Optimizing Decision Diagrams for Measurements of Quantum Circuits

Variational quantum algorithm (VQA) is a promising near-term quantum algorithm to efficiently generate quantum states for various applications from shallow parametrized quantum circuits (PQCs). To fully utilize VQA, it is essential to have measurement methods that efficiently extract desired information from the quantum states. Classical shadow is such method that measures each qubit onto one of three Pauli bases uniformly at random. It has been attracting active research for characterizing the quantum states of PQCs due to its requiring only polynomial number of measurements, in the number of qubits, in contrast to the exponential-measurement quantum state tomography. There are several variants of classical shadow to improve the accuracy of measurement. A highly accurate classical shadow whose choices of Pauli bases are based on a decision diagram (DD) has been recently proposed in designing PQCs. Here, we further extend the DD-based classical shadow by novel modification and application of conventional techniques to optimize DD. We develop a method to optimize the size of DD that can lead to even fewer number of measurements for optimization instances in quantum chemistry as confirmed by numerical experiments. Our results show another facet of the usefulness of DD in the design of PQCs.