Cluster-state quantum computing methods and systems

A cluster-state quantum computing system, comprising:

• an array of photon subtractors configured to transform a Gaussian graph state into a non-Gaussian percolated graph state by probabilistically subtracting one photon from each of a corresponding plurality of modes forming the Gaussian graph state, wherein each of the photon subtractors includes a single-photon detector configured to output a detector signal;
• and
• a renormalizer configured to:
• process the detector signal outputted by each single-photon detector to determine cat-basis qubits of the non-Gaussian percolated graph state for which one photon was successfully subtracted from a corresponding one of the modes;
• identify in the non-Gaussian percolated graph state a renormalized graph of logical qubits connected by percolation highways, wherein the logical qubits and percolation highways are formed from the cat-basis qubits;
• and
• output the renormalized graph and the non-Gaussian percolated graph state to a one-way quantum computer.