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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.13271 |
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| _version_ | 1866913125615271936 |
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| author | Kumar, Simanshu Bisht, Nandan S |
| author_facet | Kumar, Simanshu Bisht, Nandan S |
| contents | Photon loss and dephasing rapidly degrade the sensitivity of quantum sensors, yet systematic methods for designing error-correcting codes whose geometry is simultaneously adapted to the sensing task and the noise channel do not exist. Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge $\ell$ induces a phase-space rotation $θ_\ell=\ellπ/\ell_{\max}$, corresponding to a family of twisted GKP stabilizer lattices. Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $\ell$, the lattice aspect ratio $r$, and the finite-energy envelope $ε$ to maximise quantum Fisher information subject to $P_{\rm err}\leq10^{-3}$. The optimum occurs at the fractional charge $\ell=1.5$ ($θ=67.5^\circ$), implementable with a half-integer spiral phase plate, which reduces $P_{\rm err}$ by $23.9\times$ relative to the square-lattice baseline while leaving $\mathcal{F}_Q$ unchanged to within $0.2\%$. This surpasses the best integer value ($\ell=2$, $15.7\times$) and arises from an exact $180^\circ$ periodicity of the $P_{\rm err}(θ)$ landscape, confirmed analytically and numerically. We derive a transcendental balance equation for the optimal angle $θ^*(η,γ,r)$ and prove that it decreases with both $γ$ and $η$. A Shannon-inspired metrological capacity $\mathcal{C}=\mathcal{F}_Q\cdot(-\ln P_{\rm err})$, maximised at $\ell=1.5$ with a $41\%$ gain over the square lattice, quantifies the joint sensitivity--fault-tolerance resource. These results establish a geometric design principle for noise-adaptive quantum sensors and a fully open-source differentiable template extensible to other bosonic code families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13271 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing Kumar, Simanshu Bisht, Nandan S Quantum Physics 81P40 81P68 81P70 78A60 65K10 J.2 Photon loss and dephasing rapidly degrade the sensitivity of quantum sensors, yet systematic methods for designing error-correcting codes whose geometry is simultaneously adapted to the sensing task and the noise channel do not exist. Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge $\ell$ induces a phase-space rotation $θ_\ell=\ellπ/\ell_{\max}$, corresponding to a family of twisted GKP stabilizer lattices. Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $\ell$, the lattice aspect ratio $r$, and the finite-energy envelope $ε$ to maximise quantum Fisher information subject to $P_{\rm err}\leq10^{-3}$. The optimum occurs at the fractional charge $\ell=1.5$ ($θ=67.5^\circ$), implementable with a half-integer spiral phase plate, which reduces $P_{\rm err}$ by $23.9\times$ relative to the square-lattice baseline while leaving $\mathcal{F}_Q$ unchanged to within $0.2\%$. This surpasses the best integer value ($\ell=2$, $15.7\times$) and arises from an exact $180^\circ$ periodicity of the $P_{\rm err}(θ)$ landscape, confirmed analytically and numerically. We derive a transcendental balance equation for the optimal angle $θ^*(η,γ,r)$ and prove that it decreases with both $γ$ and $η$. A Shannon-inspired metrological capacity $\mathcal{C}=\mathcal{F}_Q\cdot(-\ln P_{\rm err})$, maximised at $\ell=1.5$ with a $41\%$ gain over the square lattice, quantifies the joint sensitivity--fault-tolerance resource. These results establish a geometric design principle for noise-adaptive quantum sensors and a fully open-source differentiable template extensible to other bosonic code families. |
| title | OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing |
| topic | Quantum Physics 81P40 81P68 81P70 78A60 65K10 J.2 |
| url | https://arxiv.org/abs/2605.13271 |