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arXiv:2610.04075

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

Kazunari Hashimoto, Chikako Uchiyama

quant-phSubmitted Oct 2, 2026• Announced Oct 6, 2026• 0 citations
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Abstract

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.

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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)U(1)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.
Quantum non-Markovianity represents memory during system dynamics, which is typically weakened by temperature. We study here the effects of environmental temperature on the non-Markovianity of an open quantum system by virtue of collision models. The environment is simulated by a chain of ancillary qubits that are prepared in thermal states with a finite temperature TTT. Two distinct non-Markovian mechanisms are considered via two types of collision models, one where the system SSS consecutively interacts with ancillas and a second where SSS collides only with an intermediate system ${S}^{\ensuremath{'}}$, which in turn interacts with the ancillas. We show that in both models the relation between non-Markovianity and temperature is nonmonotonic. In particular, revivals of non-Markovianity may occur as temperature increases. We find that the physical reason behind this behavior can be revealed by examining a peculiar system-environment coherence exchange, leading to ancillary qubit coherence larger than system coherence, which triggers information backflow from the environment to the system. These results provide insights into the mechanisms underlying the counterintuitive phenomenon of temperature-enhanced quantum memory effects.
Hamiltonian dynamics have been widely implemented on noisy intermediate-scale quantum devices in recent years. In contrast, experimental demonstrations of Markovian quantum dynamics remain limited, because implementing nonunitary evolution on quantum computers is challenging. Quantum collision models provide a natural approach to this problem by coupling the system to ancillas to realize dissipation. However, previous implementations of quantum collision models on quantum computers have typically been restricted to one or two system qubits and fewer than 12 time steps, owing to noise, circuit depth, the overhead of ancilla reset, and limited qubit resources. In this work, we experimentally simulate Markovian quantum processes with local and nonlocal dissipation on both trapped-ion and superconducting quantum computers. By employing hardware-specific ancilla strategies, we realize simulations with up to seven system qubits, corresponding to 13 qubits in total, and 40 time steps. Our results demonstrate that, even for the same physical model, the optimal implementation strategy depends strongly on the hardware characteristics of the quantum computer.
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 develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing time evolutions of the total (system, bath, and interaction) Hamiltonian and intermittent tracing out the environment degrees of freedom. This results in a unified framework where any near-term Hamiltonian simulation algorithm can be incorporated to implement an arbitrary number of such collisions on early fault-tolerant quantum computers: we do not assume access to specialized oracles such as block encodings and minimize the number of ancilla qubits needed. In particular, using the correspondence between Lindbladian evolution and completely positive trace-preserving maps arising out of memoryless collisions, we provide an end-to-end quantum algorithm for simulating Lindbladian dynamics. For a system of nnn-qubits, we exhaustively compare the circuit depth needed to estimate the expectation value of an observable with respect to the reduced state of the system after time ttt while employing different near-term Hamiltonian simulation techniques, requiring at most n+2n+2n+2 qubits in all. We compare the cnot gate counts of the various approaches for estimating the transverse field magnetization of a 10-qubit XX-Heisenberg spin chain under amplitude damping. Finally, we also develop a framework to efficiently simulate an arbitrary number of memory-retaining collisions, i.e., where environments interact, leading to non-Markovian dynamics. Overall, our methods can leverage quantum collision models for both Markovian and non-Markovian dynamics on early fault-tolerant quantum computers, shedding light on the advantages and limitations of simulating open systems dynamics using this framework.
Quantum computing has attracted the attention of the scientific community in the past few decades. However, despite some relevant advantages, near-term quantum devices remain severely limited by thermal effects, which induce decoherence and restrict coherent control at finite temperature. In this regard, this work reports a gate-based quantum algorithm that prepares the finite-temperature vacuum of Thermofield Dynamics (TFD) and tracks its real-time evolution. The circuit depth scales linearly with system size and requires only single-qubit rotations and nearest-neighbor CNOT gates, making it NISQ-friendly. We benchmark the protocol on the PennyLane simulator: magnetization of a spin-1/21/21/2 particle in a magnetic field agrees with the exact result M(β)=tanh⁡(βω/2)M(β)=\tanh(βω/2)M(β)=tanh(βω/2) to machine precision, and the coherent precession acquires a temperature-dependent damping that quantitatively matches the analytical TFD prediction. Our work provides a ready-to-deploy toolbox for thermal quantum simulations and opens a route to study dissipative phase transitions, quantum thermodynamics and thermal machine-learning models on near-term devices.
In this work we investigate a model of thermalization wherein a single ancillary qubit randomly interacts with the system to be thermalized. This not only sheds light on the emergence of Gibbs states in nature, but also provides a routine for preparing arbitrary thermal states on a digital quantum computer. For desired βββ and random interaction GGG the routine boils down to time independent Hamiltonian simulation and is represented by the channel Φ:ρ↦EGTrEnv[e−i(H+αG)t(ρ⊗e−βHEZ)ei(H+αG)t]Φ: ρ\mapsto \mathbb{E}_G {\rm Tr}_{\rm Env} \left[ e^{-i(H + αG)t} \left(ρ\otimes \frac{e^{-βH_E}}{\mathcal{Z}}\right) e^{i (H + αG)t} \right]Φ:ρ↦EG​TrEnv​[e−i(H+αG)t(ρ⊗Ze−βHE​​)ei(H+αG)t]. We rigorously prove that these dynamics reduce to a Markov chain process in the weak-coupling regime with the thermal state as the approximate fixed point. We upper bound the total simulation time required in terms of the Markov chain spectral gap λ⋆λ_\starλ⋆​, which we compute exactly in the ground state limit. These results are independent of any eigenvalue knowledge of the system, but we are further able to show that with knowledge of eigenvalue differences λS(i)−λS(j)λ_S(i) - λ_S(j)λS​(i)−λS​(j), then the total simulation time is dramatically reduced. The ratio of the complete ignorance simulation cost to the perfect knowledge simulation cost scales as O~(∥HS∥7δmin7ε3.5λ⋆(β)3.5)\widetilde{O} \left({\frac{\|{H_S}\|^7}{δ_{\rm min}^7 ε^{3.5} λ_\star(β)^{3.5}}}\right)O(δmin7​ε3.5λ⋆​(β)3.5∥HS​∥7​), where δmin⁡δ_{\min}δmin​ is related to the eigenvalue differences of the system. Additionally, we provide more specific results for single qubit and harmonic oscillator systems as well as numeric experiments with hydrogen chains. In addition to the algorithmic merits, these results can be viewed as broad extensions of the Repeated Interactions model to generic Hamiltonians with unknown interactions, giving a complete picture of the thermalization process for quantum systems.