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arXiv:2403.19408 · Physical Review A

Queued quantum collision models

Guilherme Fiusa, Gabriel Teixeira Landi

Published Mar 26, 2025• 5 citations
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Abstract

Collision models describe the sequential interactions of a system with independent ancillas. Motivated by recent advances in neutral atom arrays, here we investigate a model where the ancillas are governed by a classical controller that allows them to queue up while they wait for their turn to interact with the system. The ancillas can undergo individual open dynamics while they wait, which could cause them to, e.g., decohere. The system, which plays the role of the server in the queue, can also undergo its own open dynamics whenever it is idle. We show that this framework greatly generalizes existing approaches for quantum collision models, recovering the deterministic and stochastic formulations in the appropriate limits. Next, we show how the combination of queueing dynamics with quantum collisions introduces rich dynamical phenomena, including phase transitions and a sharp dependence on the queue statistics.

DOI
10.1103/physreva.111.032220

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Collision models describe the sequential interactions of a system with independent ancillas. Motivated by recent advances in neutral atom arrays, here we investigate a model where the ancillas are governed by a classical controller that allows them to queue up while they wait for their turn to interact with the system. The ancillas can undergo individual open dynamics while they wait, which could cause them to, e.g., decohere. The system, which plays the role of the server in the queue, can also undergo its own open dynamics whenever it is idle. We show that this framework greatly generalizes existing approaches for quantum collision models, recovering the deterministic and stochastic formulations in the appropriate limits. Next, we show how the combination of queueing dynamics with quantum collisions introduces rich dynamical phenomena, including phase transitions and a sharp dependence on the queue statistics.
Most literature on quantum collision models (CMs) usually considers periodic weak collisions featuring a fixed waiting time between two next collisions. Some works have yet addressed CMs with random waiting time and strong collisions (stochastic CMs). This short paper discusses how the open dynamics arising from these two types of models can be formally mapped with one another. This can be achieved for a given stochastic CM by constructing an associated periodic CM such that the waiting time randomness of the former is turned into the mixedness of the ancilla’s initial state of the latter, introducing at the same time an additional state of the ancilla. Through this mapping, non-Markovian behaviour arising from a constrained number of stochatic collisions can be linked to initial ancilla–ancilla correlations of the associated periodic CM.
Abstract Collision models (CMs) describe an open system interacting in sequence with elements of an environment, termed ancillas. They have been established as a useful tool for analyzing non-Markovian open quantum dynamics based on the ability to control the environmental memory through simple feedback mechanisms. In this work, we investigate how ancilla–ancilla (AA) entanglement can serve as a mechanism for controlling the non-Markovianity of an open system, focusing on an operational approach to generating correlations within the environment. To this end, we first demonstrate that the open dynamics of CMs with sequentially generated correlations between groups of ancillas can be mapped onto a composite CM, where the memory part of the environment is incorporated into an enlarged Markovian system. We then apply this framework to an all-qubit CM, and show that non-Markovian behavior emerges only when the next incoming pair of ancillas are entangled prior to colliding with the system. On the other hand, when system-ancilla collisions precede AA entanglement, we find the open dynamics to always be Markovian. Our findings highlight how certain qualitative features of inter-ancilla correlations can strongly influence the onset of system non-Markovianity.
A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R\mathcal{R}R as consisting of a large collection of elementary ancillas: the dynamics of the open system S\mathcal{S}S results from successive collisions of S\mathcal{S}S with the ancillas of R\mathcal{R}R. Here, we present a general formulation of memoryless composite CMs, where S\mathcal{S}S is partitioned into the very open system under study SSS coupled to one or more auxiliary systems Si{{S}_{i}}Si​. Their composite dynamics occurs through internal $S\ensuremath{-}{{S}_{i}}$ collisions interspersed with external ones involving Si{{S}_{i}}Si​ and the reservoir R\mathcal{R}R. We show that important known instances of quantum non-Markovian dynamics of SSS---such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise---can be mapped on to such memoryless composite CMs.
Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a ppp-impurity model is non-Markovian, then the corresponding (p+1)(p+1)(p+1)-impurity model is also non-Markovian, implying the existence of a critical ppp at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical ppp, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.
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.
We investigate the emergent open dynamics of a quantum system that undergoes rapid repeated unitary interactions with a sequence of ancillary systems. We study in detail how decoherence appears as a subleading effect when a quantum system is bombarded by a quick succession of ancillas. In the most general case, these ancillas are (a) taken from an ensemble of quantum systems of different dimensions, (b) prepared in different states, and (c) interacting with the system through different Hamiltonians. We derive an upper bound on decoherence rates in this regime, and show how a rich variety of phenomena in open dynamics (such as projection, thermalization, purification, and dephasing) can emerge out of our general model of repeated interaction. Furthermore, we show a fundamental link between the strength of the leading-order dissipation and the intrinsic ``unpredictability'' in the system-ancilla interaction. We also discuss how these results encompass and extend results obtained with other earlier models of repeated interaction.