RobustState: Boosting Fidelity of Quantum State Preparation via
  Noise-Aware Variational Training
Hanrui Wang Yilian Liu Pengyu Liu Jiaqi Gu Zirui Li Zhiding Liang Jinglei Cheng Yongshan Ding Xuehai Qian Yiyu Shi David Z. Pan Frederic T. Chong Song Han
Quantum state preparation, a crucial subroutine in quantum computing,
involves generating a target quantum state from initialized qubits. Arbitrary
state preparation algorithms can be broadly categorized into arithmetic
decomposition (AD) and variational quantum state preparation (VQSP). AD employs
a predefined procedure to decompose the target state into a series of gates,
whereas VQSP iteratively tunes ansatz parameters to approximate target state.
VQSP is particularly apt for Noisy-Intermediate Scale Quantum (NISQ) machines
due to its shorter circuits. However, achieving noise-robust parameter
optimization still remains challenging.
  We present RobustState, a novel VQSP training methodology that combines high
robustness with high training efficiency. The core idea involves utilizing
measurement outcomes from real machines to perform back-propagation through
classical simulators, thus incorporating real quantum noise into gradient
calculations. RobustState serves as a versatile, plug-and-play technique
applicable for training parameters from scratch or fine-tuning existing
parameters to enhance fidelity on target machines. It is adaptable to various
ansatzes at both gate and pulse levels and can even benefit other variational
algorithms, such as variational unitary synthesis.
  Comprehensive evaluation of RobustState on state preparation tasks for 4
distinct quantum algorithms using 10 real quantum machines demonstrates a
coherent error reduction of up to 7.1 $\times$ and state fidelity improvement
of up to 96\% and 81\% for 4-Q and 5-Q states, respectively. On average,
RobustState improves fidelity by 50\% and 72\% for 4-Q and 5-Q states compared
to baseline approaches.