Related papers: Quantum Time-Space Tradeoffs for Matrix Problems
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Many search-based quantum algorithms that achieve a theoretical speedup are not practically relevant since they require extraordinarily long coherence times, or lack the parallelizability of their classical counterparts.This raises the…
In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time,…
We prove a general upper bound on the tradeoff between time and space that suffices for the reversible simulation of irreversible computation. Previously, only simulations using exponential time or quadratic space were known. The tradeoff…
The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…
Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
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…
In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…