker rank (number of tensor-basis functions in Tucker type representation). The results also indicate a smaller Tucker rank for the accurate representation of the electron density and is only weakly dependent on the system sizes studied. The promising success of tensor-structured techniques in resolving the electronic structure of material systems has enabled us to take a step further. In this study, we propose a systematic way of computing a globally adapted Tucker-type basis for solving the Kohn–Sham DFT problem by using a separable approximation of the Kohn–Sham Hamiltonian. Further, the resulting Kohn–Sham eigenvalue problem is projected into the aforementioned Tucker basis and is solved for ground-state energy using a self-consistent field iteration. The rank of the resulting Tucker representation and the computational complexity of the calculation are examined on representative benchmark examples involving metallic and insulating systems.

•Jan 1, 2014•0 citations

Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

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Abstract We present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

arXiv:2011.11917•npj Computational Materials•Apr 12, 2021•14 citations

Quantum-Accelerated Density Functional Theory with Adaptive Basis Set Compression for Materials Discovery

Freederia AI Researcher

**Abstract:** This paper introduces a novel computational framework for accelerating Density Functional Theory (DFT) calculations, a cornerstone of materials discovery research, through the integration of quantum-accelerated linear algebra and adaptive basis set compression. Our approach, termed Quantum-Accelerated Adaptive DFT (QAADFT), leverages variational quantum eigensolvers (VQEs) for optimized solution to the Kohn-Sham equations, coupled with a dynamically adjusting basis set tailored to the evolving electron density. This synergistic combination leads to significant computational speedups, particularly for complex materials exhibiting strongly correlated electronic behavior, while maintaining accuracy comparable to conventional DFT methods. The system is designed for immediate commercial application in materials design, offering a 5-10x reduction in computational time and enabling more comprehensive exploration of chemical spaces for targeted material properties.

•Nov 24, 2025•0 citations
While quantum computers have shown significant promise for electronic structure calculations, their potential to accelerate density functional theory (DFT) calculations remains unclear. In this work, we present a qubit-efficient encoding scheme for wavefunctions in Kohn--Sham (KS) DFT, together with a quantum algorithm that computes all occupied orbitals simultaneously. We further show that our algorithm is particularly well suited to the Harris functional, enabling the total energy to be evaluated with a potential exponential speedup over classical approaches by entirely avoiding the costly readout of the electronic density. In addition, we propose a second method for achieving self-consistent DFT calculations using multiple copies of the wavefunction, which likewise circumvents density readout. The applicability of our algorithms is demonstrated through several numerical examples, and their efficiency is compared with that of existing approaches.
At the heart of quantum chemistry and materials science lies the critical task of estimating ground-state properties. We present a quantum algorithm for this task by quantizing the density-functional theory (DFT). A key aspect of imple-menting DFT faithfully is the requirement for self-consistent calculations, which involve repeated di-agonalizations of the Hamiltonian. This procedure, however, creates a significant bottleneck, as a classical algorithm generally demands a computational complexity that grows cubically with the number of electrons, restricting the scalability of DFT for tackling large-scale problems that involve complex chemical environments and microstructures. This article presents the first quantum algorithm that has provided substantial speedup for the ground state computation, by improving the complexity to one with a linear scaling with the number of atoms. The algorithm leverages the exponential speedup by the quantum singular value transformation to generate a quantum circuit to encode the density-matrix, followed by an efficient estimation method for the output electron density, which constitutes a simple hybrid approach for achieving self-consistency. Moreover, the algorithm produces the ground state Hamiltonian, from which the ground state energy and band structures can be efficiently computed. The proposed framework is accompanied by a rigorous error analysis that establishes the convergence and quantifies various sources of error and the overall computational complexity. The combination of effi-ciency and precision opens new avenues for exploring large-scale physical systems.
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.
We present a first-quantization, all-electron, full-potential Kohn-Sham density functional theory method for quantum computers, based on a classically optimized quantum-circuit eigensolver for the self-consistent field (SCF) eigenproblems in any orthonormal basis. The plane-wave-orthonormalized-orbital (PWOO) basis combines plane waves with atomic orbitals (AOs) orthonormalized against them and one another. The eigensolver has a dual-basis form: after full-basis bootstrap steps, it solves each SCF step in a contracted basis of KKK functions (⌈log⁡2K⌉\lceil\log_2 K\rceil⌈log2​K⌉ qubits), updated in the full basis when the residual outside it exceeds a threshold. For an H8_88​ chain (SVWN, K=8K=8K=8), the state-vector-emulated SCF agrees with classical calculations within 0.02 mHa for 32768 plane waves and PWOO bases up to cc-pVTZ; contraction changes these PWOO energies by at most 5.7 μμμHa. With emulated shot noise, the STO-3G PWOO SCF converges near the noise-free fixed point. On IonQ Forte-1, three-qubit-register readout reproduces the noise-free PWOO-AO energy difference within one standard deviation.
Quantum-mechanical calculations based on Kohn–Sham density functional theory (DFT) played a significant role in accurately predicting various aspects of materials behavior over the past decade. The Kohn–Sham approach to DFT reduces the many-body Schrodinger (eigen value) problem of interacting electrons into an equivalent problem of noninteracting electrons in an effective mean field that is governed by electron-density. Despite the reduced computational complexity of Kohn–Sham DFT, large-scale DFT calculations are still computationally very demanding with the resulting computational complexity scaling cubically with number of atoms in a given materials system. Numerical algorithms with reduced scaling behavior which are robust, computationally efficient and scalable on parallel computing architectures are always desirable to enable simulations at larger scales and on more complex systems. Following this line of thought, this study explores the use of tensor structured methods for ab-initio numerical solution of Kohn–Sham equations arising in DFT calculations. Earlier studies on tensor-structured methods have been quite successful in the accurate calculation of Hartree and the nonlocal exchange operators arising in the Hartree–Fock equations. A recent investigation of low-rank Tucker-type decomposition of the electron-density of large aluminum clusters (obtained from the finite-element discretization of orbital free DFT) shows the exponential decay of approximation error with respect to Tucker rank (number of tensor-basis functions in Tucker type representation). The results also indicate a smaller Tucker rank for the accurate representation of the electron density and is only weakly dependent on the system sizes studied. The promising success of tensor-structured techniques in resolving the electronic structure of material systems has enabled us to take a step further. In this study, we propose a systematic way of computing a globally adapted Tucker-type basis for solving the Kohn–Sham DFT problem by using a separable approximation of the Kohn–Sham Hamiltonian. Further, the resulting Kohn–Sham eigenvalue problem is projected into the aforementioned Tucker basis and is solved for ground-state energy using a self-consistent field iteration. The rank of the resulting Tucker representation and the computational complexity of the calculation are examined on representative benchmark examples involving metallic and insulating systems.
Abstract We present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.
**Abstract:** This paper introduces a novel computational framework for accelerating Density Functional Theory (DFT) calculations, a cornerstone of materials discovery research, through the integration of quantum-accelerated linear algebra and adaptive basis set compression. Our approach, termed Quantum-Accelerated Adaptive DFT (QAADFT), leverages variational quantum eigensolvers (VQEs) for optimized solution to the Kohn-Sham equations, coupled with a dynamically adjusting basis set tailored to the evolving electron density. This synergistic combination leads to significant computational speedups, particularly for complex materials exhibiting strongly correlated electronic behavior, while maintaining accuracy comparable to conventional DFT methods. The system is designed for immediate commercial application in materials design, offering a 5-10x reduction in computational time and enabling more comprehensive exploration of chemical spaces for targeted material properties.