Related papers: Quantum Legendre-Fenchel Transform
We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory,…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
An $\mathcal{O}(N(\log N)^2/\log\!\log N)$ algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev…
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and…
Partial differential equations (PDEs) are ubiquitous in science and engineering. Prior quantum algorithms for solving the system of linear algebraic equations obtained from discretizing a PDE have a computational complexity that scales at…
Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within…
We present a quantum algorithm to solve dynamic programming problems with convex value functions. For linear discrete-time systems with a $d$-dimensional state space of size $N$, the proposed algorithm outputs a quantum-mechanical…
We explore the potential for quantum speedups in convex optimization using discrete simulations of the Quantum Hamiltonian Descent (QHD) framework, as proposed by Leng et al., and establish the first rigorous query complexity bounds. We…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
We introduce the Shifted Legendre Symbol Problem and some variants along with efficient quantum algorithms to solve them. The problems and their algorithms are different from previous work on quantum computation in that they do not appear…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
A recent result characterizes the fully order reversing operators acting on the class of lower semicontinuous proper convex functions in a real Banach space as certain linear deformations of the Legendre-Fenchel transform. Motivated by the…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…