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理论物理通讯：英文版

Controllable Subspaces of Open Quantum Dynamical Systems

Zhang, Ming Ming, Dai Dai, Hong-Yi, Gong, Er-Ling, Xie Xie, Hongwei, Hu, De-Wen

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

这篇论文为开的量讨论可控制的潜水艇空格的概念动态系统。有在开的量系统上执行开环的协调控制的能力的 decoherence 免费的潜水艇空格的联合结构的特征将允许 decoherence 免费的潜水艇空格可控制，这积极地被表明。这与观察相对照动态系统不是的那开的量开环可控制。到某个程度，这篇论文给其他的控制 decoherence 免费的潜水艇空格为什么能为量计算是有用的理论解释。

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Controllable Subspaces of Open Quantum Dynamical Systems

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This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.

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Lyapunov control on quantum open systems in decoherence-free subspaces

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On the Complexity of Finding Decoherence Free Subspaces

Evan Borras

Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the $k$-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality $k \geq 5$, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.

quant-pharXiv:2609.26769•Sep 23, 2026•0 citations
这篇论文为开的量讨论可控制的潜水艇空格的概念动态系统。有在开的量系统上执行开环的协调控制的能力的 decoherence 免费的潜水艇空格的联合结构的特征将允许 decoherence 免费的潜水艇空格可控制，这积极地被表明。这与观察相对照动态系统不是的那开的量开环可控制。到某个程度，这篇论文给其他的控制 decoherence 免费的潜水艇空格为什么能为量计算是有用的理论解释。
This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
A scheme to drive and manipulate a finite-dimensional quantum system in decoherence-free subspaces (DFSs) by Lyapunov control is proposed. Control fields are established by the Lyapunov function. This proposal can drive the open quantum system into DFSs and manipulate it to any desired eigenstate of the free Hamiltonian. An example which consists of a four-level system with three long-lived states driven by two lasers is presented to demonstrate the scheme. We have performed numerical simulations of the dynamics of the four-level system, which show that the scheme works well.
Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the kkk-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality k≥5k \geq 5k≥5, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.