Minimum optical depth multi-port interferometers for approximating any unitary transformation and any pure state

• URL: http://arxiv.org/abs/2002.01371v4
• Date: Tue, 10 May 2022 19:20:44 GMT
• Title: Minimum optical depth multi-port interferometers for approximating any unitary transformation and any pure state
• Authors: Luciano Pereira, Alejandro Rojas, Gustavo Ca\~nas, Gustavo Lima, Aldo Delgado, and Ad\'an Cabello
• Abstract summary: We show that any pure state, in any dimension $d$, can be prepared with infidelity $le 10-15$ using multi-port interferometers. The schemes in [Phys. Rev. Lett. textbf73, 58 (1994) and Optica text3, 1460, 1460, only achieves an infidelity in the order of $10-7$ for block-diagonal unitary transformations.
• Score: 52.77024349608834
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reconfigurable devices capable to implement any unitary operation with a given fidelity are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Here, we address the problems of approximating with a given infidelity any unitary operation and any pure state using multi-port interferometers, which are of current interest due to the recent availability of multi-core fiber integrated multi-port interferometers. We show that any pure state, in any dimension $d$, can be prepared with infidelity $\le 10^{-15}$ with $3$~layers of $d$-dimensional Fourier transforms and $3$~layers of configurable phase shifters. In contrast, the schemes in [Phys. Rev. Lett. \textbf{73}, 58 (1994) and Optica \textbf{3}, 1460 (2016)], require optical depth $2(d-1)$. We also present numerical evidence that $d+1$~layers of $d$-dimensional Fourier transforms and $d+2$~layers of configurable phase shifters can produce any unitary with infidelity $\le 10^{-14}$, while the scheme in [Phys. Rev. Lett. \textbf{124}, 010501 (2020)] only achieves an infidelity in the order of $10^{-7}$ for block-diagonal unitary transformations

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