Percolation thresholds for photonic quantum computing

Mihir Pant (), Don Towsley, Dirk Englund and Saikat Guha
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Mihir Pant: MIT
Don Towsley: University of Massachusetts
Dirk Englund: MIT
Saikat Guha: MIT

Nature Communications, 2019, vol. 10, issue 1, 1-11

Abstract: Abstract Despite linear-optical fusion (Bell measurement) being probabilistic, photonic cluster states for universal quantum computation can be prepared without feed-forward by fusing small n-photon entangled clusters, if the success probability of each fusion attempt is above a threshold, $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$ λ c ( n ) . We prove a general bound $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)} \ge 1/(n - 1)$$ λ c ( n ) ≥ 1 ∕ ( n - 1 ) , and develop a conceptual method to construct long-range-connected clusters where $${\mathrm{\lambda }}_{\mathrm{c}}^{(n)}$$ λ c ( n ) becomes the bond percolation threshold of a logical graph. This mapping lets us find constructions that require lower fusion success probabilities than currently known, and settle a heretofore open question by showing that a universal cluster state can be created by fusing 3-photon clusters over a 2D lattice with a fusion success probability that is achievable with linear optics and single photons, making this attractive for integrated-photonic realizations.

Date: 2019
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DOI: 10.1038/s41467-019-08948-x

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