Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

Baker, Thomas E.; Poulin, David

doi:10.48550/arxiv.2008.05592

Cited by 2 publications

(2 citation statements)

References 94 publications

(163 reference statements)

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“…Naturally arising Hamiltonian of quantum systems exhibit local structure, which allows efficient algorithms on quantum computers to simulate the evolution of these systems. Diagonalizing these Hamiltonians, however, is a more challenging task for quantum computing, which also serves as important subroutines, for instance, of the celebrated density functional theory [1,2] for important applications of quantum simulation in chemistry, materials sciences and technologies [3]. Quantum algorithms have been developed for finding the eigenvalues and eigenstates of Hamiltonians, for instance, the one based on quantum fast Fourier transform [4].…”

Section: Introductionmentioning

confidence: 99%

A variational quantum algorithm for Hamiltonian diagonalization

Zeng¹,

Cao²,

Zhang³

et al. 2021

Quantum Sci. Technol.

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Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational quantum algorithm for Hamiltonian diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality, and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

show abstract

Section: Introductionmentioning

confidence: 99%

A variational quantum algorithm for Hamiltonian diagonalization

Zeng¹,

Cao²,

Zhang³

et al. 2021

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Naturally arising Hamiltonian of quantum systems exhibit local structure, which allows efficient algorithms on quantum computers to simulate the evolution of these systems. Diagonalizing these Hamiltonians, however, is a more challenging task for quantum computing, which also serves as important subroutines, for instance, of the celebrated Density Functional Theory (DFT) [1,2] for important applications of quantum simulation in chemistry, materials sciences and technologies [3]. Quantum algorithms have been developed for finding the eigenvalues and eigenstates of Hamiltonians, for instance the one based on quantum fast Fourier transform [4].…”

Section: Introductionmentioning

confidence: 99%

A variational quantum algorithm for Hamiltonian diagonalization

Zeng,

Cao,

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational algorithm for Hamiltonians diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

show abstract

Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

Cited by 2 publications

References 94 publications

A variational quantum algorithm for Hamiltonian diagonalization

A variational quantum algorithm for Hamiltonian diagonalization

A variational quantum algorithm for Hamiltonian diagonalization

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