NAPA: Intermediate-Level Variational Native-Pulse Ansatz for Variational Quantum Algorithms

Abstract

Variational quantum algorithms (VQAs) have demonstrated great potentials in the Noisy Intermediate Scale Quantum (NISQ) era. In the workflow of VQA, the parameters of ansatz are iteratively updated to approximate the desired quantum states. We have seen various efforts to draft better ansatz with less gates. Some works consider the physical meaning of the underlying circuits, while others adopt the ideas of neural architecture search (NAS) for ansatz generator. However, these designs do not exploit the full advantages of VQAs. Because most techniques target gate ansatz, and the parameters are usually rotation angles of the gates. In quantum computers, the gate ansatz will eventually be transformed into control signals such as microwave pulses on superconducting qubits. These control pulses need elaborate calibrations to minimize the errors such as over-rotation and under-rotation. In the case of VQAs, this procedure will introduce redundancy, but the variational properties of VQAs can naturally handle problems of over-rotation and under-rotation by updating the amplitude and frequency parameters. Therefore, we propose NAPA, a native-pulse ansatz generator framework for VQAs. We generate native-pulse ansatz with trainable parameters for amplitudes and frequencies. In our proposed NAPA, we are tuning parametric pulses, which are natively supported on NISQ computers. Given the limited availability of gradient-based optimizers for pulse-level quantum programs, we choose to deploy non-gradient optimizers in our framework. To constrain the number of parameters sent to the optimizer, we adopt a progressive way to generate our nativepulse ansatz. Experiments are conducted on both simulators and quantum devices for Variational Quantum Eigensolver (VQE) tasks to envaluate our methods. When adopted on NISQ machines, NAPA obtained improved the performance with decreased latency by an average of 86%. NAPA is able to achieve 96.482% and 99.336% accuracy for VQE tasks on H2 and HeH+ respectively. An average accuracy of 97.27% is achieved for medium-size quantum chemistry tasks on CO2, H2O, and NaH. NAPA also demonstrates advantages on quantum optimization tasks even with considerable noises in NISQ machines.