Arjan Cornelissen
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View article: Quantum Search With Generalized Wildcards
Quantum Search With Generalized Wildcards Open
In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a s…
View article: Quantum walks through generalized graph composition
Quantum walks through generalized graph composition Open
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The in…
View article: Improved Quantum Query Upper Bounds Based on Classical Decision Trees
Improved Quantum Query Upper Bounds Based on Classical Decision Trees Open
Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and pro…
View article: Quantum algorithms through graph composition
Quantum algorithms through graph composition Open
In this work, we introduce the graph composition framework, a generalization of the st-connectivity framework for generating quantum algorithms, where the availability of each of the graph's edges is computed by a span program. We provide …
View article: How to Compute the Volume in Low Dimension?
How to Compute the Volume in Low Dimension? Open
Estimating the volume of a convex body is a canonical problem in theoretical computer science. Its study has led to major advances in randomized algorithms, Markov chain theory, and computational geometry. In particular, determining the qu…
View article: Quantum Sabotage Complexity
Quantum Sabotage Complexity Open
Given a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the goal in the usual query model is to compute $f$ on an unknown input $x \in \{0,1\}^n$ while minimizing the number of queries to $x$. One can also consider a "distinguishing" problem den…
View article: A Sublinear-Time Quantum Algorithm for Approximating Partition Functions
A Sublinear-Time Quantum Algorithm for Approximating Partition Functions Open
We present a novel quantum algorithm for estimating Gibbs partition functions\nin sublinear time with respect to the logarithm of the size of the state space.\nThis is the first speed-up of this type to be obtained over the seminal\nnearly…
View article: Quantum Policy Gradient Algorithms
Quantum Policy Gradient Algorithms Open
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning…
View article: Quantum policy gradient algorithms
Quantum policy gradient algorithms Open
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning…
View article: Quantum tomography using state-preparation unitaries
Quantum tomography using state-preparation unitaries Open
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for $\ell_q$-n…
View article: Near-optimal Quantum algorithms for multivariate mean estimation
Near-optimal Quantum algorithms for multivariate mean estimation Open
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian estimato…
View article: Improved Quantum Query Upper Bounds Based on Classical Decision Trees
Improved Quantum Query Upper Bounds Based on Classical Decision Trees Open
Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and pro…
View article: Exact quantum query complexity of computing Hamming weight modulo powers of two and three
Exact quantum query complexity of computing Hamming weight modulo powers of two and three Open
We study the problem of computing the Hamming weight of an $n$-bit string modulo $m$, for any positive integer $m \leq n$ whose only prime factors are 2 and 3. We show that the exact quantum query complexity of this problem is $\left\lceil…
View article: Near-Optimal Quantum Algorithms for Multivariate Mean Estimation
Near-Optimal Quantum Algorithms for Multivariate Mean Estimation Open
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian estimato…
View article: Quantum algorithms for multivariate Monte Carlo estimation
Quantum algorithms for multivariate Monte Carlo estimation Open
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
View article: Scalable Benchmarks for Gate-Based Quantum Computers
Scalable Benchmarks for Gate-Based Quantum Computers Open
In the near-term "NISQ"-era of noisy, intermediate-scale, quantum hardware and beyond, reliably determining the quality of quantum devices becomes increasingly important: users need to be able to compare them with one another, and make an …
View article: Span Programs and Quantum Time Complexity.
Span Programs and Quantum Time Complexity. Open
Span programs are an important model of quantum computation due to their tight correspondence with quantum query complexity. For any decision problem $f$, the minimum complexity of a span program for $f$ is equal, up to a constant factor, …
View article: Span Programs and Quantum Time Complexity
Span Programs and Quantum Time Complexity Open
Span programs are an important model of quantum computation due to their correspondence with quantum query and space complexity. While the query complexity of quantum algorithms obtained from span programs is well-understood, it is not gen…
View article: Quantum gradient estimation of Gevrey functions
Quantum gradient estimation of Gevrey functions Open
Gradient-based numerical methods are ubiquitous in optimization techniques frequently applied in industry to solve practical problems. Often times, evaluating the objective function is a complicated process, so estimating the gradient of a…
View article: Quantum gradient estimation and its application to quantum reinforcement learning
Quantum gradient estimation and its application to quantum reinforcement learning Open
In 2005, Jordan showed how to estimate the gradient of a real-valued function with a high-dimensional domain on a quantum computer. Subsequently, in 2017, it was shown by Gilyén et al. how to do this with a different input model. They also…