Analytic Theory for the Dynamics of Wide Quantum Neural Networks.

Parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.

Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets.

The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.

Quantum algorithms for quantum dynamics.

Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.

Charging a quantum battery via nonequilibrium heat current.

When a quantum system is subject to a thermal gradient it may sustain a steady nonequilibrium heat current by entering into a so-called nonequilibrium steady state (NESS). Here we show that NESS constitute a thermodynamic resource that can be exploited to charge a quantum battery. This adds to the list of recently reported sources available at the nanoscale, such as coherence, entanglement, and quantum measurements. We elucidate this concept by showing analytic and numerical studies of a two-qubit quantum battery that is alternatively charged by an incoherent heat flow and discharged by application of a properly chosen unitary gate. The presence of a NESS for the charging step guarantees steady operation with positive power output. Decreasing the duration of the charging step results in a time-periodic steady state accompanied by increased efficiency and output power. The device is amenable to implementation with different nanotechnology platforms.

Optimal efficiency of the Q-cycle mechanism around physiological temperatures from an open quantum systems approach.

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models. Here we address the problem of energy transport across the cellular membrane from an open quantum system theoretical perspective. We model the cytochrome [Formula: see text] protein complex under cyclic electron flow conditions starting from a simplified kinetic model, which is hereby revisited in terms of a Markovian quantum master equation formulation and spin-boson Hamiltonian treatment. We apply this model to theoretically demonstrate an optimal thermodynamic efficiency of the Q-cycle around ambient and physiologically relevant temperature conditions. Furthermore, we determine the quantum yield of this complex biochemical process after setting the electrochemical potentials to values well established in the literature. The present work suggests that the theory of quantum open systems can successfully push forward our theoretical understanding of complex biological systems working close to the quantum/classical boundary.