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Adiabatic quantum computing (AQC) is a promising approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for…

We present an analog version of the quantum approximate optimization algorithm suitable for current quantum annealers. The central idea of this algorithm is to optimize the schedule function, which defines the adiabatic evolution. It is…

Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…

Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit,…

Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of…

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast…

We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum…

The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure…

Quantum optimization algorithms can be used to recreate unsupervised learning clustering of data by mapping the problem to a graph optimization problem and finding the minimum energy for a MaxCut problem formulation. This research tests the…

Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are…

Constrained combinatorial optimization problems are challenging for quantum computing, particularly at utility-relevant scales and on near-term hardware. At the same time, these problems are of practical significance in industry; for…

The optimization of the power consumption of antenna networks is a problem with a potential impact in the field of telecommunications. In this work, we investigate the application of the quantum approximate optimization algorithm (QAOA) and…

The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…

Optimizing of a portfolio of financial assets is a critical industrial problem which can be approximately solved using algorithms suitable for quantum processing units (QPUs). We benchmark the success of this approach using the Quantum…

Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization…

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…

Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…

The present tutorial aims to provide a comprehensible and easily accessible introduction into the theory and implementation of the famous Quantum Approximate Optimization Algorithm (QAOA). We lay our focus on practical aspects and…

The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an…

Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass…