Related papers: Limits of quantum speed-ups for computational geom…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
We study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function $f:\mathbb{R}^n \to \mathbb{R}$ and its (sub)gradient. Our goal is to find an $\epsilon$-approximate minimum of $f$…
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…
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 first give an $\O(2^{n/3})$ quantum algorithm for the 0-1 Knapsack problem with $n$ variables. More generally, for 0-1 Integer Linear Programs with $n$ variables and $d$ inequalities we give an $\O(2^{n/3}n^d)$ quantum algorithm. For $d…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
An unstructured search for one item out of N can be performed quantum mechanically in time of order square root of N whereas classically this requires of order N steps. This raises the question of whether square root speedup persists in…
While seemingly undesirable, it is not a surprising fact that there are certain problems for which quantum computers offer no computational advantage over their respective classical counterparts. Moreover, there are problems for which there…
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…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Energy consumption in solving computational problems has been gaining growing attention as one of the key performance measures for computers. Quantum computation is known to offer advantages over classical computation in terms of various…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Simon's problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the…
We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…