• Photonics Research
  • Vol. 11, Issue 10, 1703 (2023)
Hui Zhang1、2, Lingxiao Wan2, Sergi Ramos-Calderer3、4, Yuancheng Zhan2, Wai-Keong Mok5, Hong Cai6, Feng Gao7, Xianshu Luo7, Guo-Qiang Lo7, Leong Chuan Kwek2、5、8, José Ignacio Latorre3、4、5, and Ai Qun Liu1、2、*
Author Affiliations
  • 1Institute of Quantum Technologies (IQT), The Hong Kong Polytechnic University, Hong Kong, China
  • 2Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore, Singapore
  • 3Departament de Fisica Quantica i Astrofisica and Institut de Ciencies del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Spain
  • 4Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
  • 5Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore
  • 6Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), Singapore, Singapore
  • 7Advanced Micro Foundry, Singapore, Singapore
  • 8National Institute of Education, Nanyang Technological University, Singapore, Singapore
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    DOI: 10.1364/PRJ.493865 Cite this Article Set citation alerts
    Hui Zhang, Lingxiao Wan, Sergi Ramos-Calderer, Yuancheng Zhan, Wai-Keong Mok, Hong Cai, Feng Gao, Xianshu Luo, Guo-Qiang Lo, Leong Chuan Kwek, José Ignacio Latorre, Ai Qun Liu. Efficient option pricing with a unary-based photonic computing chip and generative adversarial learning[J]. Photonics Research, 2023, 11(10): 1703 Copy Citation Text show less

    Abstract

    In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve quadratic speedup compared to classical Monte Carlo methods. The circuit consists of three modules: one loading the distribution of asset prices, one computing the expected payoff, and a third performing the quantum amplitude estimation algorithm to introduce speedups. In the distribution module, a generative adversarial network is embedded for efficient learning and loading of asset distributions, which precisely captures market trends. This work is a step forward in the development of specialized photonic processors for applications in finance, with the potential to improve the efficiency and quality of financial services.
    C(ST,K)=K(STK)dST,

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    swp=(Ip1p1ppI)I,

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    P=(M0M1Mn1),Mi=(cosθisinθisinθicosθi)

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    minGmaxDExpreal(log(Dϕ(x)))+Ezpz(log(1Dϕ(Gθ(z)))),

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    2=i=1m(xigi)2.

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    dST=STrdT+STσdWT,(A1)

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    ST=S0e(rσ22)TeσWTeN((rσ22)T,σT),(A2)

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    f(ST,K)=max(0,STK),(A3)

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    C(ST,K)=K(STK)dST,(A4)

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    D|ψini=i=0n1pi|ψin,(C1)

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    C(ST,K)=0n1pi·f(Si,K)=Si>Kn1pi·(SiK),(C2)

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    θi=max(0,arcsin(SiKSmaxK)).(C3)

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    CR=i=0n1|ψiψi|Ry(2θi).(C4)

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    |ψ=CR·i=0n1pi|ψi|0=i=0n1picosθi|ψi|0+pisinθi|ψi|1.(C5)

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    |1|ψ|2=i=0n1pi·sin2θi=C(ST,K)SmaxK.(C6)

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    CR·D·|ψini|0=cosα|ψa|0+sinα|ψb|1,(C7)

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    |ψa=i=1n1picosθi|ψi,|ψb=i=1n1pisinθi|ψi.(C8)

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    Sψ=I2i=0n1|ψiψi||00|(C9)

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    S0=I2|ψiniψini||00|,(C10)

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    Q=CR·D·S0·D·CR·Sψ.(C11)

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    Qm·CR·D·|ψini|0=cos(2m+1)α|ψa|0+sin(2m+1)α|ψb|1.(C12)

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    O(1m)O(1m),(C13)

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    Hui Zhang, Lingxiao Wan, Sergi Ramos-Calderer, Yuancheng Zhan, Wai-Keong Mok, Hong Cai, Feng Gao, Xianshu Luo, Guo-Qiang Lo, Leong Chuan Kwek, José Ignacio Latorre, Ai Qun Liu. Efficient option pricing with a unary-based photonic computing chip and generative adversarial learning[J]. Photonics Research, 2023, 11(10): 1703
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