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arXiv · 2310.20416

Linear-nonlinear duality for circuit design on quantum computing platforms

William E. Salazar·Omar Calderón-Losada·John H. Reina
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Abstract

Beam splitters (BSs) and optical parametric amplifiers (OPAs) can be described using Lie groups $SU(2)$ and $SU(1,1)$. Here, we show that the dynamical trajectories of these devices are connected via a Wick rotation on their respective group manifolds. This yields an exact amplitude-level duality between BSs of transmittance $\eta$ and OPAs of gain $g=1/\eta$. This geometric correspondence admits a compact tensor-network formulation, which we use to construct a circuit-model protocol that reproduces PDC transition amplitudes. This construction naturally leads to finite-dimensional, truncated PDC unitaries that exactly reproduce the first $q$ amplitudes of an ideal parametric amplifier. Our results demonstrate that key amplitude-level features of nonlinear optical processes can be simulated using only native single-qubit unitaries and measurement-based primitives on existing digital quantum hardware. This extends PDC-inspired entanglement-generation mechanisms beyond photonic architectures.

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William E. Salazar, Omar Calderón-Losada, John H. Reina. 2023-10-31. Linear-nonlinear duality for circuit design on quantum computing platforms. https://arxiv.org/abs/2310.20416

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