Graph States and Stabilizer Eigenstates

A guided research project in Quantum Computing.

← Quantum Computing projects

Experience Research Quantum Computing

Question

How does a graph describe an entangled state and its stabilizer equations?

The neighbourhood of each vertex determines one stabilizer that fixes the whole graph state.
The neighbourhood of each vertex determines one stabilizer that fixes the whole graph state.
An X-type ancilla qubit joined to a data qubit.
A stabilizer-measurement building block from the surface-code research materials.

Goals

  • Construct graph states from vertices and edges.
  • Derive and verify their stabilizer eigenvalue relations.

Method

Associate one qubit with each vertex and an entangling gate with each edge.

  • Prepare all qubits in \(|+\rangle\) and apply controlled-Z gates along the graph edges.
  • Build the stabilizer generator for every vertex.
  • Verify the state algebraically or in a simulator and explore graph transformations.