Applications of quantum circuit learning model using particle-number-conserving state on quantum chemical calculations

Abstract

Although the variational quantum eigensolver is a typical quantum algorithm utilized in near-term quantum devices, many measurements are required in an iterative closed feedback loop between the classical and quantum computers to obtain sufficient accuracy. In this study, we attempt to construct a quantum circuit learning model to infer potential energy surfaces and atomic forces without using the iterative loop to optimize parameters for every bond length. To realize a high, accurate inference performance, measurement is introduced in the middle of the circuit. When the proposed quantum circuit learning model is applied to the H2 molecule, the energies and atomic forces can be estimated with high accuracy in a single feed-forward calculation with varying bond lengths. A nonlinear relation between outcomes from data-encoding layer and inputs can also be used to eliminate the data-encoding layer, allowing for our quantum circuit model with lower learning costs by reducing the number of parameters to be optimized. Our model can be also extended to six-qubit systems, such as the H3 molecule, and to the water molecule with two internal degrees of freedom. Finally, we use the IBM Quantum backend to perform inference with a real quantum computer and show the effect of noise on the actual quantum device.