Xuehua He

Publications (6)4.54 Total impact

• Article: Factorization algorithm based on the periodicity measurement of a CTES

  Vincenzo Tamma, Heyi Zhang, Xuehua He, Augusto Garuccio, Yanhua Shih
  [show abstract] [hide abstract]
  ABSTRACT: We introduce a new factorization algorithm based on the measurement of the periodicity of a determined function, similar to Shor's algorithm. In particular, such a function is given by a generalized continuous truncated exponential sum (CTES). The CTES interference pattern satisfies a remarkable scaling property, which allows one to plot the interferogram as a function of a suitable continuous variable depending on the number to factorize. This allows one, in principle, to factorize arbitrary numbers with a single interferogram. In particular, information about the factors is encoded in the location of the interference maxima, which repeat periodically in the interferogram. A possible analogue computer for the implementation of such an algorithm can be realized using multi-path optical interferometers, with polychromatic light sources and a high-resolution spectrometer. The experimental accuracy in the realization of the CTES interferogram and the bandwidth of the polychromatic sources determine the largest number Nmax factorable. Once the CTES interferogram is recorded, all the numbers with value up to Nmax can be factorable, without performing any further measurement.
  Physica Scripta 09/2010; 2010(T140):014036. · 1.20 Impact Factor
• Article: New factorization algorithm based on a continuous representation of truncated Gauss sums

  Vincenzo Tamma, Heyi Zhang, Xuehua He, Augusto Garuccio, Yanhua Shih
  [show abstract] [hide abstract]
  ABSTRACT: In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j > 2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a single run without precalculating the ratio N/l, where l are all the possible trial factors. Continuous truncated exponential sums turn out to be a powerful tool for distinguishing factors from non-factors (we also suggest, with regard to this topic, to read an interesting paper by S. Wölk et al. also published in this issue [Wölk, Feiler, Schleich, J. Mod. Opt. in press]) and factorizing different numbers at the same time. We will also describe two possible M-path optical interferometers, which can be used to experimentally realize this algorithm: a liquid crystal grating and a generalized symmetric Michelson interferometer.
  Journal of Modern Optics 10/2009; 56(Nos. 18-19):2125-2132. · 1.17 Impact Factor
• Conference Proceeding: CTES Factorization Algorithm.

  Vincenzo Tamma, Heyi Zhang, Xuehua He, Augusto Garuccio, Yanhua Shih
  Quantum Communication and Quantum Networking, First International Conference, QuantumComm 2009, Naples, Italy, October 26-30, 2009, Revised Selected Papers; 01/2009
• Source

  Available from: ArXiv

  Article: Exponential Sums Algorithm based on Optical Interference: Factorization of arbitrary large numbers in a single run

  Vincenzo Tamma, Heyi Zhang, Xuehua He, Augusto Garuccio, Yanhua Shih
  [show abstract] [hide abstract]
  ABSTRACT: This article presents a new factorization algorithm based on the implementation of exponential sums using optical interference and exploiting the spectrum of the light source. Such a goal is achievable with the use of two different kinds of optical interferometers with variable optical paths: a liquid crystal grating and a generalized symmetric Michelson interferometer. This algorithm allows, for the first time, to find, in a single run, all the factors of an arbitrary large number N.
  12/2008;
• Article: Near‐infrared response of photorefractive crystals (K0.5Na0.5)0.2(Sr0.75Ba0.25)0.9Nb2O6:Cu and LiNbO3:Fe

  Bo Guo, Li Yan, Heyi Zhang, Xuehua He, Yanhua Shih
  [show abstract] [hide abstract]
  ABSTRACT: Material response relevant to volume holographic storage for photorefractive crystals (K 0.5 Na 0.5 ) 0.2 (Sr 0.75 Ba 0.25 ) 0.9 Nb 2 O 6 :Cu (KNSBN:Cu) and LiNbO 3 :Fe was studied in the near‐infrared region. The dark decay time for KNSBN:Cu was measured to be on the order of 10⁶ s. The light‐induced erasure time at the 1 mW/cm² read beam intensity can be ≳1000 h for both KNSBN:Cu and LiNbO 3 :Fe. Read beam diffraction efficiencies of 28.7% for KNSBN:Cu and 50% for LiNbO 3 :Fe were obtained at 706 nm when the refractive index grating was written at 706 nm. The decay rate of the refractive index grating with an extraordinary‐wave read beam is about 3.6 times smaller than that with an ordinary‐wave read beam for KNSBN:Cu. The results show that near‐infrared light can be used to read holograms in the photorefractive volume holographic storage application. © 1996 American Institute of Physics.
  Journal of Applied Physics 02/1996; · 2.17 Impact Factor
• Article: Factoring numbers with a single interferogram

  Vincenzo Tamma, Heyi Zhang, Xuehua He, Augusto Garuccio, Wolfgang P. Schleich, Yanhua Shih
  [show abstract] [hide abstract]
  ABSTRACT: We construct an analog computer based on light interference to encode the hyperbolic function f(ζ)≡1/ζ into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
  Phys. Rev. A. 83(2).