This paper analyzes the topology of quantum control landscapes with dynamic symmetry, which is referred to as the optimization objective as a functional of control fields. We find that the ruggedness of the landscape, which determines the search efficiency for global optima, is dependent with the dynamic symmetry. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dynamic symmetry group. We show that multiple local false traps (i.e., non-global suboptima) exist even if the target gate is realizable and that the number of these traps is increased by the loss of controllability, while the controllable systems are always devoid of false traps.This paper analyzes the topology of quantum control landscapes with dynamic symmetry, which is referred to as the optimization objective as a functional of control fields. We find that the ruggedness of the landscape, which determines the search efficiency for global optima, is dependent with the dynamic symmetry. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dynamic symmetry group. We show that multiple local false traps (i.e., non-global suboptima) exist even if the target gate is realizable and that the number of these traps is increased by the loss of controllability, while the controllable systems are always devoid of false traps.

Chinese Control Conference (CCC)Jul 29, 20100 citations

Dark state role in time-reversal symmetry breaking

Dario Fasone, Rita Veilande, Luigi Giannelli +5 more

We investigate the role of the global driving phase $Φ$ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires $Φ=0,π$ , leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P $Φ$ S), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P $Φ$ S that extend to generic $n$ -level configurations, with $n$ even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.We investigate the role of the global driving phase $Φ$ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires $Φ=0,π$, leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P$Φ$S), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P$Φ$S that extend to generic $n$-level configurations, with $n$ even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.

quant-pharXiv:2603.16512Mar 18, 20260 citations

Controllability of Quantum Systems

Sonia G. Schirmer, I. C. H. Pullen, A. I. Solomon

arXiv:quant-ph/0302121IFAC Proceedings VolumesApr 1, 200324 citations

Nonuniversality from conserved superoperators in unitary circuits

Marco Lastres, Frank Pollmann, Sanjay Moudgalya

An important result in the theory of quantum control is the “universality” of 2-local unitary gates, i.e., the fact that any global unitary evolution of a system of L qudits can be implemented by composition of 2-local unitary gates. Surprisingly, recent results have shown that universality can break down in the presence of symmetries: in general, not all globally symmetric unitaries can be constructed using k -local symmetric unitary gates. This also restricts the dynamics that can be implemented by symmetric local Hamiltonians. In this paper, we show that obstructions to universality in such settings can in general be understood in terms of superoperator symmetries associated with unitary evolution by restricted sets of gates. These superoperator symmetries lead to block decompositions of the operator Hilbert space, which dictate the connectivity of operator space, and hence the structure of the dynamical Lie algebra. We demonstrate this explicitly in several examples by systematically deriving the superoperator symmetries from the gate structure using the framework of commutant algebras, which has been used to systematically derive symmetries in other quantum many-body systems. We clearly delineate two different types of nonuniversality, which stem from different structures of the superoperator symmetries, and discuss its signatures in physical observables. In all, our work establishes a comprehensive framework to explore the universality of unitary circuits and derive physical consequences of its absence.An important result in the theory of quantum control is the “universality” of 2-local unitary gates, i.e., the fact that any global unitary evolution of a system of L qudits can be implemented by composition of 2-local unitary gates. Surprisingly, recent results have shown that universality can break down in the presence of symmetries: in general, not all globally symmetric unitaries can be constructed using k -local symmetric unitary gates. This also restricts the dynamics that can be implemented by symmetric local Hamiltonians. In this paper, we show that obstructions to universality in such settings can in general be understood in terms of superoperator symmetries associated with unitary evolution by restricted sets of gates. These superoperator symmetries lead to block decompositions of the operator Hilbert space, which dictate the connectivity of operator space, and hence the structure of the dynamical Lie algebra. We demonstrate this explicitly in several examples by systematically deriving the superoperator symmetries from the gate structure using the framework of commutant algebras, which has been used to systematically derive symmetries in other quantum many-body systems. We clearly delineate two different types of nonuniversality, which stem from different structures of the superoperator symmetries, and discuss its signatures in physical observables. In all, our work establishes a comprehensive framework to explore the universality of unitary circuits and derive physical consequences of its absence.

arXiv:2409.11407Physical review. B./Physical review. BDec 9, 20252 citations

We investigate the role of the global driving phase

Φ

in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires

Φ=0,π

, leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P

Φ

S), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P

Φ

S that extend to generic

n

-level configurations, with

n

even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.