A quantum unstructured search algorithm for discrete optimisation: the use case of portfolio optimisation

Titos Matsakos and Adrian Lomas

Papers from arXiv.org

Abstract: We propose a quantum unstructured search algorithm to find the extrema or roots of discrete functions, $f(\mathbf{x})$, such as the objective functions in combinatorial and other discrete optimisation problems. The first step of the Quantum Search for Extrema and Roots Algorithm (QSERA) is to translate conditions of the form $f(\mathbf{x}_*) \simeq f_*$, where $f_*$ is the extremum or zero, to an unstructured search problem for $\mathbf{x}_*$. This is achieved by mapping $f(\mathbf{x})$ to a function $u(z)$ to create a quantum oracle, such that $u(z_*) = 1$ and $u(z \neq z_*) = 0$. The next step is to employ Grover's algorithm to find $z_*$, which offers a quadratic speed-up over classical algorithms. The number of operations needed to map $f(\mathbf{x})$ to $u(z)$ determines the accuracy of the result and the circuit depth. We describe the implementation of QSERA by assembling a quantum circuit for portfolio optimisation, which can be formulated as a combinatorial problem. QSERA can handle objective functions with higher order terms than the commonly-used Quadratic Unconstrained Binary Optimisation (QUBO) framework. Moreover, while QSERA requires some a priori knowledge of the extrema of $f(\mathbf{x})$, it can still find approximate solutions even if the conditions are not exactly satisfied.

Date: 2025-05
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2505.14645 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2505.14645

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().