Abstract We analyze the controllability of three quantum systems that belong to a specific class of four-level quantum systems with twice degenerate highest excited energy level and with forbidden transition between the two remaining non-degenerate levels. For this purpose we perform numerical computation, construct the dynamical Lie algebras generated by all commutators of the free and interaction Hamiltonians, and show that two quantum systems are irreducible and controllable while the third system is reducible and hence uncontrollable. The reducibility and uncontrollability are proved by constructing a conserved Hermitian operator (physical quantity). The controllability is proved by constructing the dynamical Lie algebra and showing that it has maximal rank. These findings indicate that depending on the values of certain particular matrix entries of the interaction Hamiltonian, quantum systems in the class under consideration can be either uncontrollable or controllable.Abstract We analyze the controllability of three quantum systems that belong to a specific class of four-level quantum systems with twice degenerate highest excited energy level and with forbidden transition between the two remaining non-degenerate levels. For this purpose we perform numerical computation, construct the dynamical Lie algebras generated by all commutators of the free and interaction Hamiltonians, and show that two quantum systems are irreducible and controllable while the third system is reducible and hence uncontrollable. The reducibility and uncontrollability are proved by constructing a conserved Hermitian operator (physical quantity). The controllability is proved by constructing the dynamical Lie algebra and showing that it has maximal rank. These findings indicate that depending on the values of certain particular matrix entries of the interaction Hamiltonian, quantum systems in the class under consideration can be either uncontrollable or controllable.

Proceedings of the Steklov Institute of MathematicsJun 1, 20233 citations

Some Mathematical Problems of Control of Quantum Systems

Alexander Nikolaevich Pechen

Journal of Mathematical SciencesJul 29, 20193 citations

Efficient Quantum Control via Automatic Control Skips

Peleg Emanuel, Eyal Cornfeld, Alon, Ravid +2 more

Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of gates and overall circuit depth. However, these methods are specialized and circuits frequently need to be implemented manually. This paper presents a generic method for finding "skippable" patterns without having to tailor implementations for each algorithm. We prove that finding the optimal operations to be skipped is generally NP-hard. Nevertheless, sub-optimal, polynomial approximation algorithms that find skippable subcircuits can lead to over $50\%$ improvement in circuit metrics for real-world applications.Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of gates and overall circuit depth. However, these methods are specialized and circuits frequently need to be implemented manually. This paper presents a generic method for finding "skippable" patterns without having to tailor implementations for each algorithm. We prove that finding the optimal operations to be skipped is generally NP-hard. Nevertheless, sub-optimal, polynomial approximation algorithms that find skippable subcircuits can lead to over $50\%$ improvement in circuit metrics for real-world applications.

arXiv:2505.18256May 23, 20250 citations

Control problems in quantum systems

Re-Bing Wu, Jing Zhang, Chunwen Li +2 more

Chinese Science BulletinApr 22, 201212 citations

Control of Quantum Systems: Theory and Methods

Shuang Cong

Feb 27, 201436 citations

Controllable Subspaces of Open Quantum Dynamical Systems

Ming Zhang, Hong‐Yi Dai, Gong Er-Ling +2 more

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.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.

Communications in Theoretical PhysicsJan 1, 20085 citations

50\%

improvement in circuit metrics for real-world applications.