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arXiv:2609.39084

Engineered Dissipation for Thermal-State Tracking Across Quantum Criticality

Saikat Mistry, Dibyajyoti Sahu, Suhas Gangadharaiah

quant-phcond-mat.stat-mechSubmitted Sep 30, 2026• Announced Oct 1, 2026• 0 citations• Revised Oct 5, 2026 (v2)
v1 · Sep 30, 2026v2 · Oct 5, 2026
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Abstract

Engineering dissipation has emerged as a powerful strategy for controlling quantum many-body dynamics, complementing purely coherent control for state preparation. However, finite-time driving across a quantum critical point generates nonadiabatic excitations and coherences, and existing dissipation-engineering approaches have largely characterized how a fixed environment modifies critical dynamics rather than actively steering a system toward a prescribed thermal trajectory. Here we develop a Markovian dissipative framework for finite-time thermal-state tracking based on engineered population currents with non-negative transition rates, and apply it to the transverse-field Ising model driven across its quantum critical point. Compared with unitary dynamics and a natural thermal bath, the engineered dynamics strongly suppresses thermal excitation deviations and provides additional control over coherence damping through a free common current $Q_k$, while exhibiting a substantially steeper residual scaling, $δn_{\mathrm{ex}}^{\mathrm{th}}\sim(v/v_{\mathrm{ch}})^2$, than the Kibble--Zurek behavior recovered for unitary evolution. These results point toward engineered dissipation as a route for controlling thermal-state preparation in driven quantum critical systems.

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Engineering dissipation has emerged as a powerful strategy for controlling quantum many-body dynamics, complementing purely coherent control for state preparation. However, finite-time driving across a quantum critical point generates nonadiabatic excitations and coherences, and existing dissipation-engineering approaches have largely characterized how a fixed environment modifies critical dynamics rather than actively steering a system toward a prescribed thermal trajectory. Here we develop a Markovian dissipative framework for finite-time thermal-state tracking based on engineered population currents with non-negative transition rates, and apply it to the transverse-field Ising model driven across its quantum critical point. Compared with unitary dynamics and a natural thermal bath, the engineered dynamics strongly suppresses thermal excitation deviations and provides additional control over coherence damping through a free common current QkQ_kQk​, while exhibiting a substantially steeper residual scaling, δnexth∼(v/vch)2δn_{\mathrm{ex}}^{\mathrm{th}}\sim(v/v_{\mathrm{ch}})^2δnexth​∼(v/vch​)2, than the Kibble--Zurek behavior recovered for unitary evolution. These results point toward engineered dissipation as a route for controlling thermal-state preparation in driven quantum critical systems.
Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.
We study how the universal properties of quantum quenches across critical points are modified by a weak coupling to a thermal bath, focusing on the paradigmatic case of the transverse field Ising model. Beyond the standard quench-induced Kibble-Zurek defect production in the absence of the bath, the bath contributes extra thermal defects. We show that spatial correlations in the noise produced by the bath can play a crucial role: one obtains quantitatively different scaling regimes depending on whether the correlation length of the noise is smaller or larger than the Kibble-Zurek length associated with the quench speed, and the thermal length set by the temperature. For the case of spatially correlated bath noise, additional thermal defect generation is restricted to a window that is both quantum critical and excluded from the nonequilibrium regime surrounding the critical point. We map the dissipative quench problem to a set of effectively independent dissipative Landau-Zener problems. Using this mapping along with both analytic and numerical calculations allows us to find the scaling of the excess defect density produced in the quench, and it suggests a generic picture for such dissipative quenches.
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
The controlled preparation of quantum many-body states is a central challenge for quantum technologies. While preparing target states coherently is possible in principle, it is often fragile and experimentally demanding. Dissipative state preparation, where engineered environments drive the system toward desired steady states, provides a complementary and powerful paradigm. This thesis explores dissipative methods for preparing complex many-body states along three distinct directions. First, we investigate the dissipative stabilization of injective matrix product states (MPS). Injective MPS are particularly well suited for dissipative preparation because they arise as ground states of frustration-free parent Hamiltonians, allowing for tailored jump operators to steer the system directly into the target state. We showcase the surprising result that such state preparation works even in the dilute limit where steering only acts on a single link. Moreover, we introduce a formalism for engineering additional coherent interactions, extending the set of accessible states. Second, and complementary to steering, we develop and analyze a universal cooling scheme capable of preparing ground states even in frustrated quantum systems. In contrast to steering methods, universal cooling can overcome the glass floor that forbids steering methods to prepare such frustrated ground states. A key insight here is that the presented cooling scheme is completely system-agnostic making it extremely robust. Finally, we pursue dressing of the system eigenstates by means of either classical drives or coherent interactions as a means to influence the action of dissipation on the system. Focusing first on time-dependent systems, we propose a generalized numerical implementation of non-adiabatic master equations suitable for the use of optimal control tools. Additionally, we investigate how the collective coupling between a spin ensemble and a cavity can steer the system into a spin-squeezed steady state. Together, these three avenues illustrate how tailored dissipative dynamics can extend the frontier of many-body state preparation, from stabilizing injective MPS to cooling complex frustrated systems and generating non-classical steady states in the dressed framework.
We study shortcuts to adiabaticity (STAs) through counterdiabatic driving in quantum critical systems in the presence of dissipation. We evaluate unitary as well as nonunitary controls, such that the system density matrix follows a prescribed trajectory corresponding to the eigenstates of a time-dependent reference Hamiltonian at any instant of time. The strength of the dissipator control term for the low-energy states shows universal scaling close to criticality. Using the example of free-fermionic systems, in particular, the transverse-field Ising model, we show that in contrast to STAs in closed quantum critical systems, here, STAs may require multibody interactions terms, even away from criticality, owing to the change in entropy of the time-dependent target state. Further, the associated heat current shows an extremum, while power dissipation changes curvature, close to criticality, and analogous to unitary control, no operational cost is associated with implementation of the exact counterdiabatic Hamiltonian. We believe the counterdiabatic protocol studied here could be of fundamental importance for understanding STAs in many-body open quantum systems and could be highly relevant for varied topics involving open many-body quantum systems, such as quantum computation and many-body quantum heat engines.
We study finite-time driving across second-order dissipative quantum phase transitions described by Lindblad dynamics. We show that the nonadiabatic entropy production, which quantifies deviations from the instantaneous nonequilibrium steady state, exhibits universal power-law scaling with the ramp duration in analogy to the Kibble-Zurek mechanism for closed systems. This establishes the universality of irreversible dissipation induced by driving an open quantum system near criticality. Furthermore, in systems described by bosonic Gaussian states, our scaling laws predict that the nonadiabatic entropy production is independent of driving speed to leading order, revealing a distinctive feature of Gaussian dissipative quantum phase transitions. We validate these analytical predictions in the thermodynamic limit of the driven-dissipative Dicke model and via finite-size scaling in the open Kerr model. Our results establish a general framework for understanding universal nonequilibrium response and thermodynamic irreversibility in critical open quantum systems.