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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Demonstration of a Low-Depth Universal Linear Optical Circuit

Tomofumi Odagawa, Kazuki Sakaino, Shogo Kimura, Takuya Inagaki, Hanzhi Tang, Ken Tanizawa, Kazuhiro Ikeda, Makoto Okano, Mitsuru Takenaka, Hirohito Yamada, Nobuyuki Matsuda

Published Jun 26, 2023• 0 citations

Abstract

Universal linear optical (ULO) circuit is a versatile device that plays a fundamental role in quantum computation, optical machine learning, and MIMO processing for optical communications. The design of the ULO, i.e., a universal multiport interferometer, was initially proposed by Reck et al. in 1994 [1] and improved in terms of circuit depth and robustness to optical losses by Clements et al. in 2016 [2]. Recently, a further compactified circuit design was proposed Bell and Walmsley [3]. In Bell's scheme, the circuit layout consists of a network of symmetric Mach-Zehnder interferometers (MZI) with two variable phase shifters in each arm. The design significantly reduces the whole device length compared to the conventional designs, where the circuit consists of a network of asymmetric MZIs, each of which has a phase shifter in one arm and an external phase shifter outside of itself. This downsizing becomes significantly important toward the realization of large-scale ULOs in the limited chip area, particularly when each phase shifter is long or when the spacing between phase shifters cannot be made small. This time we experimentally demonstrate that Bell's scheme can express arbitrary unitary matrices as well as Clements' scheme.

DOI: 10.1109/cleo/europe-eqec57999.2023.10232014

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Universal linear optical (ULO) circuit is a versatile device that plays a fundamental role in quantum computation, optical machine learning, and MIMO processing for optical communications. The design of the ULO, i.e., a universal multiport interferometer, was initially proposed by Reck et al. in 1994 [1] and improved in terms of circuit depth and robustness to optical losses by Clements et al. in 2016 [2]. Recently, a further compactified circuit design was proposed Bell and Walmsley [3]. In Bell's scheme, the circuit layout consists of a network of symmetric Mach-Zehnder interferometers (MZI) with two variable phase shifters in each arm. The design significantly reduces the whole device length compared to the conventional designs, where the circuit consists of a network of asymmetric MZIs, each of which has a phase shifter in one arm and an external phase shifter outside of itself. This downsizing becomes significantly important toward the realization of large-scale ULOs in the limited chip area, particularly when each phase shifter is long or when the spacing between phase shifters cannot be made small. This time we experimentally demonstrate that Bell's scheme can express arbitrary unitary matrices as well as Clements' scheme.

Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach–Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach–Zehnder. It subsequently became apparent that with symmetric Mach–Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach–Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach–Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.

Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)PRLTAO0031-900710.1103/PhysRevLett.73.58]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities of implementing reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires

2N+3

stages of phase shifters for $N\ifmmode\times\else\texttimes\fi{}N$ matrices. However, it is beneficial to reduce the number of phase-shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase-shifter stages in the proposed structure can be reduced to

N+2

and

N+3

for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.

Multiport interferometers with

N

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

N

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.

Linear optics underpins fundamental tests of quantum mechanics and quantum technologies. We demonstrate a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of that circuit. Our six-mode universal system consists of a cascade of 15 Mach-Zehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons, and their measurement with a 12-single-photon detector system. We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards. We implemented 100 Haar random unitaries with an average fidelity of 0.999 ± 0.001. Our system can be rapidly reprogrammed to implement these and any other linear optical protocol, pointing the way to applications across fundamental science and quantum technologies.

Universal multi-port interferometers that can be reconfigured to implement any unitary operation are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Recently, Saygin et al. [Phys. Rev. Lett. 124, 010501 (2020)] have presented numerical evidence that an extremely compact arrangement consisting in

d

layers of

d

-dimensional Fourier transforms and

d+1

layers of configurable phase shifters might be universal in any dimension

d

. Here, we first present counterexamples to this statement. We show that for

d=3

and

4

, around 5% of the unitary matrices from a Haar-uniform distribution cannot be recovered with high fidelity using Saygin et al.'s scheme. We also identify a family of unitary matrices with elements that cannot be recovered with high fidelity for any

5\leq d \leq 10

. Secondly, we present numerical evidence that universality is recovered in all dimensions by adding a Fourier transformation and a layer of phase shifters, which preserves the compactness of the scheme and its robustness against imperfections.