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Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
We present a quantum interior-point method (IPM) for second-order cone programming (SOCP) that runs in time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$ where $r$ is the rank and $n$…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
Quantum Interior Point Methods (QIPMs) have been attracting significant interests recently due to their potential of solving optimization problems substantially faster than state-of-the-art conventional algorithms. In general, QIPMs use…
The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a…
Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve…
Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a…
Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major challenge is that QLSAs are inexact and sensitive to the condition number of the coefficient matrices of linear systems.…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
Quantum interior point methods (QIPMs) promise polynomial speed-ups over classical solvers for linear programming by outsourcing the solution of Newton linear systems to quantum linear solvers (QLSAs). However, asymptotic speed-ups do not…
Vigorous optimization of quantum gates has led to bipotent quantum architectures, where the optimized gates are available for some qubits but not for others. However, such gate-level improvements limit the application of user-side…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
This paper presents three quantum interior-point methods (QIPMs) tailored to tackle the DC optimal power flow (DCOPF) problem using noisy intermediate-scale quantum devices. The optimization model is redefined as a linearly constrained…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
We present an algorithm which efficiently estimates the intrinsic long-term value of a portfolio of assets on a quantum computer. The method relies on quantum amplitude estimation to estimate the mean of a novel implementation of the…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…