Related papers: An evolving objective function for improved variat…

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the…

We incorporate the conditional value-at-risk (CVaR) quantity into a generalized class of Pickands estimators. By introducing CVaR, the newly developed estimators not only retain the desirable properties of consistency, location, and scale…

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading…

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertainty. As an example, we focus on the so-called Conditional…

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem…

We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we…

Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the…

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…

We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly…

Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…

Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…

The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA…

A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can…

Quantum enhanced optimization of classical cost functions is a central theme of quantum computing due to its high potential value in science and technology. The variational quantum eigensolver (VQE) and the quantum approximate optimization…

Risk sensitive decision making finds important applications in current day use cases. Existing risk measures consider a single or finite collection of random variables, which do not account for the asymptotic behaviour of underlying…

Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…