Stationary states of quantum many-body Hamiltonians are invariant under the Hamiltonian evolution. Besides ground and thermal states, this class includes microcanonical ensembles that are of fundamental importance in statistical physics. We consider the preparation of general stationary states by leveraging recent advances in the field of open-system dynamics. In particular, constructions based on exact KMS-detailed balance with respect to Gibbs states of noncommuting Hamiltonians have only recently been proposed as a tool for their efficient preparation and, by extension to small temperatures, for ground state preparation. We extend these constructions to the problem of stationary state preparation, providing general criteria that characterize when such states have efficient implementations, along with specific results on the approximation of microcanonical ensembles. An interesting application of our work are tests of conjectured ensemble equivalences for local observables between microcanonical and Gibbs ensembles.
Stationary states of quantum many-body Hamiltonians are invariant under the Hamiltonian evolution. Besides ground and thermal states, this class includes microcanonical ensembles that are of fundamental importance in statistical physics. We consider the preparation of general stationary states by leveraging recent advances in the field of open-system dynamics. In particular, constructions based on exact KMS-detailed balance with respect to Gibbs states of noncommuting Hamiltonians have only recently been proposed as a tool for their efficient preparation and, by extension to small temperatures, for ground state preparation. We extend these constructions to the problem of stationary state preparation, providing general criteria that characterize when such states have efficient implementations, along with specific results on the approximation of microcanonical ensembles. An interesting application of our work are tests of conjectured ensemble equivalences for local observables between microcanonical and Gibbs ensembles.
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many scenarios where this is not possible and one must instead use another ensemble, such as the diagonal, microcanonical or generalized Gibbs ensembles. However, these all require detailed information about the energy or other conserved quantities to be constructed. Here we propose a general and computationally easy approach to determine the stationary probability distribution of observables with few outcomes. Interpreting coarse measurements at equilibrium as noisy communication channels, we provide general analytical arguments in favor of the applicability of a maximum entropy principle for this class of observables. We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 non-weakly interacting spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework in both quantum integrable and chaotic models.
Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems, with Hamiltonians with vanishingly small energy spacings that forbid that approximation. The equation satisfies a general form of detailed balance, called KMS (Kubo-Martin-Schwinger), which ensures exact convergence to the many-body Gibbs state. Unlike the more common notion of GNS (Gelfand-Naimark-Segal) detailed balance, this notion is compatible with the absence of the rotating wave approximation. We show that the resulting Lindbladian dynamics not only reproduces the thermal equilibrium point up to a small renormalization of the system Hamiltonian, but it also approximates the true system evolution with an error that grows at most linearly in time, giving an exponential improvement upon previous estimates. This master equation has quasilocal jump operators, can be efficiently simulated on a quantum computer, and reduces to the usual Davies dynamics in the limit of a coarse-graining time much larger than the inverse of the smallest frequency difference. With it, we provide a rigorous model of many-body thermalization relevant to both open quantum systems and quantum algorithms.
We investigate quantum thermal state preparation algorithms based on system-bath interactions and uncover a surprising phenomenon in the weak-coupling regime. We rigorously prove that, if the system-bath interaction is engineered so that the transition part of the approximate Lindbladian generator satisfies the Kubo--Martin--Schwinger (KMS) detailed balance condition, then the unique fixed point of the dynamics can be made arbitrarily close to the Gibbs state in the weak-coupling limit, regardless of the structure of the Lamb shift term. Importantly, this remains true even when the approximate Lindbladian differs substantially from the ideal Davies generator and the Lamb shift term does not commute with the thermal state. Our result shows that the role of the KMS detailed balance condition extends well beyond standard Lindbladian dynamics, serving as a general principle for a broader class of dissipative systems. Furthermore, by combining this with a general perturbation framework, we bound the mixing time of the dynamics and establish an end-to-end complexity of O(ε−1) for Gibbs state preparation. These guarantees apply to any Hamiltonian whose associated KMS-detailed-balance Lindbladian is known to be fast mixing.
Estimating thermal expectation values of quantum many-body systems is a central challenge in physics, chemistry, and materials science. Standard quantum Gibbs sampling protocols address this task by preparing the Gibbs state from scratch after every measurement, incurring a full mixing time cost at each step. Recent advances in single-trajectory Gibbs sampling [Jiang et al. 2026] substantially reduce this overhead: once stationarity is reached, measurements can be collected along a single trajectory without re-thermalizing, provided the measurement channel preserves the Gibbs ensemble. However, explicit constructions of such non-destructive measurements have been limited primarily to observables that commute with the Hamiltonian. In this work, we fundamentally extend the single-trajectory framework to arbitrary, non-commuting observables. We provide two measurement constructions that extract measurement information without fully destroying the Gibbs state, thereby eliminating the need for full re-mixing between samples.
First, we construct a measurement that satisfies exact detailed balance. This ensures the system remains in equilibrium throughout the trajectory, allowing measurement outcomes to decorrelate in an autocorrelation time that could be significantly shorter than the global mixing time. Second, assuming the underlying quantum Gibbs sampler has a positive spectral gap, we design a simplified measurement scheme that ensures the post-selected state serves as a warm start for rapid re-mixing. This approach successfully decouples the resampling cost from the global mixing time. Both measurement schemes admit efficient quantum circuit implementations, requiring only polylogarithmic Hamiltonian simulation time.
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced dissipative evolution, inspired by existing models of open system thermalization, has been shown to be efficiently implementable on a quantum computer. Here, we prove that, at high enough temperatures, this evolution reaches the Gibbs state in time scaling logarithmically with system size. The result holds for Hamiltonians that satisfy the Lieb-Robinson bound, such as local Hamiltonians on a lattice, and includes long-range systems. To the best of our knowledge, these are the first results rigorously establishing the rapid mixing property of high-temperature quantum Gibbs samplers, which is known to give the fastest possible speed for thermalization in the many-body setting. We then apply our result to the problem of estimating partition functions at high temperature, showing an improved performance over previous classical and quantum algorithms.
Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of noncommuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Together, these results show that dissipation can be a powerful tool for ground state preparation, with potential applications across condensed matter physics, quantum materials science, and beyond.