Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous establishment of synchronization in open quantum systems. In such models, the repeated pairwise interactions between the system and the environment and also the possible coupling between different environmental units are typically modeled using the coherent partial SWAP (PSWAP) operation as it is known to be a universal homogenizer. In this study, we investigate the dynamical behavior of incoherent collision models, where the interactions between different units are modeled by the incoherent controlled SWAP (CSWAP) operation, which is also a universal homogenizer. Even though the asymptotic dynamics of the open system in cases of both coherent and incoherent swap interactions appear to be identical, its transient dynamics turns out to be significantly different. Here, we present a comparative analysis of the consequences of having coherent or incoherent couplings in collision models, namely, PSWAP or CSWAP interactions, respectively, for the emergence of memory effects for a single-qubit system and for the onset synchronization between a pair of qubits, both of which are strictly determined by the transient dynamics of the open system.Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous establishment of synchronization in open quantum systems. In such models, the repeated pairwise interactions between the system and the environment and also the possible coupling between different environmental units are typically modeled using the coherent partial SWAP (PSWAP) operation as it is known to be a universal homogenizer. In this study, we investigate the dynamical behavior of incoherent collision models, where the interactions between different units are modeled by the incoherent controlled SWAP (CSWAP) operation, which is also a universal homogenizer. Even though the asymptotic dynamics of the open system in cases of both coherent and incoherent swap interactions appear to be identical, its transient dynamics turns out to be significantly different. Here, we present a comparative analysis of the consequences of having coherent or incoherent couplings in collision models, namely, PSWAP or CSWAP interactions, respectively, for the emergence of memory effects for a single-qubit system and for the onset synchronization between a pair of qubits, both of which are strictly determined by the transient dynamics of the open system.

arXiv:2501.16313EntropyFeb 15, 20253 citations

A Brief Journey through Collision Models for Multipartite Open Quantum Dynamics

Marco Cattaneo, Gian Luca Giorgi, Roberta Zambrini +1 more

The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.

arXiv:2209.15476Open Systems & Information DynamicsSep 1, 202222 citations

Frontiers of Open Quantum System Dynamics

Bassano Vacchini

arXiv:1907.07516Lecture notes of the Unione Matematica ItalianaJan 1, 20191 citation

Open Quantum Systems Dynamics

Gonzalo Manzano Paule

Springer thesesJan 1, 20180 citations

Gate-Based Quantum Simulation of Finite-Temperature Open-System Dynamics: A Post-Processing Reconstruction Approach for Collision Models

Kazunari Hashimoto, Chikako Uchiyama

Simulating open-system dynamics on gate-based quantum computers offers a route to exploring dissipative quantum phenomena through programmable quantum processing. Collision models provide a direct and flexible framework by representing the environment through sequential system--ancilla collisions. At finite temperatures, however, they typically require repeated preparation of thermal ancillas, adding circuit overhead and gate errors. Here, we show that, for a broad class of $U(1)$ -symmetric system--ancilla interactions, finite-temperature dynamics can instead be reconstructed from simulations with pure ancillas in orthogonal basis states. The target temperature enters only through classical post-processing of the resulting pure-branch data, allowing the same data to be reused for different temperatures without additional quantum processing. Bypassing explicit thermal-state preparation reduces ancilla-preparation overhead and preparation-induced errors.Simulating open-system dynamics on gate-based quantum computers offers a route to exploring dissipative quantum phenomena through programmable quantum processing. Collision models provide a direct and flexible framework by representing the environment through sequential system--ancilla collisions. At finite temperatures, however, they typically require repeated preparation of thermal ancillas, adding circuit overhead and gate errors. Here, we show that, for a broad class of $U(1)$-symmetric system--ancilla interactions, finite-temperature dynamics can instead be reconstructed from simulations with pure ancillas in orthogonal basis states. The target temperature enters only through classical post-processing of the resulting pure-branch data, allowing the same data to be reused for different temperatures without additional quantum processing. Bypassing explicit thermal-state preparation reduces ancilla-preparation overhead and preparation-induced errors.

quant-pharXiv:2610.04075Oct 6, 20260 citations

U(1)

-symmetric system--ancilla interactions, finite-temperature dynamics can instead be reconstructed from simulations with pure ancillas in orthogonal basis states. The target temperature enters only through classical post-processing of the resulting pure-branch data, allowing the same data to be reused for different temperatures without additional quantum processing. Bypassing explicit thermal-state preparation reduces ancilla-preparation overhead and preparation-induced errors.