Expressibility of linear combination of ansatz circuits

Variational Quantum Eigensolver is considered promising for medium-scale noisy quantum computers. Expressibility is an important metric for measuring the capability of a variational quantum Ansatz circuit. A commonly used method to increase expressibility is to increase the circuit depth. However, increasing the circuit depth also introduces more noise. We propose to use a linear combination of ansatzes to improve the expressibility of variational circuits, thus avoiding the increase of circuit depth. Concurrently, we introduce a novel measurement strategy that circumvents the necessity for the Hadamard test, thereby significantly diminishing the reliance on two-qubit gates, which are presently the predominant contributors to quantum noise. We also provide a corresponding gradient calculation method, which makes it convenient to update the parameters. Compared with the method of increasing the circuit depth, our method of improving expressibility is more practical. Numerical simulations demonstrate the effectiveness of our method.