Quantum Information and Algorithms for Correlated Quantum Matter

Head-Marsden, Kade; Flick, Johannes; Ciccarino, Christopher J.; Narang, Prineha

doi:10.1021/acs.chemrev.0c00620

Cited by 109 publications

(93 citation statements)

References 921 publications

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“…Other quantum algorithms of interest are a variational quantum algorithm for nonlinear problems, [78] and quantum algorithms for the damped nonlinear Schrodinger equation [79] and the Gross-Pitaevskii equation. [80] For recent quantum algorithms for quantum chemistry, see References [81,82].…”

Section: Discussionmentioning

confidence: 99%

Finding Solutions of the Navier‐Stokes Equations through Quantum Computing—Recent Progress, a Generalization, and Next Steps Forward

Gaitan

2021

Adv Quantum Tech

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Efficient simulation of a quantum system's dynamics is expected to be an important application area for quantum computers as existing classical computers cannot do this. However, quantum systems are not unique in being hard to simulate. For example, classical nonlinear continuum systems and fields are governed by nonlinear partial differential equations whose solution is also hard for classical computers. Solving such equations is essential for many economically important industries/applications such as the aerospace industry, weather-forecasting, fiber-optics communication, and plasma magneto-hydrodynamics. This raises the question: can a quantum computer speed-up solving these equations? In this Review, a new quantum algorithm is described for solving nonlinear partial differential equations for which the answer is yes. First, a new quantum algorithm is discussed for solving the Navier-Stokes nonlinear partial differential equations which govern the flow of a viscous fluid. Its construction, verification, and computational cost are described, and it is shown that a significant quantum speed-up is possible. Its generalization to a quantum algorithm for solving nonlinear partial differential equations is described. The Review closes with a discussion of next steps forward. These new quantum algorithms open up a large new application area for quantum computing with substantial economic impact, including the trillion-dollar aerospace industry.

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Section: Discussionmentioning

confidence: 99%

Finding Solutions of the Navier‐Stokes Equations through Quantum Computing—Recent Progress, a Generalization, and Next Steps Forward

Gaitan

2021

Adv Quantum Tech

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“…Recently, the development of quantum computers has led to an increased interest in novel quantum algorithms, especially for computational quantum chemistry, which is widely seen as a potential "killer app" of quantum computers [40][41][42] . Some quantum algorithms for quantum chemistry, such as the quantum phase estimation (QPE) 43 and unitary coupled cluster (UCC) 44,45 , offer exponential speedups when large faulttolerant quantum computers are available 46,47 .…”

Section: Introductionmentioning

confidence: 99%

Localized Quantum Chemistry on Quantum Computers

Otten

Hermes

Pandharkar

et al. 2021

Preprint

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Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today’s quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed “local active space unitary coupled cluster” (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2 molecules.

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“…Polariton chemistry has emerged in recent years as a new front for controlling photochemical reactions and for designing advanced energy materials. [1][2][3][4][5][6][7][8][9] When a photochrome is placed into a microcavity, one of its excited states can be strongly coupled to the photonic modes with comparable energy from the microcavity and form hybrid exciton-photon states, which are now known as the excitonic polaritons. The formation of polaritonic states has been observed for single molecules in a plasmonic microcavity, 10,11 as well as for many molecules in planar Fabry-Pérot cavities.…”

Section: Introductionmentioning

confidence: 99%

“…20-22 a) Electronic mail: yuezhi.mao@stanford.edu b) Electronic mail: qiou@tsinghua.edu.cn c) Electronic mail: yihan.shao@ou.edu Theoretical modeling has been a central component of polaritonic chemistry research. [4][5][6][7] To date, such modeling is mostly based on model Hamiltonians such as the Jaynes-Cummings (JC) model 66 for single-molecule polaritons and the Tavis-Cummings (TC) model 67 for many-molecule polaritons, which combines one or several lowest electronic states of the molecule and a cavity quantum electrodynamics (cQED) description of the photon modes. For example, a TC-based simulation protocol with one excited state from each molecule was used to model the electron-nuclear dynamics of up to 1000 or 1600 rhodamine molecules in the microcavity.…”

Section: Introductionmentioning

confidence: 99%

Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient

Yang

Pei

Leon

et al. 2021

Preprint

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Following the formulation of cavity quantum electrodynamical time-dependent density functional theory (cQED-TDDFT) models [Flick et al., ACS Photonics 6, 2757-2778 (2019); Yang et al., J. Chem. Phys. 155, 064107 (2021)], here we report the derivation and implementation of the analytic energy gradient for the polaritonic states of a single photochrome within the cQED-TDDFT models. Such gradient evaluation is also applicable to a complex of explicitly-specified photochromes, or, with proper scaling, a set of parallel-oriented, identical-geometry, non-interacting molecules in the microcavity.

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Quantum Information and Algorithms for Correlated Quantum Matter

Cited by 109 publications

References 921 publications

Finding Solutions of the Navier‐Stokes Equations through Quantum Computing—Recent Progress, a Generalization, and Next Steps Forward

Finding Solutions of the Navier‐Stokes Equations through Quantum Computing—Recent Progress, a Generalization, and Next Steps Forward

Localized Quantum Chemistry on Quantum Computers

Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient

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