Related papers: Decomposition and Gluing for Adiabatic Quantum Opt…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
Controllable adiabatic evolution of a multi-qubit system can be used for adiabatic quantum computation (AQC). This evolution ends at a configuration where the Hamiltonian of the system encodes the solution of the problem to be solved. As a…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting…
Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales,…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Quantum algorithms for combinatorial optimization typically encode constraints as soft penalties within the objective function, which can reduce efficiency and scalability compared to state-of-the-art classical methods that instead exploit…
A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation generated considerable interest, motivating efforts to design efficient…
We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n…
Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers…
Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires…
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size,…
Quantum annealing aims at solving hard computational problems through adiabatic state preparation. Here, I propose to use inhomogeneous longitudinal magnetic fields to enhance the efficiency of the annealing. Such fields are able to bias…
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…
The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and…
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($k\geq 3$) terms to quadratic terms…
The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…