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Frontiers in Optics

Bayesian quantum phase estimation on an integrated Silicon photonic device

Stefano Paesani, Antonio A. Gentile, Raffaele Santagati, Jianwei Wang, Nathan Wiebe, Shigehito Miki, Tsuyoshi Yamashita, Hirotaka Terai, Mikio Fujiwara, Masahide Sasaki, Michael G. Tanner, Chandra M. Natarajan, Robert H. Hadfield, David P. Tew, Jeremy L. O’Brien, Mark G. Thompson

Published Jan 1, 2016• 0 citations
Publisher

Abstract

We demonstrate a Bayesian approach for practical and robust implementation of the quantum phase estimation algorithm. We implement it on a reconfigurable Silicon quantum photonic device, demonstrating its importance for future quantum applications.
DOI
10.1364/fio.2016.ftu3g.5

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Summary form only given. Quantum Phase Estimation (PE) is a fundamental building block in the framework of Quantum Computing. Accurate estimation of the true eigenphase φ0of a known eigenstate |φ〉 is fundamental for the implementation of many promising quantum algorithms. The interest in PE is also due to the modest quantum hardware requirements of the Iterative Phase Estimation Algorithm (IPEA) implementation [1], successfully implemented on small-scale devices [2]. However, IPEA makes hard decisions at each step of the algorithm, relying on majority voting schemes for its robustness against noise. It has been observed how non-error-corrected machines may enter a regime where error-rates for IPEA diverge quickly, making this approach impractical [3]. New Bayesian approaches, such as the Rejection Filtering Phase Estimation (RFPE), have been recently proposed to overcome these limitations [4]. Here, we report the implementation of RFPE in a photonic device embedding state-of-art integrated elements. Spontaneous Four Wave Mixing sources generate photon pairs. State preparation and evolution are accomplished via integrated Mach-Zehnder interferometers and thermo-optical phase shifters operating in the hundreds of kHz regime. Fast reconfigurability is key for RFPE, as the algorithm adaptively chooses the parameters for each experiment. Arbitrary CU(2) controlled operations are made possible by an entanglement-based scheme, integrated on this chip for the first time.
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a single phase, applications to the simultaneous estimation of several phases may bring substantial advantages; for instance, in the presence of spatial or temporal constraints. In this work, we study a Bayesian algorithm for the parallel (simultaneous) estimation of multiple arbitrary phases. The protocol gives access to correlations in the Bayesian multiphase distribution resulting in covariance matrix elements scaling as $O({N}_{T}^{\ensuremath{-}2})$, with respect to the total number of quantum resources NT{N}_{T}NT​. The parallel estimation allows to surpass the sensitivity of sequential single-phase estimation strategies for optimal linear combinations of phases. Furthermore, the algorithm proves a certain noise resilience and can be implemented using single photons and standard optical elements in currently accessible experiments.
Abstract The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation, yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum (NISQ) devices due to their excessive depth and circuit complexity. We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement. The iterative framework of the algorithm, combined with the independence from controlled unitary operations, inherently mitigates circuit depth and complexity limitations. Through an experimental realization on the photonic system, we demonstrate high-precision estimation of diverse phase differences, showing root-mean-square errors (RMSE) below the standard quantum limit O ( 1 / N ) and reaching the Heisenberg scaling O ( 1 / N ) after a certain number of iterations. Our scheme provides a critical advantage in quantum resource-constrained scenarios, and advances practical implementations of quantum information tasks under realistic hardware constraints.