New Journal of Physics (Jan 2024)

A noise-robust quantum dynamics learning protocol based on Choi–Jamiolkowski isomorphism: theory and experiment

  • Xin-Yu Chen,
  • Pan Gao,
  • Chu-Dan Qiu,
  • Ya-Nan Lu,
  • Fan Yang,
  • Yuanyuan Zhao,
  • Hang Li,
  • Jiang Zhang,
  • Shijie Wei,
  • Tonghao Xing,
  • Xin-Yu Pan,
  • Dong Ruan,
  • Feihao Zhang,
  • Keren Li,
  • Guilu Long

DOI
https://doi.org/10.1088/1367-2630/ad309d
Journal volume & issue
Vol. 26, no. 3
p. 033023

Abstract

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With the rapid development of quantum technology, the growing manipulated Hilbert space makes learning the dynamics of the quantum system a significant challenge. Machine learning technique has brought apparent advantages in some learning strategies, therefore, we introduce it to indirect learning in this paper. Based on Choi–Jamiolkowski isomorphism, we propose a protocol that learns the dynamics of an inaccessible quantum system using a quantum device at hand. For an n -qubit system, the learning task can be done iteratively, with operational complexity $\mathcal{O}(\text{poly}(n, L)/\epsilon^2)$ in each iteration, where L is the circuit depth and ε is the measurement error. Then we theoretically prove its noise resilience to global depolarization, state preparation and measurement noise, and unitary noise in gates implementation, where we find the learned dynamics stay invariant. Finally, we investigate the protocol experimentally on a nitrogen-vacancy center system with a natural noise source. The results show that the behavior of a relatively intractable nuclear spin can be learned through an easily accessible electron spin under different noise models, demonstrating the protocol’s feasibility.

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