We study noise-averaged observables for a system of exchange-coupled quantum spins (qubits), each subject to a stochastic drive, by establishing mappings onto stochastic models in the strongnoise limit. Averaging over noise yields Lindbladian equations of motion; when these are subjected to a strong-noise perturbative treatment, classical master equations are found to emerge. The dynamics of noise averages of operators displays diffusive behaviour or exponential relaxation, depending on whether the drive conserves one of the spin components or not. In the latter case, the second moment of operators -from which the average subsystem purity and out-of-time-order correlation functions can be extracted -is described by the Fredrickson-Andersen model, originally introduced as a model of cooperative relaxation near the glass transition. It is known that fluctuations of a ballistically propagating front in the model are asymptotically Gaussian in one dimension. We extend this by conjecturing, with strong numerical evidence, that in two dimensions the long-time fluctuations are in the Kardar-Parisi-Zhang universality class, complementing a similar observation in random unitary circuits.

It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent, where all probes are measured simultaneously in an entangled basis; and adaptive, where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strategies yield the same precision. Secondly, we construct an example of a noisy multipartite quantum system where coherent readout yields considerably better precision than adaptive readout. This highlights a fundamental difference between classical and quantum parameter estimation. From the practical point of view, our findings are relevant for the optimal design of precisionmeasurement quantum devices.

We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.

We describe a method to predict and control the lattice parameters of hexagonal and gyroid mesoporous materials formed by liquid crystal templating. In the first part, we describe a geometric model with which the lattice parameters of different liquid crystal mesophases can be predicted as a function of their water/surfactant/oil volume fractions, based on certain geometric parameters relating to the constituent surfactant molecules. We demonstrate the application of this model to the lamellar (Lα), hexagonal (H1), and gyroid bicontinuous cubic (V1) mesophases formed by the binary Brij-56 (C16EO10)/water system and the ternary Brij-56/hexadecane/water system. In this way, we demonstrate predictable and independent control over the size of the cylinders (with hexadecane) and their spacing (with water). In the second part, we produce mesoporous platinum using as templates hexagonal and gyroid phases with different compositions and show that in each case the symmetry and lattice parameter of the metal nanostructure faithfully replicate those of the liquid crystal template, which is itself in agreement with the model. This demonstrates a rational control over the geometry, size, and spacing of pores in a mesoporous metal.