One-particle Green's functions from the quantum equation of motion algorithm

Rizzo, Jacopo; Libbi, Francesco; Tacchino, Francesco; Ollitrault, Pauline J.; Marzari, Nicola; Tavernelli, Ivano

doi:10.48550/arxiv.2201.01826

Cited by 4 publications

(6 citation statements)

References 46 publications

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“…The overlap between the ground state and the S 2 excited state is non-zero in the qEOM formalism, leading to the spurious value of the dipole transition moment. Rizzo and co-workers have also talked about the issue of non-orthogonality of ground and excited states in the qEOM approach in their work [62]. It should be noted that both q-sc-EOM and q-proj-EOM approaches satisfy the killer condition which ensures that the ground and excited states are always orthogonal to each other, leading to a reliable and accurate simulation of the excited state properties.…”

Section: A H2mentioning

confidence: 99%

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Quantum simulation of molecular response properties

Kumar¹,

Asthana²,

Abraham³

et al. 2023

Preprint

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Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm.

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Section: A H2mentioning

confidence: 99%

“…Important recent developments have been made in computing response properties on a quantum computer [58][59][60][61][62]. The variational quantum response (VQR) algorithm developed by Huang and coworkers [58] is notable in this regard.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of molecular response properties

Kumar¹,

Asthana²,

Abraham³

et al. 2023

Preprint

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“…The Green's function is a central quantity in various fields, e.g., quantum transport theory [55], polarization propagator methods [56], photoemission spectroscopy, making it an important target for investigation. In the past couple of years several quantum algorithms have been proposed to compute GFs on a quantum computer [19,22,25,30,39,40]. The method which is most similar to ours is the Lanczos recursion method [40], which variationally prepare the Lanczos states on a quantum computer, and compute the one-particle GF based on the continued fraction representation of the GF.…”

Section: The Green's Functionmentioning

confidence: 99%

“…Similarly, variational linear system solvers were applied to response function calculations [29]. QSE and quantum Equation-of-Motion [12] methods were adapted for Green's function evaluation [25,30]. Most of these methods are fairly specific to the properties being estimated.…”

Section: Introductionmentioning

confidence: 99%

A Near-Term Quantum Algorithm for Computing Molecular and Materials Properties based on Recursive Variational Series Methods

Jensen¹,

Johnson²,

Kunitsa³

2022

Preprint

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Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is: how might we use imperfect near-term quantum computers to solve problems of practical value? We propose a quantum algorithm to estimate properties of molecules using near-term quantum devices. The method is a recursive variational series estimation method, where we expand an operator of interest in terms of Chebyshev polynomials, and evaluate each term in the expansion using a variational quantum algorithm. We test our method by computing the one-particle Green's function in energy domain and the autocorrelation function in time domain, finding some advantages to this approach over existing methods.

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“…The former exploits the Lehman representation and calculates the excitation energies of the system through the subspacesearch variational quantum eigensolver (SSVQE) [14], and an alternative approach has been recently presented in Ref. [15], where the SSVQE is replaced with a generalized quantum equation of motion (qEOM) technique [16] for charged excitations. The second approach of Ref.…”

Section: Introductionmentioning

confidence: 99%

Effective calculation of the Green's function in the time domain on near-term quantum processors

Libbi¹,

Rizzo²,

Tacchino³

et al. 2022

Preprint

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We propose an improved quantum algorithm to calculate the Green's function through realtime propagation, and use it to compute the retarded Green's function for the 2-, 3-and 4-site Hubbard models. This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the |N ± 1 states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.

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One-particle Green's functions from the quantum equation of motion algorithm

Cited by 4 publications

References 46 publications

Quantum simulation of molecular response properties

Quantum simulation of molecular response properties

A Near-Term Quantum Algorithm for Computing Molecular and Materials Properties based on Recursive Variational Series Methods

Effective calculation of the Green's function in the time domain on near-term quantum processors

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