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  • Open Access

Efficient Simulation of Nontrivial Dissipative Spin Chains via Stochastic Unraveling

Andrew Pocklington1,2,* and Aashish A. Clerk2,†

  • *Contact author: abpocklington@uchicago.edu
  • †Contact author: aaclerk@uchicago.edu
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PRX Quantum 6, 030349 – Published 15 September, 2025

DOI: https://doi.org/10.1103/vptq-xy6h

Abstract

We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from Jordan-Wigner strings appearing in the jump operators, despite the fact that these models cannot be mapped to quadratic fermionic master equations. We show that many such Lindblad master equations admit an exact stochastic unraveling, with individual trajectories evolving as Gaussian fermionic states, even though the full master equation describes a system inequivalent to free fermions. This allows one to calculate arbitrary observables efficiently without sign problems, and with bounded sampling complexity. We utilize this new technique to study three paradigmatic dissipative effects: the melting of antiferromagnetic order in the presence of local loss, many-body subradiant phenomenon in systems with correlated loss, and nonequilibrium steady states of a 1D dissipative transverse-field Ising model. Beyond simply providing a powerful numerical technique, our method can also be used to gain both qualitative and quantitative insights into the role of interactions in these models.

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One-dimensional exactly solvable spin chains have been an invaluable resource in our understanding of quantum systems. However, coupling to the environment is unavoidable, especially in current noisy quantum experiments. Moreover, it is well known that dissipation in quantum systems can fundamentally alter their behavior, such as the nature of quantum phase transitions. Hence, the ability to exactly simulate noisy quantum systems is fundamental to advancing our understanding of the nature of quantum phenomenon, but often an exactly solvable closed system becomes immediately intractable even when adding the simplest possible dissipation, such as local spin relaxation, severely limiting the ability to simulate large systems.

To circumvent this, we develop a new numerical technique based on stochastic unravelings of a quantum master equation. Under each stochastic trajectory, an initially simple (Gaussian) quantum state remains Gaussian. Because the state space of Gaussian states scales polynomially in the system size instead of exponentially, this provides an exponentially faster simulation technique. We stress that the average dynamics do not remain Gaussian, but we can sample observables from the true state by stochastically generating Gaussian trajectories that converge to the true state. This can be done with bounded sampling complexity and is sign-problem free. Moreover, this is more than a numerical technique, as it gives us direct insights and often allows us to make qualitative analytical predictions of the behavior of open systems.

This represents a significant advancement in the ability to simulate dissipative quantum systems, opening up an extremely broad and relevant class of models that were previously intractable. Moreover, there is also a surprising connection between our work and Z2 gauge theories, which extends the set of systems we can simulate beyond one dimension to other solvable gauge theories such as a noisy Kitaev honeycomb. Going forward, this new technique can provide both quantitative and intuitive understanding to the behavior of novel quantum systems, with applications from condensed matter to quantum information theory.

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PRX Quantum 6, 030349– Published 15 September, 2025
  • Received 10 April 2025
  • Revised 24 June 2025
  • Accepted 6 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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