Quantum State Filter with Disturbance and Noise

Jiaojiao Zhang, Shuang Cong, Qing Ling, Kezhi Li, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A quantum state filter (QSF) is proposed in this paper to estimate a low-rank quantum density matrix from informationally incomplete and contaminated measurements. There exist sparse disturbances on the quantum density matrix and Gaussian noise in the measurements. A proximal Jacobian variant of the alternating direction method of multipliers (PJ-ADMM) is proposed to design the QSF. The closed-form solutions to three resulting subproblems are given and the iterative QSF is developed. The proposed QSF is proved to be convergent and its superiority is demonstrated in the numerical illustrations compared with different state-of-the-art methods.

Original languageEnglish (US)
Article number8794729
Pages (from-to)2856-2866
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Alternating direction method of multipliers (ADMM)
  • convergence
  • proximal Jacobian
  • quantum state filter (QSF)

Cite this