NAPA: Intermediate-level Variational Native-pulse Ansatz for Variational Quantum Algorithms

TL;DR

NAPA tackles the inefficiency of gate-based variational quantum algorithms on NISQ devices by introducing a native-pulse ansatz that directly manipulates trainable pulse parameters (amplitudes and frequencies). By combining single-qubit native pulses and cross-resonance two-qubit pulses within a progressive, non-gradient learning framework, it achieves substantial latency reductions while maintaining high accuracy on VQE tasks, validated on simulators and six IBM NISQ backends. Key contributions include hardware-extracted native pulses, progressive growth to manage parameter count, and empirical evidence that pulse-frequency tuning enhances performance. The approach promises practical improvements in VQA scalability and robustness on noisy quantum hardware, with potential extension to other quantum algorithms beyond VQAs.

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 native-pulse ansatz. Experiments are conducted on both simulators and quantum devices for Variational Quantum Eigensolver (VQE) tasks to evaluate our methods.

Figures (14)

• Figure 1: Comparison between compilation process for gate level and pulse level. Gate-level workflow consists of several layers and introduces redundancy, pulse-level workflow consists fewer layers that can provide reduction of circuit latency.
• Figure 2: Illustrations of the redundancy introduced by current gate-level compilation workflow. In the case of gate-level compilation, pulses with fixed parameters are inserted to first rotate the qubit to another axis. With pulse-level controls, we can avoid such redundancy and reduce latency without loss of capability to explore the Hilbert space.
• Figure 3: The overview of design and implementation of NAPA. The proposed pulse ansatz is composed of single-qubit native pulses (SNP) and cross-resonance pulses (CR). During the training process, the ansatz is "grown" after each step. In this progressive way, older parameters from the last step are unchanged as a "fixed list", while newer parameters added in this step are updated by the optimizer through optimization iterations as a "partial list".
• Figure 4: Reachable space comparison on Weyl Chamber for a) Single-CR. b) Multi-CRs. While a single-CR pulse can only cover one dimension on the Weyl Chamber, multi-CRs cover one of the surfaces of the Weyl Chamber.
• Figure 5: Cross-resonance pulses have several components other than the intended ZX interaction. While this poses challenges for gate-level calibrations, it doesn't affect parametric pulses.