Quantum computation of molecular response properties

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), 10.1103/PhysRevLett.103.150502] 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.