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arXiv:2002.01371 · Physical Review A

Minimum optical depth multiport interferometers for approximating arbitrary unitary operations and pure states

Luciano Pereira, Alejandro Rojas, G. Lima, A. Delgado, Gustavo Cañas, Adán Cabello

Published Jun 2, 2025• 5 citations
arXivHTMLPDF

Abstract

Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers, approximating with a given infidelity any pure-state preparation and any unitary operation. By means of numerical calculations, we show that pure states, in any dimension $d$, can be prepared with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}15}$ with three layers of $d$-dimensional Fourier transforms and three layers of configurable phase shifters. 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 operation with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}14}$. The conclusions are achieved by numerical simulations in the range from $d=3$ to $d=10$. These results are interesting in light of the recent availability of multicore fiber-integrated multiport interferometers.

DOI
10.1103/physreva.111.062603

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Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers, approximating with a given infidelity any pure-state preparation and any unitary operation. By means of numerical calculations, we show that pure states, in any dimension ddd, can be prepared with infidelity \ensuremath≤10\ensuremath−15\ensuremath{\le}{10}^{\ensuremath{-}15}\ensuremath≤10\ensuremath−15 with three layers of ddd-dimensional Fourier transforms and three layers of configurable phase shifters. We also present numerical evidence that d+1d+1d+1 layers of ddd-dimensional Fourier transforms and d+2d+2d+2 layers of configurable phase shifters can produce any unitary operation with infidelity \ensuremath≤10\ensuremath−14\ensuremath{\le}{10}^{\ensuremath{-}14}\ensuremath≤10\ensuremath−14. The conclusions are achieved by numerical simulations in the range from d=3d=3d=3 to d=10d=10d=10. These results are interesting in light of the recent availability of multicore fiber-integrated multiport interferometers.
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We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on 2d2d2d modes using a pair of circuits for the same operation on ddd modes. The circuits operate on path-encoded qudits and realize ddd-dimensional unitary transformations on these states using linear optical networks with O(d2)O\left({d}^{2}\right)O(d2) optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.
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Multiport interferometers with NNN ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with NNN components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.