ClusterSim¶

A cluster state simulator for measurement-based quantum computation, in browser. Try it here: https://clustersim.app

Based on the paper ‘Fast simulation of stabilizer circuits using a graph state representation’ by Simon Anders and Hans J. Briegel (here)

Installation¶

To install, use:

pip install .

After installation, run

python grid3dfigure.py

This implementation is based around graph states. These were introduced in the paper about entanglement purification (here) to study the entanglement properties of certain multi-qubit systems
Takes their name from graphs in maths
Each qubit corresponds to a vertex of the graph, and each edge indicates which qubits have interacted.
There is a bijection between stabilizer states (the states that can appear in a stabilizer circuit) and graph states. That is, every graph state has a corresponding stabilizer state, and every stabilizer state has a corresponding graph state.
This can be shown as: Any stabilizer state can be transformed to a graph state by applying a tensor product of local Clifford operations. These are known as vertex operators (VOPs). See this paper and this paper.
The standard approach is to store a tableau of stabillzer operators (an $n \times n$ matrix of Pauli operators).
The improved algorithm needs only the graph state and the list of VOPs, and requires space $\mathcal{O}(n \log n)$.
To then change the state, measurement is studied in this paper, and gate application in the paper mentioned above.