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A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
In finance, assessing the creditworthiness of loan applicants requires lenders to cluster borrowers using rating scales. Financial institutions must define the scales in compliance with strict institutional constraints, resulting in solving…
Designing molecules with optimized properties remains a fundamental challenge due to the intricate relationship between molecular structure and properties. Traditional computational approaches that address the combinatorial number of…
Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of…
Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. VQAs are based on a parameterized quantum circuit optimized in a closed loop via a classical algorithm. This hybrid…
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA),…
Variational quantum algorithms are a promising hybrid framework for solving chemistry and physics problems with broad applicability to optimization as well. They are particularly well suited for noisy intermediate scale quantum (NISQ)…
Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful…
We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary operator is…
The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a…
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…
Considerable effort has been made recently in the development of heuristic quantum algorithms for solving combinatorial optimization problems. Meanwhile, these problems have been studied extensively in classical computing for decades. In…
Variational Quantum Eigensolver (VQE) faces significant challenges due to hardware noise and the presence of barren plateaus and local traps in the optimization landscape. To mitigate the detrimental effects of these issues, we introduce a…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
With the applications of quantum computing becoming more and more widespread, finding ways that allow end users without experience in the field to apply quantum computers to solve their individual problems is becoming a crucial task.…
Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here,…
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this work, we introduce a new benchmark for variational quantum algorithm (VQA), recently proposed as…