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The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…
In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than…
Quantum computing is expected to transform a range of computational tasks beyond the reach of classical algorithms. In this work, we examine the application of variational quantum algorithms (VQAs) for unsupervised image segmentation to…
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…
Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…
This paper presents the Pauli-based Circuit Optimization, Analysis, and Synthesis Toolchain (PCOAST), a framework for quantum circuit optimizations based on the commutative properties of Pauli strings. Prior work has demonstrated that…
Quantum computing has emerged as a promising alternative for solving combinatorial optimization problems. The standard approach for encoding optimization problems on quantum processing units (QPUs) involves transforming them into their…
A central challenge of applying near-term quantum optimization algorithms to industrially relevant problems is the need to incorporate complex constraints. In general, such constraints cannot be easily encoded in the circuit, and the…
Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…
Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. For instance, the complexity of implementing the permutation of some given unitary transformations can be strictly decreased by allowing…
Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…
Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have…
In recent years, quantum, quantum-inspired, and hybrid algorithms are increasingly showing promise for solving software engineering optimization problems. However, best-intended practices for conducting empirical studies have not yet well…
Computational chemistry is the leading application to demonstrate the advantage of quantum computing in the near term. However, large-scale simulation of chemical systems on quantum computers is currently hindered due to a mismatch between…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…