相关论文: Approximate optimization of MAXCUT with a local sp…

The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum…

Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA)…

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general…

The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…

The $L_0$-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has…

QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which…

Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…

Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit,…

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground state properties are essential in understanding these materials, however, computational complexity limits…

We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The objective is to maximise $\omega$ subject to $Ax \le 1$, $Cx \ge \omega 1$, and $x \ge 0$ for nonnegative matrices $A$ and $C$. The…

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…

In quantum chemistry, self-consistent field (SCF) algorithms define a nonlinear optimization problem, with both continuous and discrete components. In this work, we derive Hartree-Fock-inspired SCF algorithms that can be exactly written as…

Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…

The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model,…

We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional…

Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…