Abstract
Accurately predicting response properties of molecules such as the 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 one hand, we prove that 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 achieves an exponential speedup over existing classical algorithms. On the other hand, we introduce a variational hybrid quantum-classical variant of the proposed algorithm, which is more practical for near-term quantum devices.
Highlights
How molecules respond to the action of external fields determines the properties of materials
Depending on the subroutine employed for determining auxiliary states, the resulting variant of the proposed algorithm can be considered as the analog of quantum phase estimation (QPE) or variational quantum eigensolver (VQE) for molecular response properties. While the latter variational hybrid quantum-classical variant is more practical for nearterm quantum devices, we prove that in combination with the quantum linear system algorithm invented by Harrow, Hassidim, and Lloyd (HHL) [38], the runtime complexity of the quantum variant of our algorithm scales polynomially in the molecular system size, instead of the dimension of the exponentially large many-electron Hilbert space
Just as QPE and VQE have been applied to the ground-state problem, we attempt to utilize the advantage of quantum algorithms for linear systems of equations [38,39,40,41,42,43,44] in computing molecular response properties
Summary
How molecules respond to the action of external fields determines the properties of materials. While dynamical properties can alternatively be obtained by Fourier transform of the corresponding correlation functions in the time domain [16,34,35] determined from real-time Hamiltonian simulations, analogous to the classical computation side [2,4,5], it is highly desirable to have a quantum algorithm for computing a target response property such as αi j (ω) or βi jk (ω1, ω2) at given frequencies directly This is because in many molecular applications [2,4] only a small range of frequencies is of interest, including the simulations of (hyper)polarizabilities at specific frequencies of applied electromagnetic fields [8,36], absorption spectra in a visible/ultraviolet/X-ray region of interest [5], and multidimensional spectroscopies for studying couplings between selected modes [37]. An exponential speedup can be achieved compared with the classical FCI-based approach [7,8], which established a firm foundation for future applications of quantum computation in predicting molecular response properties
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