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Brief description on the state of the art of some local optimization methods: Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal…
Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result…
Quantum annealing devices such as the ones produced by D-Wave systems are typically used for solving optimization and sampling tasks, and in both academia and industry the characterization of their usefulness is subject to active research.…
The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…
We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum…
Optimizing the training of a machine learning pipeline helps in reducing training costs and improving model performance. One such optimizing strategy is quantum annealing, which is an emerging computing paradigm that has shown potential in…
The difficulty of training variational quantum algorithms and quantum machine learning models is well established. In particular, quantum loss landscapes are often highly non-convex and dominated by poor local minima. While this renders…
All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
The use of quantum annealers in black-box optimization to obtain the desired properties of a product with a small number of trials has attracted attention. However, the application of this technique to engineering design problems is still…
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial…
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…
Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…
Quantum annealing has emerged as a powerful platform for simulating and optimizing classical and quantum Ising models. Quantum annealers, like other quantum and/or analog computing devices, are susceptible to nonidealities including…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical…
Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such…
Decoherence severely limits the performance of quantum processors, posing challenges to reliable quantum computation. Probabilistic error cancellation, a quantum error mitigation method, counteracts noise by quasiprobabilistically…