Performance analysis and approximation theory for quantum dynamical estimator

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K21127
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science; Control engineering/System engineering
• Research Institution: Kyoto University
• Principal Investigator: Ohki Kentaro 京都大学, 情報学研究科, 助教 (40639233)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 平均場型量子フィルタ

Outline of Final Research Achievements

In quantum information processing, the control of spin systems is essential. In particular, error correction requires measurement-based feedback control, and the quantum state must be properly estimated from the measurement outcomes. Besides, this needs real time processing, and cannot be done in practice if the spin system becomes large. Therefore, decentralized processing is also important.
In this study, we extend the concept of mean-field games, which are large-scale non-cooperative games in classical systems, to quantum systems and introduce a mean-field quantum filter to realize distributed processing. Although this application is limited to specific quantum systems, it can approximate very large dimensional problems to very low order problems.

Free Research Field

量子制御理論

Academic Significance and Societal Importance of the Research Achievements

古典系では，所望の制御目標を達成するために測定された信号を計算機を用いて自由に整形することが可能であり，計算量の工夫も多く知られている．一方，量子系の信号処理では，その次元の大きさが膨大になることから，古典系よりも計算量の工夫が必要であり，それは適切な近似問題として表すことができる．
本研究は，イジング模型と呼ばれる量子系に対して，そのフィードバック制御における状態推定の低次元近似問題を平均場近似で与えることで，次元が大きければ大きいほど近似精度がよくなる結果が得られた．これは量子制御の実装がより容易になったことを意味する．