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Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in…
Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
With the evolution of numerical methods, we are now aiming at not only qualitative understanding but also quantitative prediction and design of quantum many-body phenomena. As a novel numerical approach, machine learning techniques have…
Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…
Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…
Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…
Machine learning techniques have led to broad adoption of a statistical model of computing. The statistical distributions natively available on quantum processors are a superset of those available classically. Harnessing this attribute has…
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…
We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the D\"urr-Hoyer algorithm for quantum…
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…
We investigate the Maximum Cut (MaxCut) problem on different graph classes with the Quantum Approximate Optimization Algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…
The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on specific families of graphs,…
The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…