Quantum trajectory simulation of two-dimensional non-equilibrium steady states with a trapped ion quantum processor
Anna Dalmasso, Arash Jafarizadeh, Julian Boesl, Jared Jeyaretnam, Sheng-Hsuan Lin, Andrew G. Green, Frank Pollmann, Michael Knap, Juan P. Garrahan, Henrik Dreyer, Adam Gammon-Smith
quant-phcond-mat.stat-mechcond-mat.str-elSubmitted May 8, 2026• Announced May 12, 2026• 0 citations
Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the dynamics of interacting open quantum systems. Using the Quantinuum System Model H1 trapped-ion quantum computer, we experimentally realise quantum trajectories for a two-dimensional system of (interacting) particles-hard-core bosons or fermions-undergoing stochastic driving at a source and drain at opposite corners of a square lattice. We study the non-equilibrium steady state with persistent current resulting from the this in/out flow of particles. The particle statistics, presence of interactions, and introduction of a magnetic field produce measurable effects on the steady state. Our findings highlight the rich physics in this corner driven two-dimensional setup and showcases both the power and current limitations of quantum computers as a platform to study it.
Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the dynamics of interacting open quantum systems. Using the Quantinuum System Model H1 trapped-ion quantum computer, we experimentally realise quantum trajectories for a two-dimensional system of (interacting) particles-hard-core bosons or fermions-undergoing stochastic driving at a source and drain at opposite corners of a square lattice. We study the non-equilibrium steady state with persistent current resulting from the this in/out flow of particles. The particle statistics, presence of interactions, and introduction of a magnetic field produce measurable effects on the steady state. Our findings highlight the rich physics in this corner driven two-dimensional setup and showcases both the power and current limitations of quantum computers as a platform to study it.
Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.
Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore non-unitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states.
Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-1/2 driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.
Digital quantum computers have the potential to study the dynamics of many-body quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we explore the feasibility of studying steady-state transport in strongly interacting many-body quantum systems on a digital quantum computer. To do so, we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven XXZ spin chain. More specifically, we investigate how the depth of the quantum circuit is affected by how close we want the steady state to be to the one expected from the underlying master equation. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the XXZ spin chains are subject to nonuniform magnetic fields and show that, although the circuit depths required to reach steady states are still prohibitive for today's hardware, few collisions are enough to suggest a strong rectifying power.
<!--HTML--> In this talk, I will review the fundamental principles of quantum information processing and provide an update on the Innsbruck trapped-ion quantum computer [1]. Using strings of trapped ions, we realize a programmable quantum processor capable of performing universal operations. I will give an overview of the experimental quantum toolbox and discuss current strategies for scaling the system to larger sizes. The versatility of this platform is illustrated through both analog and digital quantum simulations. By exploiting the trapped-ion toolbox for entanglement-enhanced Ramsey interferometry, we identify optimal parameters for quantum metrology [2]. Employing universal quantum computation, we explore the dynamics of the Lattice Schwinger model [3] - a one-dimensional gauge theory of quantum electrodynamics - and, using a hybrid quantum-classical variational approach, we determine steady-state properties of the corresponding Hamiltonian [4]. Finally, with a trapped-ion qudit quantum processor, in which quantum information is encoded in multiple internal states, we simulate a two-dimensional lattice gauge theory [5}. [1] I. Pogorelov et al., PRX Quantum 2, 020343 (2021) [2] C. D. Marciniak et al., Nature 603, 604 (2022) [3] E. A. Martinez et al., Nature 534, 516 (2016) [4] C. Kokail et al., Nature 569, 355–360 (2019) [5] M. Meth et al., Nature Physics 21, 570 (2025)
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.