Related papers: Quantum algorithms for Young measures: application…
Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major challenge is that QLSAs are inexact and sensitive to the condition number of the coefficient matrices of linear systems.…
Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in…
We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Software defect prediction is a critical aspect of software quality assurance, as it enables early identification and mitigation of defects, thereby reducing the cost and impact of software failures. Over the past few years, quantum…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…