2019年4月26日

# Generalization of the output of variational quantum eigensolver by parameter interpolation with low-depth ansatz

PHYSICAL REVIEW APPLIED
• Kosuke Mitarai
• ,
• Tennin Yan
• ,
• Keisuke Fujii

11
4

DOI
10.1103/PhysRevApplied.11.044087

AMER PHYSICAL SOC

The variational quantum eigensolver (VQE) is an attracting possible
application of near-term quantum computers. Originally, the aim of the VQE is
to find a ground state for a given specific Hamiltonian. It is achieved by
minimizing the expectation value of the Hamiltonian with respect to an ansatz
state by tuning parameters $$\bm{\theta}$$ on a quantum circuit which
constructs the ansatz. Here we consider an extended problem of the VQE, namely,
our objective in this work is to "generalize" the optimized output of the VQE
just like machine learning. We aim to find ground states for a given set of
Hamiltonians $$\{H(\bm{x})\}$$, where $$\bm{x}$$ is a parameter which specifies
the quantum system under consideration, such as geometries of atoms of a
molecule. Our approach is to train the circuit on the small number of
$$\bm{x}$$'s. Specifically, we employ the interpolation of the optimal circuit
parameter determined at different $$\bm{x}$$'s, assuming that the circuit
parameter $$\bm{\theta}$$ has simple dependency on a hidden parameter
$$\bm{x}$$ as $$\bm{\theta}(\bm{x})$$. We show by numerical simulations that,
using an ansatz which we call the Hamiltonian-alternating ansatz, the optimal
circuit parameters can be interpolated to give near-optimal ground states in
between the trained $$\bm{x}$$'s. The proposed method can greatly reduce, on a
rough estimation by a few orders of magnitude, the time required to obtain
ground states for different Hamiltonians by the VQE. Once generalized, the
ansatz circuit can predict the ground state without optimizing the circuit
parameter $$\bm{\theta}$$ in a certain range of $$\bm{x}$$.

Web of Science ® 被引用回数 : 1

リンク情報
DOI
https://doi.org/10.1103/PhysRevApplied.11.044087
arXiv
http://arxiv.org/abs/arXiv:1810.04482
Web of Science