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Which is the qaoa algorithm for the MaxCut problem?
In this tutorial we implement the quantum approximate optimization algorithm (QAOA) for the MaxCut problem as proposed by Farhi, Goldstone, and Gutmann (2014). First, we give an overview of the MaxCut problem using a simple example, a graph with 4 vertices and 4 edges.
Which is better qaoa or max-cut for 3 regular graphs?
The QAOA is known to do just a little better better than random guessing for Max-Cut on 3-regular graphs at p=1. You can use very similar logic to the code above, but now instead of relying on the QAOA to decied your S_partition and T_partition you can just pick then randomly:
How to get a cut using the qaoa?
To get cuts using the QAOA we will first need to extract the best control parameters found during the sweep: Each bitstring can be seen as a candidate cut in the graph. The qubits that measured 0 correspond to that qubit being in one cut partition and a qubit that measured to 1 corresponds to that qubit being in the other cut partition.
How to find maximum cut in Pennylane qaoa?
We then show how to find the maximum cut by running the QAOA algorithm using PennyLane. The aim of MaxCut is to maximize the number of edges (yellow lines) in a graph that are “cut” by a given partition of the vertices (blue circles) into two sets (see figure below). Consider a graph with m m edges and n n vertices.
How is qaoa used to solve combinatorial optimization problems?
QAOA takes the approach of classical approximate algorithms and looks for a quantum analogue that will likewise produce a classical bit string x ∗ that with high probability is expected to have a good approximation ratio α. Before discussing the details, let us first present the general idea of this approach.
How is the quantum approximate optimization algorithm used?
The general idea behind this approach is to supplement the noisy intermediate-scale quantum (NISQ) devices with classical computers. In this blog post, we discuss the Quantum Approximate Optimization Algorithm (QAOA), which is a hybrid algorithm, alongside some of its applications. QAOA is used for optimizing combinatorial problems.
What is the approximate solution to the MaxCut problem?
For the MAXCUT problem there is a famous approximate algorithm due to Goemans and Williamson 2 . This algorithm is based on an SDP relaxation of the original problem combined with a probabilistic rounding technique that yields an with high probability approximate solution x ∗ that has an approximation ratio of α ≈ 0.878.