Related papers: Quantum Worst-Case to Average-Case Reduction for M…
A particular instance of the Shortest Vector Problem (SVP) appears in the context of Compute-and-Forward. Despite the NP-hardness of the SVP, we will show that this certain instance can be solved in complexity order $O(n\psi\log(n\psi))$…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied,…
We study beyond worst-case dimensionality reduction for $s$-sparse vectors. Our work is divided into two parts, each focusing on a different facet of beyond worst-case analysis: We first consider average-case guarantees. A folklore upper…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
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…
As a general framework, Matrix Exponential Dimensionality Reduction (MEDR) deals with the small-sample-size problem that appears in linear Dimensionality Reduction (DR) algorithms. High complexity is the bottleneck in this type of DR…
Vector Quantized Variational Autoencoders (VQ-VAEs) leverage self-supervised learning through reconstruction tasks to represent continuous vectors using the closest vectors in a codebook. However, issues such as codebook collapse persist in…
Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and…
This whitepaper surveys the current landscape and short- to mid-term prospects for quantum-enabled optimization and machine learning use cases in industrial settings. Grounded in the QCHALLenge program, it synthesizes hardware trajectories…
Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that under reasonable assumptions, there is no non-adaptive worst-case to average-case reduction that bases the average-case hardness of an NP-problem on the worst-case…
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…
Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…
We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
Quantum circuit optimization is essential for improving the performance of quantum algorithms, particularly on Noisy Intermediate-Scale Quantum (NISQ) devices with limited qubit connectivity and high error rates. Pattern matching has proven…
In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program,…