Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices

Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz

A large ongoing research effort focuses on variational quantum algorithms (VQAs), representing leading candidates to achieve computational speed-ups on current quantum devices. The scalability of VQAs to a large number of qubits, beyond the simulation capabilities of classical computers, is still debated. Two major hurdles are the proliferation of low-quality variational local minima, and the exponential vanishing of gradients in the cost-function landscape, a phenomenon referred to as barren plateaus. In this work, we show that by employing iterative search schemes, one can effectively prepare the ground state of paradigmatic quantum many-body models, also circumventing the barren plateau phenomenon. This is accomplished by leveraging the transferability to larger system sizes of a class of iterative solutions, displaying an intrinsic smoothness of the variational parameters, a result that does not extend to other solutions found via random-start local optimization. Our scheme could be directly tested on near-term quantum devices, running a refinement optimization in a favorable local landscape with nonvanishing gradients

Quantum approximate optimization algorithm applied to the binary perceptron

We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At variance with the usual QAOA applications to MaxCut, or to quantum spin-chains ground state preparation, the classical is characterized by highly non-local multi-spin interactions. Yet, we provide evidence for the existence of optimal solutions for the QAOA parameters, which are among typical instances of the same problem, and we prove numerically an enhanced performance of QAOA over traditional QA. We also investigate on the role of the landscape geometry in this problem. \revision{By artificially breaking this geometrical structure, we show that the detrimental effect of a gap-closing transition, encountered in QA, is also negatively affecting the performance of our QAOA implementation

Complex regional pain syndrome - phenotypic characteristics and potential biomarkers

Complex regional pain syndrome (CRPS) is a pain condition that usually affects a single limb, often following an injury. The underlying pathophysiology seems to be complex and probably varies between patients. Clinical diagnosis is based on internationally agreed-upon criteria, which consider the reported symptoms, presence of signs and exclusion of alternative causes. Research into CRPS biomarkers to support patient stratification and improve diagnostic certainty is an important scientific focus, and recent progress in this area provides an opportunity for an up-to-date topical review of measurable disease-predictive, diagnostic and prognostic parameters. Clinical and biochemical attributes of CRPS that may aid diagnosis and determination of appropriate treatment are delineated. Findings that predict the development of CRPS and support the diagnosis include trauma-related factors, neurocognitive peculiarities, psychological markers, and local and systemic changes that indicate activation of the immune system. Analysis of signatures of non-coding microRNAs that could predict the treatment response represents a new line of research. Results from the past 5 years of CRPS research indicate that a single marker for CRPS will probably never be found; however, a range of biomarkers might assist in clinical diagnosis and guide prognosis and treatment