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Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum…
This paper introduces a new method that combines Artificial Intelligence (AI) and quantum-inspired techniques to improve the efficiency of multi-variable optimization experiments. By using advanced software simulations, this approach…
We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…
Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum…
We study a Grover-type method for Quadratic Unconstrained Binary Optimization (QUBO) problems. For an $n$-dimensional QUBO problem with $m$ nonzero terms, we construct a marker oracle for such problems with a tuneable parameter, $\Lambda…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…
We present a novel quantum optimization-based route compression technique that significantly reduces storage requirements compared to conventional methods. Route optimization systems face critical challenges in efficiently storing selected…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
This paper presents a novel approach to Grover adaptive search (GAS) for a combinatorial optimization problem whose objective function involves spin variables. While the GAS algorithm with a conventional design of a quantum dictionary…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary…
This study proposes a novel method for simplifying inequality constraints in Higher-Order Binary Optimization (HOBO) formulations. The proposed method addresses challenges associated with Quadratic Unconstrained Binary Optimization (QUBO)…
Solving NP-hard constrained combinatorial optimization problems using quantum algorithms remains a challenging yet promising avenue toward quantum advantage. Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
Quantum search algorithms, such as Grover's algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit…