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arXiv:2510.05872 · Physical Review Research

Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects

Kiyoto Nakamura, Joachim Ankerhold

Published Feb 19, 2026• 1 citation
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Abstract

Within a numerically exact simulation technique, the dissipative dynamics of a two-qubit architecture is considered in which each qubit couples to its individual noise source (reservoir). The goal is to reveal the role of subtle qubit-reservoir correlations including non-Markovian processes as a prerequisite to guide further improvements of quantum computing devices. This paper addresses the following three topics. First, we examine the validity of the rotating wave approximation imposed previously on the qubit-reservoir coupling with respect to the disentanglement dynamics. Second, generation of the entanglement as well as destruction are analyzed by monitoring the reduced dynamics during and after application of a iSWAP † gate, also focusing on memory effects caused by reservoirs. Finally, the performance of a Hadamard + CNOT sequence is analyzed for different gate decomposition schemes. In all three cases, various types of noise sources and qubit parameters are considered.

DOI
10.1103/b5jp-s6t2

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Within a numerically exact simulation technique, the dissipative dynamics of a two-qubit architecture is considered in which each qubit couples to its individual noise source (reservoir). The goal is to reveal the role of subtle qubit-reservoir correlations including non-Markovian processes as a prerequisite to guide further improvements of quantum computing devices. This paper addresses the following three topics. First, we examine the validity of the rotating wave approximation imposed previously on the qubit-reservoir coupling with respect to the disentanglement dynamics. Second, generation of the entanglement as well as destruction are analyzed by monitoring the reduced dynamics during and after application of a iSWAP † gate, also focusing on memory effects caused by reservoirs. Finally, the performance of a Hadamard + CNOT sequence is analyzed for different gate decomposition schemes. In all three cases, various types of noise sources and qubit parameters are considered.
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In this paper, we review some results concerning the dissipative dynamics of two coupled qubits interacting with independent reservoirs. In particular, we focus on the role of counter-rotating terms in the qubit-qubit coupling, showing that their presence is the origin of stationary entanglement, which also turns out to be robust with respect to temperature. We also discuss the performances of different non-Markovian approaches in the description of the qubit-qubit dynamics, by considering a simplified exactly solvable Hamiltonian model.
As the memory effect may be helpful in quantum information processing, non-Markovian dynamics plays an important role in the description of many-body open systems. Among these topics, the system consisting of independent qubits interacting with several coupled environments is of particular interest. In this paper, we study the exact non-Markovian dynamics of two independent qubits. Each of the qubits interacts individually with its environment, and these two environments coupled with each other. We investigate the non-Markovianity measure of the system for the whole parameter regime without the rotating-wave approximation (RWA) and compare the results with that under the RWA. We find that the non-Markovianity measure for two qubits manifests a transition from a non-Markovian to Markovian regime regardless of the coupling strength between the environments. The physical origin of this transition is revealed, and a possible observation of the prediction in superconducting quantum interference devices is discussed.
We provide a thorough analysis of the entanglement dynamics of an interacting two-qubit system in the non-Markovian regime. In such a regime, the time scale on which the reservoir degrees of freedom evolve is either of the same order of magnitude or less than that on which the system evolves. We used an exact numerical method; the Quasi-Adiabatic Path Integral (QUAPI) technique, to describe the corresponding qubit dissipative dynamics in such a non-Markovian regime. We computed the time evolution of the density operator for the quibits, from which we quantified the coherences and population dynamics, as well as the qubit-bath coupling effects. Using negativity as a metric, we calculated the dynamics of non-local quantum correlations (entanglement), and indentified a non-Markovian quantum phenomena in terms of early stage disentanglement, and the collapse and revival of entanglement.
In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. \n \nIn the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. \n \nIn the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. \n \nThe dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.
Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a deterministic protocol, working in the presence of cavity losses, for the generation of a W-state of one qubit and two cavity fields and we describe a probabilistic scheme to entangle one of the atoms with the reservoir (cavity field) of the other atom.