arXiv subjects

Giacomo Nannicini

Publications and source records attributed to Giacomo Nannicini.

27 records · Page 2Linked to original sources

arXiv2020

An Introduction to Quantum Computing, Without the Physics

This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics, stressing the differences with classical computers, and finally describe two well-known algorithms (Simon's algorithm and Grover's algorithm) using the formalism developed in previous sections. This paper does not touch on the physics of the devices, and therefore does not require any notion of quantum mechanics. Numerical examples on an implementation of Grover's algorithm using open-source software are provided.

cs.DM↗

arXiv2019

Leveraging Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits

In a recent paper, we showed that secondary storage can extend the range of quantum circuits that can be practically simulated with classical algorithms. Here we refine those techniques and apply them to the simulation of Sycamore circuits with 53 and 54 qubits, with the entanglement pattern ABCDCDAB that has proven difficult to classically simulate with other approaches. Our analysis shows that on the Summit supercomputer at Oak Ridge National Laboratories, such circuits can be simulated with high fidelity to arbitrary depth in a matter of days, outputting all the amplitudes.

quant-ph↗

arXiv2018

Performance of hybrid quantum/classical variational heuristics for combinatorial optimization

The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.

quant-ph↗

arXiv2018

Toward breaking the curse of dimensionality: an FPTAS for stochastic dynamic programs with multidimensional actions and scalar states

We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by parametric linear programs. This type of problems finds applications in the area of optimal planning under uncertainty, and can be thought of as the problem of optimally managing a single non-discrete resource over a finite time horizon. We show that under a value oracle model for the cost functions this result for one-dimensional state space is "best possible", because a similar dynamic programming model with two-dimensional state space does not admit a PTAS. The FPTAS relies on the solution of polynomial-sized linear programs to recursively compute an approximation of the value function at each stage. Our paper enlarges the class of dynamic programs that admit an FPTAS by showing, under suitable conditions, how to deal with multidimensional action spaces and with vectors of continuous random variables with bounded support. These results bring us one step closer to overcoming the curse of dimensionality of dynamic programming.

cs.DM↗

arXiv2017

Globally Optimal Symbolic Regression

In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by rediscovering Kepler's law on planetary motion using exoplanet data and Galileo's pendulum periodicity equation using experimental data.

stat.ML↗

arXiv2017

An effective algorithm for hyperparameter optimization of neural networks

A major challenge in designing neural network (NN) systems is to determine the best structure and parameters for the network given the data for the machine learning problem at hand. Examples of parameters are the number of layers and nodes, the learning rates, and the dropout rates. Typically, these parameters are chosen based on heuristic rules and manually fine-tuned, which may be very time-consuming, because evaluating the performance of a single parametrization of the NN may require several hours. This paper addresses the problem of choosing appropriate parameters for the NN by formulating it as a box-constrained mathematical optimization problem, and applying a derivative-free optimization tool that automatically and effectively searches the parameter space. The optimization tool employs a radial basis function model of the objective function (the prediction accuracy of the NN) to accelerate the discovery of configurations yielding high accuracy. Candidate configurations explored by the algorithm are trained to a small number of epochs, and only the most promising candidates receive full training. The performance of the proposed methodology is assessed on benchmark sets and in the context of predicting drug-drug interactions, showing promising results. The optimization tool used in this paper is open-source.

cs.AI↗

arXiv2015

Layered 2D crystals by design: optimisation of Sb$_2$Te$_3$-GeTe van der Waals superlattices

Herein a genetic algorithm for optimising the design of layered 2D heterostructure is proposed. As a proof-of-concept it is applied to Sb$_2$Te$_3$-GeTe phase-change material superlattices, and the resulting lowest energy structure is grown experimentally. The similarity of the computational and experimental structures is verified with the comparison of XRD spectra. The structure is found to be within 0.92 meV/at. from the energetically most favorable known structure for Ge$_2$Sb$_2$Te$_5$.

cond-mat.mtrl-sci↗

arXiv2008

A local branching heuristic for MINLPs

Local branching is an improvement heuristic, developed within the context of branch-and-bound algorithms for MILPs, which has proved to be very effective in practice. For the binary case, it is based on defining a neighbourhood of the current incumbent solution by allowing only a few binary variables to flip their value, through the addition of a local branching constraint. The neighbourhood is then explored with a branch-and-bound solver. We propose a local branching scheme for (nonconvex) MINLPs which is based on iteratively solving MILPs and NLPs. Preliminary computational experiments show that this approach is able to improve the incumbent solution on the majority of the test instances, requiring only a short CPU time. Moreover, we provide algorithmic ideas for a primal heuristic whose purpose is to find a first feasible solution, based on the same scheme.

math.CO↗

arXiv2007

Fast paths in large-scale dynamic road networks

Efficiently computing fast paths in large scale dynamic road networks (where dynamic traffic information is known over a part of the network) is a practical problem faced by several traffic information service providers who wish to offer a realistic fast path computation to GPS terminal enabled vehicles. The heuristic solution method we propose is based on a highway hierarchy-based shortest path algorithm for static large-scale networks; we maintain a static highway hierarchy and perform each query on the dynamically evaluated network.

cs.NI↗