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arXiv:1911.00293 · Physical Review Research

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

Taichi Kosugi, Yu‐ichiro Matsushita

Published Jul 9, 2020• 19 citations
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Abstract

This work proposes a generic construction scheme for the quantum circuit implementing a nonunitary operator appearing in electronic-structure calculations. The authors demonstrate that the scheme enables one via probabilistic state preparation to calculate the linear-response functions of diatomic molecules, where simulated measurements and full configuration-interaction results are compared.

DOI
10.1103/physrevresearch.2.033043

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This work proposes a generic construction scheme for the quantum circuit implementing a nonunitary operator appearing in electronic-structure calculations. The authors demonstrate that the scheme enables one via probabilistic state preparation to calculate the linear-response functions of diatomic molecules, where simulated measurements and full configuration-interaction results are compared.
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
We propose a scheme for the construction of the one-particle Green's function (GF) of an interacting electronic system via statistical sampling on a quantum computer. Although the nonunitarity of creation and annihilation operators for the electronic spin orbitals prevents us from preparing specific states selectively, probabilistic state preparation is demonstrated to be possible for the qubits. We provide quantum circuits equipped with at most two ancillary qubits for obtaining all the components of the GF. We perform simulations of such construction of GFs for LiH and H2O{\mathrm{H}}_{2}\mathrm{O}H2​O molecules based on the unitary coupled-cluster (UCC) method to demonstrate the validity of our scheme by comparing the quasiparticle and satellite spectra exact within the UCC method and those from full configuration-interaction calculations. We also examine the accuracy of the sampling method by exploiting the Galitskii-Migdal formula, which gives the total energy only from the GF.
Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise of solving this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Herein, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties, such as Green's functions, are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques.
The dynamic linear response of a quantum system is critical for understanding both the structure and dynamics of strongly interacting quantum systems, including neutron scattering from materials, photon and electron scattering from atomic systems, and electron and neutrino scattering by nuclei. We present a general algorithm for universal quantum computers to calculate the dynamic linear response function with controlled errors and to obtain information about specific final states that can be directly compared to experimental observations.
• An improved quantum circuit for the preparation of spin symmetry-adapted configuration state function is given. • The quantum circuit contains one-qubit rotations and controlled-NOT operations acting to adjacent two qubits. • The quantum circuit is fully parallelizable. • The depth of the quantum circuit is constant and independent to the number of unpaired electrons. Full configuration interaction (full-CI) calculations can be executed efficiently on quantum computers (QCs) by utilizing a quantum phase estimation algorithm (QPEA). In the QPEA-based full-CI on QCs, the preparation of the initial guess wave functions having large overlap with the full-CI root is crucial. Recently, we proposed a quantum circuit to prepare spin symmetry-adapted configuration state functions (CSFs) toward open shell electronic structure calculations of molecules on QCs. Here, we propose an improved quantum circuit, based on Serber construction of spin eigenfunctions, enabling us to prepare CSFs with much less and easier-to-implement quantum gates than the previously proposed one.