Related papers: Fast quantum subroutines for the simplex method
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
The multisilce method is an important algorithm for electron diffraction and image simulations in transmission electron microscopy. We have proposed a quantum algorithm of the multislice method based on quantum circuit model previously. In…
Superquantiles have recently gained significant interest as a risk-aware metric for addressing fairness and distribution shifts in statistical learning and decision making problems. This paper introduces a fast, scalable and robust…
This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…
We present a method for mitigating measurement errors on quantum computing platforms that does not form the full assignment matrix, or its inverse, and works in a subspace defined by the noisy input bit-strings. This method accommodates…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…
We propose a surrogate-based method for optimizing parameterized quantum circuits which is designed to operate with few calls to a quantum computer. We employ a computationally inexpensive classical surrogate to approximate the cost…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…