Related papers: Quantum walk speedup of backtracking algorithms
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
We initiate the study of quantum algorithms for optimizing approximately convex functions. Given a convex set ${\cal K}\subseteq\mathbb{R}^{n}$ and a function $F\colon\mathbb{R}^{n}\to\mathbb{R}$ such that there exists a convex function…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
In [Wolfram 1982; Wolfram 1983; Wolfram 2002], the backtracking of one-dimensional cellular automata is to find out which of the 2n possible initial configurations of width n evolve to a specific configuration. In this paper, in…
With the help of recent developments in quantum algorithms for semidefinite programming, we discuss the possibility for quantum speedup for the numerical conformal bootstrap in conformal field theory. We show that quantum algorithms may…
We give two quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with $m$ constraint matrices, each of dimension $n$, rank at most $r$, and sparsity $s$. The first algorithm…
Subset-Sum is an NP-complete problem where one must decide if a multiset of $n$ integers contains a subset whose elements sum to a target value $m$. The best-known classical and quantum algorithms run in time $\tilde{O}(2^{n/2})$ and…
In this article we will explore the concept of speedrunning as a representation of a simplified version of quantum mechanics within a classical simulation. This analogy can be seen as a simplified approach to understanding the broader idea…
To investigate the fundamental nature of matter and its interactions, particles are accelerated to very high energies and collided inside detectors, producing a multitude of other particles that are scattered in all directions. As charged…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…
Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno…
This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by…
We present new advances towards achieving exponential quantum speedups for solving optimization problems by low-depth quantum algorithms. Specifically, we focus on families of combinatorial optimization problems that exhibit symmetry and…
The efficient resolution of optimization problems is one of the key issues in today's industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to…