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.

Two matrix product states (MPS) are in the same phase in the presence of symmetries if they can be transformed into one another via symmetric short-depth circuits. We consider how symmetry-preserving measurements with feedforward alter the phase classification of MPS in the presence of global on-site symmetries. We demonstrate that, for all finite Abelian symmetries, any two symmetric MPS belong to the same phase. We give an explicit protocol that achieves a transformation between any two phases and that uses only a depth-two symmetric circuit, a single round of symmetric measurements, and a constant number of auxiliary systems per site. In the case of non-Abelian symmetries, symmetry protection prevents one from deterministically transforming symmetry-protected topological (SPT) states to product states directly via measurements, thereby complicating the analysis. Nonetheless, we provide protocols that allow for asymptotically deterministic transformations between the trivial phase, SPT phases, and GHZ phases of some non-Abelian nilpotent groups.

We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present and compare various methods and strategies to learn the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare different ans & auml,.tze based on an experimentally accessible 'learning error' which we consider as a function of the number of runs of the experiment. Initially, the learning error decreases with the inverse square root of the number of runs, as the error in the reconstructed parameters is dominated by shot noise. Eventually the learning error remains constant, allowing us to recognize missing ansatz terms. A central aspect of our approaches is to (re-)parametrize ans & auml,.tze by introducing and varying the dependencies between parameters. This allows us to identify the relevant parameters of the system, thereby reducing the complexity of the learning task. Importantly, this (re-)parametrization relies solely on classical post-processing, which is compelling given the finite amount of data available from experiments. We illustrate and compare our methods with two experimentally relevant spin models.

We present verification protocols to gain confidence in the correct performance of a device implementing an arbitrary quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and statistics to derive verification circuits that (i) strongly resemble the original circuit and (ii) can be classically efficiently simulated not only in the ideal, i.e., error free scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state.

We determine the local symmetries and local transformation properties of certain many-body states called translationally invariant matrix product states (TIMPSs). We focus on physical dimension d = 2 of the local Hilbert spaces and bond dimension D = 3 and use the procedure introduced in Sauerwein et al. [Phys. Rev. Lett. 123, 170504 (2019)] to determine all (including nonglobal) symmetries of those states. We identify and classify the stochastic local operations assisted by classical communication (SLOCC) that are allowed among TIMPSs. We scrutinize two very distinct sets of TIMPSs and show the big diversity (also compared to the case D = 2) occurring in both their symmetries and the possible SLOCC transformations. These results reflect the variety of local properties of MPSs, even if restricted to translationally invariant states with low bond dimension. Finally, we show that states with nontrivial local symmetries are of measure zero for d = 2 and D > 3.

We analyze entanglement in the family of translationally invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by local operations with a nonvanishing probability, a central question in entanglement theory. This induces a classification within this family of states, which we explicitly carry out for the simplest, nontrivial MPS. We also characterize all symmetries of translationally invariant MPS, both global and local (inhomogeneous). We illustrate our results with examples of states that are relevant in different physical contexts.