We investigate and compare two particle number conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is corroborated also analytically using mean-field approximations and a purely classical random walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.
Journal reference
Phys. Rev. Research 8, 023336. Published 25 June, 2026
We investigate and compare two particle number conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is corroborated also analytically using mean-field approximations and a purely classical random walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.
The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and timescales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and timescales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.
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.
Thermal state preparation is a central challenge in the simulation of quantum many-body systems. Yet, provably efficient algorithms for this task were only introduced recently [Chen et al. Nature 646, 561 (2025)]. These algorithms are based on dissipative Lindbladian evolution which exactly fixes the thermal state. Controlled and efficient digital simulation of this evolution, although possible in principle, remains out of reach for present-day quantum hardware. Subsequent work has therefore focused on analog approximations of the proposed Lindbladians via `collision models' with relatively modest requirements -- a resettable bath of ancilla qubits whose couplings to the system can be tuned in time-dependent fashion -- while still admitting rigorous fixed-point error bounds. Existing rigorous approaches, however, do not exploit the fact that these constructions generically implement not only the desired Lindblad dynamics, but also an additional unitary evolution generated by the system Hamiltonian which may aid convergence to the thermal state [Lloyd and Abanin arXiv:2506.21318 (2025)]. Here, we show that this unitary contribution does indeed tighten the fixed-point error bound and demonstrate that it is rigorously controlled by the system-bath coupling strength J, scaling as J2. This demonstrates that the effect of the spurious `Lamb shift' term generated by the system-bath interaction can be controlled by tuning J. We clarify the role, previously observed, of a randomized implementation in suppressing possible resonances of the drive with the many-body spectrum, and bound the additional variance that this randomization imposes on observables. Finally, we numerically study aspects of the protocol which are relevant for its practical realization, such as the mixing time.
This thesis develops new algorithms and theoretical frameworks for quantum many-body physics on near-term, noisy quantum simulators. The first half introduces dissipative "cooling algorithms" based on engineered dissipation to robustly prepare ground and thermal states. These protocols are demonstrated experimentally on Google's superconducting qubit processor, and analysed theoretically via effective quasiparticle theory and developments in connection to quantum detailed balance. The second half studies "mixed state phases" in classical non-equilibrium dynamics, and their connection to the conditional mutual information. A new numerical algorithm based on matrix-product states is introduced to compute this quantity for classical systems, and applied in the settings of spin systems quenched to high temperatures, and diffusive particle dynamics, providing new information-theoretic descriptions of non-equilibrium universality classes.
Dissipative state preparation engineers quantum many-body states as steady states of an open-system dynamics. The spatial range of the required dissipation sets both the feasibility of analog implementations and the connectivity and control complexity of digital ones. Yet how this locality quantitatively constrains preparation times remains largely unknown. Here, we establish an exact locality-preparation time relation for quadratic fermionic systems and develop a construction that optimizes the locality of the dissipative dynamics while preserving the target state. Applied to the Kitaev chain, our framework reveals sharply different locality-preparation time tradeoffs in critical and gapped regimes. At criticality, suppressing the algebraic tails of the jump operators necessarily forces the preparation time to grow algebraically with system size. By contrast, both trivial and topological gapped phases admit exponentially localized dissipation with a finite preparation time in the thermodynamic limit. Our results identify when fast dissipative preparation is compatible with local control and when criticality imposes an unavoidable dynamical cost.
Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed-matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for instance, on variational and adiabatic principles, or on dissipative state preparation. In this work, we investigate a set of cooling algorithms in a simple, solvable fermionic model that allows us to identify the mechanisms that underlie the cooling process and, also, those that prevent it. We derive analytical expressions for the cooling dynamics, steady states, and cooling rates in the weak-coupling limit. We find that multifrequency and randomized cycle strategies can significantly enhance the performance of the quantum algorithm and circumvent some of the obstacles. We also analyze the effects of noise and evaluate the conditions under which cooling remains feasible. Furthermore, we present optimized cooling protocols that can significantly enhance cooling performance in the presence of noise. Additionally, we compare cooling and dissipative state preparation and show that, in the model analyzed here, cooling generally achieves lower energies and is more resilient to noise.