Quantum computation of molecular response properties

Cai, Xiang; Fang, Wei‐Hai; Fan, Heng; Li, Zhendong

doi:10.1103/physrevresearch.2.033324

Cited by 39 publications

(29 citation statements)

References 59 publications

(134 reference statements)

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“…Previous works [33,34] focused on evaluating Green's functions in the time domain via Hamiltonian simulation. Reference [35] computes the response function, which is closely related to the Green's function, in the frequency domain. Here we will provide a preconditioned linear system method for direct computation of the Green's function in the frequency domain.…”

Section: Algorithmmentioning

confidence: 99%

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Tong

Wiebe

et al. 2021

Phys. Rev. A

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Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. We introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

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Section: Algorithmmentioning

confidence: 99%

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Tong

Wiebe

et al. 2021

Phys. Rev. A

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show abstract

“…They are therefore out of near-term capabilities of quantum computers. It is nonetheless worth noting that the convergence properties of these approaches depend on the condition number of the resulting operator and approaches to minimize the gate depth and apply the approach to dynamical quantities in quantum system have seen progress in recent years [43][44][45][46][47][48][49]. Alternatively, QPE steps can be exchanged for a more NISQ-friendly VQE algorithm to calculate individual states or construct response functions [40,[49][50][51].…”

Section: Dynamical Correlation Functions On Quantum Devicesmentioning

confidence: 99%

“…A similar scheme has also recently been proposed in Ref. 49. Furthermore, the approach does not access individual states, and so exact spectral properties at a given frequency are obtained with increasing expressibility of the quantum ansatz.…”

Section: Dynamical Correlation Functions On Quantum Devicesmentioning

confidence: 99%

A variational quantum eigensolver for dynamic correlation functions

Chen,

Nusspickel,

Tilly

et al. 2021

Preprint

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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 parameterized 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 parameterization 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.

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“…Quantum simulation offers some of the strongest prospects for practical quantum advantages. Example applications include finding ground [180,181] and excited states [169,336] of electronic degrees of freedom, vibrational degrees of freedom [298,299], and more complex degrees of freedom [113,337,338,339], or dispersion interaction between drug molecules and proteins [340]. VQEs in particular have the strong possibility of near term advantages as they scale.…”

Section: Simulating Quantum Physicsmentioning

confidence: 99%

Biology and medicine in the landscape of quantum advantages

Cordier¹,

Sawaya²,

Guerreschi³

et al. 2021

Preprint

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Quantum computing holds significant potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning approaches for subtyping cancers on the basis of clinical features. This potential is encapsulated by the concept of a quantum advantage, which is typically contingent on a reduction in the consumption of a computational resource, such as time, space, or data. Here, we distill the concept of a quantum advantage into a simple framework that we hope will aid researchers in biology and medicine pursuing the development of quantum applications. We then apply this framework to a wide variety of computational problems relevant to these domains in an effort to i) assess the potential of quantum advantages in specific application areas and ii) identify gaps that may be addressed with novel quantum approaches. Bearing in mind the rapid pace of change in the fields of quantum computing and classical algorithms, we aim to provide an extensive survey of applications in biology and medicine that may lead to practical quantum advantages.

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Quantum computation of molecular response properties

Cited by 39 publications

References 59 publications

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

A variational quantum eigensolver for dynamic correlation functions

Biology and medicine in the landscape of quantum advantages

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