Related papers: Max-Cut graph-driven quantum circuit design for pl…
Despite quantum computing's rapid development, current systems remain limited in practical applications due to their limited qubit count and quality. Various technologies, such as superconducting, trapped ions, and neutral atom quantum…
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate…
We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated…
Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is of direct relevance to combinatorial optimization and fundamental science. Search-based heuristics have difficulty with this task due to the…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising…
Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…
Many developments in science and engineering depend on tackling complex optimizations on large scales. The challenge motivates intense search for specific computing hardware that takes advantage from quantum features, nonlinear dynamics, or…
Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced…
Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and…
We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into…
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…
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…
We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glass-like…
The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the…