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Main Authors: Salazar, William E., Calderón-Losada, Omar, Reina, John H.
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2310.20416
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author Salazar, William E.
Calderón-Losada, Omar
Reina, John H.
author_facet Salazar, William E.
Calderón-Losada, Omar
Reina, John H.
contents 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 $η$ and OPAs of gain $g=1/η$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_20416
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Linear-nonlinear duality for circuit design on quantum computing platforms
Salazar, William E.
Calderón-Losada, Omar
Reina, John H.
Quantum Physics
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 $η$ and OPAs of gain $g=1/η$. 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.
title Linear-nonlinear duality for circuit design on quantum computing platforms
topic Quantum Physics
url https://arxiv.org/abs/2310.20416