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OSA Advanced Photonics Congress

SWAP-test algorithm implemented on the photonic platform for Quantum Machine Learning

Alessio Baldazzi, Nicolò Leone, Stefano Azzini, Matteo Sanna, Lorenzo Pavesi

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We design an integrated photonic chip to implement the SWAP-test algorithm: using single-particle entanglement as a resource, the circuit can be used to estimate the scalar product of two qubits for quantum kernel methods.
DOI
10.1364/iprsn.2023.ith3b.1

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Abstract The swap test is a quantum algorithm capable of computing the absolute value of the scalar product of two arbitrary wavefunctions. Scalar products represent a crucial ingredient to many quantum machine learning (QML) methods, but their evaluation is not straightforward at all. For this reason, many research efforts have been made without achieving an efficient and robust implementation. Here, we present an integrated photonic circuit designed to implement the swap test algorithm. Our approach relies solely on linear optical integrated components and qudits, represented by single photons from an attenuated laser beam propagating through a set of waveguides. By utilizing 23 spatial degrees of freedom for the qudits, we can configure all the necessary arrangements to set any two-qubit state and perform the swap test. This simplifies the requirements on the circuitry elements and eliminates the need for non-linearity, heralding, or post-selection to achieve multi-qubit gates. Our photonic swap test circuit successfully encodes two qubits and estimates their scalar product with a measured root mean square error smaller than 0.05. This result paves the way for the development of integrated photonic architectures capable of performing QML tasks with robust devices operating at room temperature.
Quantum entanglement is an essential resource for quantum technologies, and the controlled swap test provides a versatile tool for its detection and quantification. Here, we propose a SWAP-based entanglement witness that applies to arbitrary two-qubit states - both pure and mixed - and provides a lower bound on the concurrence. The method is resource-efficient, robust to noise, and platform-independent. As an example, we validate the approach on a room-temperature photonic chip, where the swap test is carried out using only linear and well-established integrated optical components. The robustness of the method against photonic-hardware noise is also analysed. Our results establish a simple and reliable tool for entanglement witnessing.
We propose the implementation of the swap test using a charge qubit in a double quantum dot. The swap test is a fundamental quantum subroutine in quantum machine learning and other applications for estimating the fidelity of two unknown quantum states by measuring an auxiliary qubit. Our proposal uses a controlled three-qubit gate, which is natural to quantum dot charge qubits. It allows us to implement a swap test with a circuit depth of six layers, and an estimated gate time of less than 3 ns, that is below the coherence time of double quantum dots. This work paves the way for enhancing the toolbox of quantum machine learning developments in semiconductor qubits.
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Integrated photonic chips leverage the recent developments in integrated circuit technology, along with the control and manipulation of light signals, to realize the integration of multiple optical components onto a single chip. By exploiting the power of light, integrated photonic chips offer numerous advantages over traditional optical and electronic systems, including miniaturization, high-speed data processing and improved energy efficiency. In this review, we survey the current status of quantum computation, optical neural networks and the realization of some algorithms on integrated optical chips.