Related papers: Constraint-oriented biased quantum search for gene…
In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid…
I propose a "quantum annealing" heuristic for the problem of combinatorial search among a frustrated set of states characterized by a cost function to be minimized. The algorithm is probabilistic, with postselection of the measurement…
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved…
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…
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,…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size…
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm that offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
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).…
We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…