Designing open quantum systems with known steady states: Davies generators and beyond

Jinkang Guo; Oliver Hart; Chi-Fang Chen; Aaron J. Friedman; Andrew Lucas

doi:10.22331/q-2025-01-28-1612

Designing open quantum systems with known steady states: Davies generators and beyond

Jinkang Guo¹, Oliver Hart¹, Chi-Fang Chen², Aaron J. Friedman¹, and Andrew Lucas¹

¹Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
²Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125 USA

Published:	2025-01-28, volume 9, page 1612
Editor:	Di Fang
Eprint:	arXiv:2404.14538v2
Doi:	https://doi.org/10.22331/q-2025-01-28-1612
Citation:	Quantum 9, 1612 (2025).

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Abstract

We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.

Popular summary

The preparation of entangled quantum states underpins most — if not all — tasks relevant to quantum algorithms and quantum information processing, and is often a goal unto itself. Examples range from resource states for teleportation, quantum error correction, and quantum metrology to the simulation of thermal states and quantum dynamics. Separately, time-reversal symmetry (“T”) plays an important role in the characterization and classification of generic quantum dynamics, where “T-odd” systems may realize behavior not possible in thermal equilibrium, and may provide speedups in targeting quantum states.

A common method for preparing quantum states involves Davies' generator, which is T even and generally nonlocal; in this work, we systematically derive $local$ algorithms for the dissipative preparation of large classes of quantum mixed states realizing both T-even and T-odd dynamics. We construct explicit local Lindbladians that preserve a given target state, and describe how the dissipation can be engineered in the laboratory using measurements and feedback. We also prescribe how to correct for generic sources of error and the engineering of T-odd dynamics, which lie beyond thermal equilibrium and may realize “active'' quantum matter. We illustrate these ideas using concrete examples, and draw parallels to quantum phases of matter and quantum error correction.

► BibTeX data

@article{Guo2025designingopen,
  doi = {10.22331/q-2025-01-28-1612},
  url = {https://doi.org/10.22331/q-2025-01-28-1612},
  title = {Designing open quantum systems with known steady states: {D}avies generators and beyond},
  author = {Guo, Jinkang and Hart, Oliver and Chen, Chi-Fang and Friedman, Aaron J. and Lucas, Andrew},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1612},
  month = jan,
  year = {2025}
}

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