Related papers: Quantum speedup of leverage score sampling and its…
It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that…
We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
There have been multiple attempts to design synthetic benchmark problems with the goal of detecting quantum speedup in current quantum annealing machines. To date, classical heuristics have consistently outperformed quantum-annealing based…
We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit…
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and…
Q-learning is a stochastic approximation version of the classic value iteration. The literature has established that Q-learning suffers from both maximization bias and slower convergence. Recently, multi-step algorithms have shown practical…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
Several quantum algorithms for linear algebra problems, and in particular quantum machine learning problems, have been "dequantized" in the past few years. These dequantization results typically hold when classical algorithms can access the…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA),…
Mixed Integer Programs (MIPs) model many optimization problems of interest in Computer Science, Operations Research, and Financial Engineering. Solving MIPs is NP-Hard in general, but several solvers have found success in obtaining…