Related papers: Quantum solvability of noisy linear problems by di…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum…
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring…
Recent advancements in quantum computing, alongside successful deployments of quantum communication, hold promises for revolutionizing mobile networks. While Quantum Machine Learning (QML) presents opportunities, it contends with challenges…
This paper has two messages. First, we demonstrate that neural networks that process noisy data can learn to exploit, when available, access to auxiliary noise that is correlated with the noise on the data. In effect, the network learns to…
Access to quantum computing is steadily increasing each year as the speed advantage of quantum computers solidifies with the growing number of usable qubits. However, the inherent noise encountered when running these systems can lead to…
Advancements in quantum computing have spurred significant interest in harnessing its potential for speedups over classical systems. However, noise remains a major obstacle to achieving reliable quantum algorithms. In this work, we present…
Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales,…
The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the…
Quantum computers have the potential to solve problems that are intractable to classical computers, nevertheless they have high error rates. One significant kind of errors is known as Readout Errors. Current methods, as the matrix inversion…
Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A $n$-qubit quantum system is capable of providing $2^{n}$ computational space…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…
Quantum heuristics have shown promise in solving various optimization problems, including lattice protein folding. Equally relevant is the inverse problem, protein design, where one seeks sequences that fold to a given target structure. The…
Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of…
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…