A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers

Authors:
  • APAxel Pappalardo
    Axel Pappalardo
  • PEPierre-Emmanuel Emeriau
    Pierre-Emmanuel Emeriau
  • GFGiovanni de Felice
    Giovanni de Felice
  • BVBrian Ventura
    Brian Ventura
  • HJHugo Jaunin
    Hugo Jaunin
  • RYRichie Yeung
    Richie Yeung
  • BCBob Coecke
    Bob Coecke
  • SMShane Mansfield
    Shane Mansfield
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Abstract
We present a method for gradient computation in quantum algorithms implemented on linear optical quantum computing platforms. While parameter-shift rules have become a staple in qubit gate-based quantum computing for calculating gradients, their direct application to photonic platforms has been hindered by the non-unitary nature of differentiated phase-shift operators in Fock space. We introduce a photonic parameter-shift rule that overcomes this limitation, providing an exact formula for gradient computation in linear optical quantum processors. Our method scales linearly with the number of input photons and utilizes the same parameterized photonic circuit with shifted parameters for each evaluation. This advancement bridges a crucial gap in photonic quantum computing, enabling efficient gradient-based optimization for variational quantum algorithms on near-term photonic quantum processors. We demonstrate the efficacy of our approach through numerical simulations in quantum chemistry and generative modeling tasks, showing superior optimization performance as well as robustness to noise from finite sampling and photon distinguishability compared to other gradient-based and gradient-free methods.