Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

Kosugi, Taichi; Matsushita, Yu-ichiro

doi:10.1103/physrevresearch.2.033043

Cited by 24 publications

(21 citation statements)

References 39 publications

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“…In Ref. 23, the authors similarly proposed using QPE with statistical sampling to measure the linear response functions, where the perturbed state is resulted from the action of a general electronic operator (i.e., Â and B operators) implemented as a sum of unitary operators. In both works, the ground state before the perturbation is applied is either prepared by variational algorithms or given by an oracle.…”

Section: B Green's Functions For Many-body Systemsmentioning

confidence: 99%

“…For example, the spectral density and local density of states (LDOS) of the system is given by the imaginary part of the retarded single-particle Green's function Im G R (ω). Various methods have been recently proposed for calculating Green's functions and other related quantities [20][21][22][23][24][25] using quantum computing devices. For example, the Gaussian integral transformation (GIT) [21] is used to compute the spectral density of the system by employing the qubitization technique, while statistical sampling and QPE is recently used to compute the single-particle and two-particle Green's functions of simple molecules [22,23] and similar approach is applied to compute other dynamic linear response functions [20].…”

Section: Introductionmentioning

confidence: 99%

“…Our second result is a quantum algorithm for implementing the resolvent operator to compute single-particle Green's function. This algorithm is based on a Fourier-Laplace integral transform (FIT) used in conjunction with the LCU, and it essentially only uses quantum resource, in contrast to variational [24,25] and QPE [20,22,23] methods. Our method is also the first quantum algorithm to nonvariationally prepare the ground state and compute the Green's function directly in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

Keen¹,

Dumitrescu²,

Wang³

2021

Preprint

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We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain. The algorithms are based on the linear combination of unitary (LCU) operations and essentially only use quantum resources. To prepare the ground state, we construct the operator exp(−τ Ĥ2 ) using Hubbard-Stratonovich transformation by LCU and apply it on an easy-to-prepare initial state. Our projective state preparation procedure saturates the near-optimal scaling, O( 1 γ∆ log 1 γη ), of other currently known algorithms, in terms of the spectral-gap lower bound ∆, the additive error η in the state vector, and the overlap lower bound γ between the initial state and the exact ground state. It is straightforward to combine our algorithm with spectral-gap amplification technique to achieve quadratically improved scaling O(1/ √ ∆) for ground-state preparation of frustration-free Hamiltonians, which we demonstrate with numerical results of the q-deformed XXZ chain. To compute the Green's functions, including the single-particle and other response functions, we act on the prepared ground state with the retarded resolvent operator R(ω +iΓ; Ĥ) in the LCU form derived from the Fourier-Laplace integral transform (FIT). Our resolvent algorithm has O( 1 Γ 2 log 1 Γ ) complexity scaling for the frequency resolution Γ of the response functions and the targeted error , while classical algorithms for FIT usually have polynomial scaling over the error . To illustrate the complexity scaling of our algorithms, we provide numerical results for their application to the paradigmatic Fermi-Hubbard model on a one-dimensional lattice with different numbers of sites.

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Section: B Green's Functions For Many-body Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

Keen¹,

Dumitrescu²,

Wang³

2021

Preprint

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“…In the more general context, the approach we sketch is an example of using quantum simulation for calculation of physically relevant response functions [19][20][21][22]. Although we present a formulation of the approach specific to analog trapped-ion quantum simulators, it is suitable for other hardware platforms with bosonic degrees of freedom (e.g., circuit-QED [23] or cavity-QED [24]), and there is a natural digitization of the approach, e.g., through Trotterization, which we will comment on at the end in Sec.…”

Section: ()mentioning

confidence: 99%

Quantum simulation of weak-field light-matter interactions

Young¹,

Sarovar²

2021

Preprint

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Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such lightmatter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

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“…Note added. During the review process of this work, we became aware of a related work [66] in which a different algorithm was proposed for constructing the linear-response functions of molecules via quantum phase estimation and statistical sampling.…”

Section: Extensions To General Response Propertiesmentioning

confidence: 99%

Quantum computation of molecular response properties

Cai

Fang

Fan

et al. 2020

Phys. Rev. Research

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Accurately predicting the response properties of molecules, such as dynamic polarizability and hyperpolarizability, using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical simulation techniques in quantum chemistry are hampered by the exponential growth of the many-electron Hilbert space as the system size increases. In this work, we propose an algorithm for computing linear and nonlinear molecular response properties on quantum computers by first reformulating the target property into a symmetric expression more suitable for quantum computation via introducing a set of auxiliary quantum states, and then determining these auxiliary states via solving the corresponding linear systems of equations on quantum computers. On the one hand, we prove that when using the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] as a subroutine, the proposed algorithm scales only polynomially in the system size instead of the dimension of the exponentially large Hilbert space, and hence it achieves an exponential speedup over existing classical algorithms. On the other hand, we introduce a variational hybrid quantum-classical variant of the proposed algorithm that is more practical for near-term quantum devices.

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Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

Cited by 24 publications

References 39 publications

Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

Quantum simulation of weak-field light-matter interactions

Quantum computation of molecular response properties

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