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Physical Review A

Continuous dynamical decoupling in non-Hermitian two-level systems

Yu-bing Yao, Xiang-Fa Zhou, Xingxiang Zhou, Xingxiang Zhou

Published May 23, 2025• 1 citation
Publisher

Abstract

Dynamical decoupling is an effective approach to suppress noise-induced decoherence for the implementation of quantum information processing and quantum technologies. However, current studies of dynamical decoupling mainly focus on Hermitian systems. In this paper, we propose a new approach to implement continuous dynamical decoupling in non-Hermitian two-level systems. For parity-time ($\mathcal{PT}$)-symmetric non-Hermitian Hamiltonians, since the dynamics of the system can be transformed into an effective Hermitian case using the vielbein formalism, we theoretically prove and numerically verify that the constructed driving field succeeds in suppressing the noises. We also demonstrate that this method can be extended to systems without $\mathcal{PT}$ symmetries. Our work is beneficial for further studies and applications of dynamic decoupling and non-Hermitian physics in noisy quantum systems.

DOI
10.1103/physreva.111.052622

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Dynamical decoupling is an effective approach to suppress noise-induced decoherence for the implementation of quantum information processing and quantum technologies. However, current studies of dynamical decoupling mainly focus on Hermitian systems. In this paper, we propose a new approach to implement continuous dynamical decoupling in non-Hermitian two-level systems. For parity-time (PT\mathcal{PT}PT)-symmetric non-Hermitian Hamiltonians, since the dynamics of the system can be transformed into an effective Hermitian case using the vielbein formalism, we theoretically prove and numerically verify that the constructed driving field succeeds in suppressing the noises. We also demonstrate that this method can be extended to systems without PT\mathcal{PT}PT symmetries. Our work is beneficial for further studies and applications of dynamic decoupling and non-Hermitian physics in noisy quantum systems.
Parity-time (PT\mathcal{PT}PT)-symmetric non-Hermitian Hamiltonians bring about many novel features and interesting applications such as quantum gates faster than those in Hermitian systems and topological state transfer. The performance of evolutions under PT\mathcal{PT}PT-symmetric Hamiltonians is degraded by the inevitable noise and errors due to system-environment interaction and experimental imperfections. In contrast to Hermitian Hamiltonians, the fluctuations in dissipative beams that are utilized to generate non-Hermitian contributions in the PT\mathcal{PT}PT-symmetric Hamiltonians cause additional errors. Here we achieve the protection of PT\mathcal{PT}PT-symmetric Hamiltonians against noise acting along the qubit's quantization axis by combining quantum evolutions with dynamical decoupling sequences. We demonstrate the performance of our method by numerical simulations. Realistic noise sources and parameters are chosen including constant detuning error, time-varying detuning noise, and dissipative-beam noise. The fidelity of states after protected evolutions is well above those after unprotected evolutions under all the above situations. Our work paves the way for further studies and applications of non-Hermitian PT\mathcal{PT}PT-symmetric physics in noisy quantum systems.
We construct new types of two-level qubit systems through incorporating non-Hermiticity with joint Parity-Time and anti-Parity-Time symmetries and present a framework to analytically find the dynamics for such systems. As a result, observe improved properties of decoherence, von Neumann entanglement entropy and quantum Fisher information. This suggests that non-Hermitian PT and APT-symmetric qubits may be better suited for quantum computing and quantum information processing than conventional Hermitian qubits.
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.
The conventional time-dependent perturbation theory in quantum mechanics is established within the framework of Hermitian Hamiltonians, applicable for describing quantum transitions and associated energy level responses in such systems. However, this theory has fundamental limitations when applied to non-Hermitian systems. Consequently, researchers have systematically extended time-dependent perturbation theory to non-Hermitian systems, establishing a corresponding mature framework. Building on this foundation, this study extends the theory to investigate the transition dynamics induced by non-Hermitian interactions in non-Hermitian Hamiltonian systems. We employ a biorthogonal basis representation for a three-level non-Hermitian system. This work investigates a system comprising an unperturbed static non-Hermitian Hamiltonian and a periodically driven time-dependent perturbation Hamiltonian. Taking the three-level system as a concrete example, we combine analytical methods with numerical simulations to solve and analyze its dynamical evolution equations. These complementary approaches reveal that when system parameters complete a full cycle around an exceptional point, the transitional behavior exhibits specific evolutionary patterns. In this system, quantum transition probabilities exhibit significant asymmetry and non-conservation that depend on the initial and final states, revealing inherent directional characteristics in the dynamical process. Furthermore, for a three-level, periodically driven non-Hermitian system with time-dependent perturbations, this asymmetry is even more pronounced, manifesting as a distinct disparity between forward and reverse transition probabilities. The periodic driving actively amplifies the asymmetry in the transition process. By designing the perturbation spectrum, selective manipulation of specific quantum states can be achieved. Moreover, transition probabilities can be significantly enhanced under resonance conditions, while non-Hermiticity further breaks the system's inherent symmetry, leading to substantial amplification of transitions in a single direction. By precisely tuning the drive frequency, interactions between specific coupling channels can be selectively enhanced or suppressed. The amplification of channel asymmetry by non-Hermitian properties provides a novel mechanism for directional control of quantum states and opens new pathways for realizing related quantum technologies.
Resilience to noise and to decoherence processes is an important ingredient for the implementation of quantum information processing, and quantum technologies. To this end, techniques such as pulsed and continuous dynamical decoupling have been proposed to reduce noise effects. In this paper, we suggest a new approach to implementing continuous dynamical decoupling techniques, that uses an extra control parameter; namely, the ability to shape the time dependence of the detuning. This approach reduces the complexity of the experimental setup, such that we are only left with noise originating from the frequency of the driving field, which is much more robust than the amplitude (Rabi frequency) noise. As an example, we show that our technique can be utilized for improved sensing.
Quantum dynamics of two XXXXXX interacting PT-symmetric non-Hermitian qubits: enhancement of quantum annealing
Quantum information platforms enable analog quantum simulations, such as quantum annealing, offering a promising route to solving complex combinatorial optimization problems. Here, we propose a quantum information architecture based on networks of interacting parity-time (PT)-symmetric non-Hermitian qubits. While the dynamics of individual PT-symmetric qubits have been experimentally demonstrated across multiple platforms including NV centers, superconducting circuits, and trapped-ion systems yet coherent dynamics in interacting systems remain largely unexplored. To address this issue we theoretically investigate stationary and time-dependent Hamiltonians relevant to quantum annealing using a minimal model of two interacting XX-coupled PT-symmetric non-Hermitian qubits. We analyze both symmetry-preserving and symmetry-broken regimes and demonstrate that adding even tiny PT-symmetric non-Hermitian terms in the qubits Hamiltonian allows to greatly enhance the probability of reaching the ground state after annealing.