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Demonstration of Shor's quantum factoring algorithm using photonic qubits
Chao-Yang Lu, Daniel E. Browne, Tao Yang, Jian-Wei Pan
TL;DR
The work addresses the challenge of experimentally realizing Shor’s algorithm with genuine quantum behavior. Using four photonic qubits and a simplified optical network, it demonstrates factorization of 15 for period r = 2, observes genuine multiparticle entanglement, and advances photonic implementations toward larger-scale realizations.
Problem
Experimental realization of Shor’s algorithm remains difficult because it requires coherent multiqubit manipulation and entanglement, while prior NMR demonstrations did not exhibit entanglement during computation.
Method
The experiment uses four photonic qubits and a simplified linear-optics network to implement modular exponential evaluation and the semiclassical quantum Fourier transform for factoring N = 15 with period r = 2.
Results
The demonstration successfully obtains the period r = 2 and factors 15 into 3 and 5, while confirming genuine three-photon GHZ entanglement with fidelity Fψ = 0.74 ± 0.02.
Takeaways & Limitations
The experiment provides a proof-of-principle photonic demonstration with observed genuine multiparticle entanglement supporting the implementation’s quantum nature.
Takeaways & Limitations
The simplified optical two-qubit gates are probabilistic and postselected, so scalability is not directly implied by the present experiment.
Abstract
from arXiv · showhide
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semi-classical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents a step toward full realization of Shor's algorithm and scalable linear optics quantum computation.