Phase transition of computational power in the resource states for one-way quantum computation

Abstract

We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, we show that single qubit measurements on the faulty lattice can be efficiently simulated classically. We observe a phase transition at the threshold when the amount of entanglement in the faulty lattice directly relevant to the computational power changes exponentially.

12 pages, 10 figures, and a Michelangelo quote. published version: some improvements in presentation following referee comments

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• Physical-depth architectural requirements for generating universal photonic cluster states
• Quantum complexity phase transitions in monitored random circuits
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Timing constraints due to real-time graph traversal algorithms on incomplete cluster states in photonic measurement-based quantum computing
• Efficient classical simulation of cluster state quantum circuits with alternative inputs