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量子系における最適制御 : 最適状態保護と最速制御 (本文)

若村, 浩明 慶應義塾大学

2021.02.01

概要

量子情報科学は物理学と情報科学の融合分野である.そしてその目指すべきところは理学と工学の双方に存在する.量子情報科学の工学としての目的は,量子計算や量子通信といった量子情報処理を実現させることである.これらは高速な計算や秘匿な通信を可能にすると期待されており,公的な研究機関だけでなく民間企業によっても活発に研究が行われるほどに多大な注目を集めている.一方で量子情報科学の理学としての目的は,物理学を情報科学や応用工学の観点から捉え直し理解することである.例えば,情報処理における不可逆過程を熱力学的な観点から捉え直した R. Landauer は(古典)計算を物理過程と捉え,

“We particularly stress the fact that not only does physics determine what com- puters can do, but what computers can do, in turn, will define the ultimate nature of the laws of physics.”

と述べている [1].すなわち,計算機が物理法則に従っているだけでなく,計算機が行えることのすべてが逆に物理法則を特徴づけていることを強調した.計算や通信などの情報処理を物理的過程と捉える上では,上記を量子計算や量子通信と置き換えても同様である.量子計算に代表される量子情報処理を研究する理学的意義は,自然現象を情報処理過程とみなしたときの能力を調べることで,逆に自然現象そのものを理解できるという点にある.量子複製不可能定理 [2–4] とそれに付随する不完全複製の研究 [5, 6] や,状態識別 [7–10],誤差と擾乱の不確定性関係 [11–14] の研究などはまさにこの目的に沿った研究であろう.

量子系の制御(量子制御),特に最適な量子制御は量子情報科学の根本的な話題である.なぜなら全ての量子情報処理は,詰まるところ量子系を制御することによって実現されるためである.ここで制御とは,系を欲している状態に保つあるいは変化させることを指す.何らかの基準に即して可能な限り良い情報処理を実現するためには,最適な制御が何かを明らかにする必要がある.また最適制御の解明は,量子力学の一種の限界の解明に等しい.量子系の最適制御は実用上必要であるだけではなく,系に対して可能な制御の限界を表してもいるからである.特に古典制御との比較によって量子力学の特性まで浮き彫りにされる.以上より,量子系における最適制御の研究は基礎と応用の両面にとって重要であり価値がある.

一口に最適制御といっても,当然その目的は様々である.例えばある人は精確な通信を行 いたいもしれないし,他のある人は素早く計算を行いたいかもしれない.つまり何を「良い」とみなすかによって考えるべき制御は大きく異る.しかし今触れた 2 つ,精確な制御と素早い制御は多くの状況で有用だと考えられる.したがって本論文では,量子系を外乱から保護する制御と,量子系の状態を素早く遷移させる制御を主題として議論する.

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