Related papers: The Short Path Algorithm Applied to a Toy Model
We propose a circuit-model quantum algorithm for eigenpath traversal that is based on a combination of concepts from Grover's search and adiabatic quantum computation. Our algorithm deploys a sequence of reflections determined from…
We analyze generalizations of quantum algorithms based on the short path framework first proposed by Hastings~[\textit{Quantum} 2, 78 (2018)], which has been extended and shown by Dalzell~et~al.~[STOC~'23] to achieve super-Grover speedups…
With the recent influx in demand for multi-robot systems throughout industry and academia, there is an increasing need for faster, robust, and generalizable path planning algorithms. Similarly, given the inherent connection between control…
Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this…
The short-path quantum algorithm introduced by Hastings (Quantum 2018, 2019) is a variant of adiabatic quantum algorithms that enables an easier worst-case analysis by avoiding the need to control the spectral gap along a long adiabatic…
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…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
We study the process-level dynamics of Thompson sampling and related sampling-based bandit algorithms in the ``small gap'' regime, where the gaps between the arm means are of order $\sqrt{\gamma}$ or smaller and the time horizon is of order…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
We provide and analyze examples that counter the widely made claim that tunneling is needed for a quantum speedup in optimization problems. The examples belong to the class of perturbed Hamming-weight optimization problems. In one case,…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Two directions in algorithms and complexity involve: (1) classifying which optimization problems can be solved in polynomial time, and (2) understanding which computational problems are hard to solve \emph{on average} in addition to the…
In robotics, methods and softwares usually require optimizations of hyperparameters in order to be efficient for specific tasks, for instance industrial bin-picking from homogeneous heaps of different objects. We present a developmental…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…