Permutational quantum computing
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TL;DR: This work considers a model of quantum computation that disregards even the topology of the particle trajectory, and computes by permuting particles, whereas topological quantum computation requires anyons.
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Abstract: In topological quantum computation the geometric details of a particle trajectory areirrelevant; only the topology matters Taking this one step further, we consider a model ofcomputation that disregards even the topology of the particle trajectory, and computesby permuting particles Whereas topological quantum computation requires anyons,permutational quantum computation can be performed with ordinary spin-1/2 particles,using a variant of the spin-network scheme of Marzuoli and Rasetti We do not knowwhether permutational computation is universal It may represent a new complexityclass within BQP Nevertheless, permutational quantum computers can in polynomialtime approximate matrix elements of certain irreducible representations of the symmetricgroup and approximate certain transition amplitudes from the Ponzano-Regge spin foammodel of quantum gravity No polynomial time classical algorithms for these problemsare known
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Citations
The Computational Complexity of Linear Optics
Scott Aaronson,Alex Arkhipov +1 more
TL;DR: In this paper, it was shown that even an approximate or noisy classical simulation would already imply a collapse of the polynomial hierarchy, and hence the hierarchy collapses to the third level.
Boson Sampling on a Photonic Chip
Justin B. Spring,Benjamin J. Metcalf,Peter C. Humphreys,W. Steven Kolthammer,Xian-Min Jin,Xian-Min Jin,Marco Barbieri,Aanimesh Datta,Nicholas Thomas-Peter,Nathan K. Langford,Nathan K. Langford,Dmytro Kundys,James C. Gates,Brian J. Smith,Pete Smith,Ian A. Walmsley +15 more
TL;DR: A quantum boson-sampling machine (QBSM) is constructed to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically.
The computational complexity of linear optics
Scott Aaronson,Alex Arkhipov +1 more
- 06 Jun 2011
TL;DR: In this paper, it was shown that even an approximate or noisy classical simulation would already imply a collapse of the polynomial hierarchy, and hence the hierarchy collapses to the third level.
Experimental boson sampling
Max Tillmann,Max Tillmann,Borivoje Dakić,René Heilmann,Stefan Nolte,Alexander Szameit,Philip Walther,Philip Walther +7 more
TL;DR: In this paper, Aaronson and Arkhipov's model of computation with photons in integrated optical circuits was implemented and the authors set a benchmark for a type of quantum computer that can potentially outperform a conventional computer by using only a few photons and linear optical elements.
894
Photonic Boson Sampling in a Tunable Circuit
Matthew A. Broome,Alessandro Fedrizzi,Saleh Rahimi-Keshari,Justin Dove,Scott Aaronson,Timothy C. Ralph,Andrew White +6 more
TL;DR: The central premise of boson sampling was tested, experimentally verifying that three-photon scattering amplitudes are given by the permanents of submatrices generated from a unitary describing a six-mode integrated optical circuit.
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