Related papers: Quantum Adiabatic Computation and the Travelling S…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
A quantum search algorithm based on the partial adiabatic evolution\cite{Tulsi2009} is provided. We calculate its time complexity by studying the Hamiltonian in a two-dimensional Hilbert space. It is found that the algorithm improves the…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to…
We propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm…
The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known algorithms in the worst case instances…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…
Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. The association step naturally leads to discrete optimization problems. As these optimization…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
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…
Perturbed Hamming weight problems serve as examples of optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work we study the efficiency of the adiabatic algorithm for solving…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…
The potential analysis of the capabilities of quantum computing, especially before fault tolerance at scale, is difficult due to the variety of existing hardware technologies with a wide spread of maturity. Not only the result of…
We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal,…
We study the glued-trees problem of Childs et. al. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the…
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
The cost and the error of the adiabatic theorem for preparing the final eigenstate are discussed in terms of path length. Previous studies in terms of the norm of the Hamiltonian and its derivatives with the spectral gap are limited in…