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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.20416 |
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| _version_ | 1866917331733577728 |
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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 |