Photonic Boson Sampling in a Tunable Circuit

Computing Power of Quantum Mechanics There is much interest in developing quantum computers in order to perform certain tasks much faster than, or that are intractable for, a classical computer. A general quantum computer, however, requires the fabrication and operation a number of quantum logic devices (see the Perspective by Franson). Broome et al. (p. 794, published online 20 December) and Spring et al. (p. 798, published online 20 December) describe experiments in which single photons and quantum interference were used to perform a calculation (the permanent of a matrix) that is very difficult on a classical computer. Similar to random walks, quantum walks on a graph describe the movement of a walker on a set of predetermined paths; instead of flipping a coin to decide which way to go at each point, a quantum walker can take several paths at once. Childs et al. (p. 791) propose an architecture for a quantum computer, based on quantum walks of multiple interacting walkers. The system is capable of performing any quantum operation using a subset of its nodes, with the size of the subset scaling favorably with the complexity of the operation. Optical circuits are used to demonstrate a quantum-enhanced calculation. [Also see Perspective by Franson] Quantum computers are unnecessary for exponentially efficient computation or simulation if the Extended Church-Turing thesis is correct. The thesis would be strongly contradicted by physical devices that efficiently perform tasks believed to be intractable for classical computers. Such a task is boson sampling: sampling the output distributions of n bosons scattered by some passive, linear unitary process. We tested the central premise of boson sampling, 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. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Scaling this to large numbers of photons should be a much simpler task than building a universal quantum computer.

[1]  Peter W. Shor,et al.  Estimating Jones polynomials is a complete problem for one clean qubit , 2007, Quantum Inf. Comput..

[2]  J. Ashby.  References and Notes , 1999 .

[3]  P.C.W. Davies.  The implications of a cosmological information bound for complexity, quantum information and the nature of physical law , 2007 .

[4]  Sae Woo Nam,et al.  Conclusive quantum steering with superconducting transition-edge sensors , 2011, Nature Communications.

[5]  Cheng-Zhi Peng,et al.  Observation of eight-photon entanglement , 2011, Nature Photonics.

[6]  Stephen M. Barnett,et al.  Quantum information , 2005, Acta Physica Polonica A.

[7]  M P Almeida,et al.  Reducing multi-photon rates in pulsed down-conversion by temporal multiplexing. , 2011, Optics express.

[8]  T. Ralph,et al.  Quantum process tomography of a controlled-NOT gate. , 2004, Physical review letters.

[9]  Daniel A. Spielman,et al.  Exponential algorithmic speedup by a quantum walk , 2002, STOC '03.

[10]  Paul,et al.  Photon chopping: New way to measure the quantum state of light. , 1996, Physical review letters.

[11]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[12]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[13]  M. J. Withford,et al.  Two-photon quantum walks in an elliptical direct-write waveguide array , 2011, 1103.0604.

[14]  Johannes Kofler,et al.  Experimental generation of single photons via active multiplexing , 2010, 1007.4798.

[15]  Aaron J. Miller,et al.  Counting near-infrared single-photons with 95% efficiency. , 2008, Optics express.

[16]  W. Marsden.  I and J , 2012 .

[17]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[18]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.

[19]  Samuel L. Braunstein,et al.  Detection devices in entanglement-based optical state preparation , 2001 .

[20]  Sergio Boixo,et al.  Parameter estimation with mixed-state quantum computation , 2007, 0708.1330.

[21]  Stephen P. Jordan,et al.  Permutational quantum computing , 2009, Quantum Inf. Comput..

[22]  Andris Ambainis,et al.  Quantum walks on graphs , 2000, STOC '01.

[23]  Andris Ambainis,et al.  One-dimensional quantum walks , 2001, STOC '01.

[24]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[25]  Dieter Jaksch,et al.  Quantum Information, Computation and Communication: Quantum information , 2012 .

[26]  A. Politi,et al.  Quantum Walks of Correlated Photons , 2010, Science.

[27]  L. Mandel.  Photon interference and correlation effects produced by independent quantum sources , 1983 .

[28]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[29]  Timothy C. Ralph,et al.  Error tolerance of the boson-sampling model for linear optics quantum computing , 2011, 1111.2426.

[30]  Daniel F. V. James,et al.  Proposal for a scalable universal bosonic simulator using individually trapped ions , 2012, 1205.1717.

[31]  B. Lanyon,et al.  Experimental quantum computing without entanglement. , 2008, Physical review letters.

[32]  M. Thompson,et al.  Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit , 2012 .

[33]  Isabelle Sagnes,et al.  Ultrabright source of entangled photon pairs , 2010, Nature.

[34]  Wei Ruan,et al.  Visualizing the atomic-scale electronic structure of the Ca2CuO2Cl2 Mott insulator. , 2013, Nature communications.

[35]  Cosimo Laneve,et al.  Theoretical Computer Science: 8th Italian Conference, ICTCS 2003, Bertinoro, Italy, October 13-15, 2003, Proceedings , 2003 .