arXiv subjects

Luca Asproni

Publications and source records attributed to Luca Asproni.

4 recordsLinked to original sources

arXiv2023

A real world test of Portfolio Optimization with Quantum Annealing

In this note, we describe an experiment on portfolio optimization using the Quadratic Unconstrained Binary Optimization (QUBO) formulation. The dataset we use is taken from a real-world problem for which a classical solution is currently deployed and used in production. In this work, carried out in a collaboration between the Raiffeisen Bank International (RBI) and Reply, we derive a QUBO formulation, which we solve using various methods: two D-Wave hybrid solvers, that combine the employment of a quantum annealer together with classical methods, and a purely classical algorithm. Particular focus is given to the implementation of the constraint that requires the resulting portfolio's variance to be below a specified threshold, whose representation in an Ising model is not straightforward. We find satisfactory results, consistent with the global optimum obtained by the exact classical strategy. However, since the tuning of QUBO parameters is crucial for the optimization, we investigate a hybrid method that allows for automatic tuning.

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arXiv2023

Diversifying Investments and Maximizing Sharpe Ratio: a novel QUBO formulation

The Portfolio Optimization task has long been studied in the Financial Services literature as a procedure to identify the basket of assets that satisfy desired conditions on the expected return and the associated risk. A well-known approach to tackle this task is the maximization of the Sharpe Ratio, achievable with a problem reformulation as Quadratic Programming. While the sole Sharpe Ratio could be efficiently optimized via classical solvers, in business scenarios it is common that multiple additional needs arise, which have to be integrated in the optimization model as either new constraints or objective function terms. Then, in general, the problem may become non-convex and hence could potentially be not efficiently solvable via classical techniques anymore. One example of such additional objective function term consists of maximizing a diversification measure penalizing portfolios holding significant portions of investments on assets belonging to the same sector, while favouring solutions that diversify over multiple sectors. The problem of optimizing both the Sharpe Ratio and a diversification term can be mapped to a QUBO and be solved via quantum annealing devices or Hybrid Computing approaches, which are expected to find high quality solutions. We propose a new QUBO formulation for the task described and provide the mathematical details and required assumptions, showing the ease of modeling the optimization as QUBO against the effort that would be required by classical strategies. We derive results via the available QUBO solvers, as well as discussing the behaviour of Hybrid approaches to tackle large scale problems in the near term. We finally elaborate on the results showing the trade-off between the observed values of the portfolio's Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

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arXiv2021

Using Shor's algorithm on near term Quantum computers: a reduced version

Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in polynomial time. However, both the number of qubits and applied gates detrimentally affect the ability to run a particular quantum circuit on the near term Quantum hardware. In this work, we help addressing both these problems by introducing a reduced version of Shor's algorithm that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices. The implementation presented in this work is general and does not use any assumptions on the number to factor. In particular, we have found noteworthy results in most cases, often being able to factor the given number with only one iteration of the proposed algorithm. Finally, comparing the original quantum algorithm with our version on simulator, the outcomes are identical for some of the numbers considered.

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arXiv2019

Accuracy and minor embedding in subqubo decomposition with fully connected large problems: a case study about the number partitioning problem

In this work we investigate the capabilities of a hybrid quantum-classical procedure to explore the solution space using the D-Wave $2000Q^{TM}$ Quantum Annealer device. Here we study the ability of the Quantum hardware to solve the Number Partitioning Problem, a well-known NP-Hard optimization model that poses some challenges typical of those encountered in real-world applications. This represents one of the most complex scenario in terms of qubits connectivity and, by increasing the input problem size, we analyse the scaling properties of the quantum-classical workflow. We find remarkable results in most instances of the model; for the most complex ones, we investigate further the D-Wave Hybrid suite. Specifically, we were able to find the optimal solutions even in the worst cases by fine-tuning the parameters that schedule the annealing time and allowing a pause in the annealing cycle.

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