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arXiv:2404.14217 · Physical Review Applied

General protocols for the efficient distillation of indistinguishable photons

Jason Saied, Jeffrey Marshall, Namit Anand, Eleanor Gilbert Rieffel

Published Mar 26, 2025• 6 citations
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Abstract

Fault-tolerant linear optical quantum computation relies on interference between identical photons to generate entanglement. Unfortunately, photons in the lab tend to be partially distinguishable, generating less entanglement and causing unheralded errors. The authors introduce families of distillation schemes that use n-photon interference and postselection to filter out ``bad'' photons and reduce distinguishability by a factor of n, with resource costs scaling only linearly in n. Along the way, the team also resolves an open problem regarding n-mode Fourier interferometers, namely that the Zero Transmission Law characterizes all suppression if and only if n is a prime power.

DOI
10.1103/physrevapplied.23.034079

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Fault-tolerant linear optical quantum computation relies on interference between identical photons to generate entanglement. Unfortunately, photons in the lab tend to be partially distinguishable, generating less entanglement and causing unheralded errors. The authors introduce families of distillation schemes that use n-photon interference and postselection to filter out ``bad'' photons and reduce distinguishability by a factor of n, with resource costs scaling only linearly in n. Along the way, the team also resolves an open problem regarding n-mode Fourier interferometers, namely that the Zero Transmission Law characterizes all suppression if and only if n is a prime power.
The foundation of fault-tolerant linear optical quantum computing is built upon the interference of identical photons to create high-fidelity entangled states. Unfortunately, fabrication limitations cause sources to emit photons that are only partially indistinguishable, leading to computational errors. To address this, the authors introduce a photon-distillation scheme based on multiphoton-interference linear optics. This protocol mitigates arbitrary indistinguishability errors in a single round. A scheme combining conventional quantum error correction and photon distillation has a higher error threshold than quantum error correction alone, and requires fewer optical components.
This thesis presents the development of resource-efficient photon-distillation schemes designed to produce highly indistinguishable photons, a key requirement for large-scale photonic quantum computing. Although photons do not naturally interact, their indistinguishability enables effective interactions through quantum interference, allowing entanglement generation using only linear optical elements and measurements. In practice, however, photons are never perfectly identical. Small differences introduce decoherence, limiting the scalability and reliability of photonic quantum technologies. Addressing indistinguishability errors is therefore essential for fault-tolerant quantum computing. The thesis first reviews the importance of photon indistinguishability and the need to mitigate related errors. It then examines experimental methods for characterizing imperfections and introduces a general model of imperfect photon states. This model captures indistinguishability errors alongside additional experimental noise from photon loss and multiphoton events. A key insight is that loss and multiphoton noise together can act as an effective source of indistinguishability error. To quantify this effect, the work defines an effective indistinguishability metric, enabling practical evaluation of photon-distillation schemes under realistic conditions. The core theoretical contribution is the development of photon-distillation protocols based on multiphoton Fourier interference. Unlike earlier approaches, these schemes can asymptotically suppress indistinguishability errors to arbitrary levels while requiring only linear scaling in photon resources relative to the desired error reduction. The analysis further suggests that photon distillation, when combined with quantum error correction, can significantly reduce the overall resource overhead for fault-tolerant photonic quantum computing. Experimentally, a three-photon Fourier-based distillation protocol was demonstrated on a high-fidelity photonic processor using a resonantly driven quantum-dot single-photon source. After subtracting excess noise contributions, a 2.2-fold reduction in indistinguishability error was achieved; when excess noise was retained, a 1.2-fold net reduction was observed. These results confirm a clear below-threshold improvement in photon quality. Additional analysis suggests that optimized distillation schemes could reduce the photon cost of a logical qubit by up to a factor of four. The thesis concludes by addressing insertion loss and outlining design strategies and future directions for integrating photon-distillation components into scalable quantum architectures.
Photonic quantum computers use the bosonic statistics of photons to construct, through quantum interference, the large entangled states required for measurement-based quantum computation. Therefore, any which-way information present in the photons will degrade quantum interference and introduce errors. While quantum error correction can address such errors in principle, it is highly resource-intensive and operates with a low error threshold, requiring numerous high-quality optical components. We experimentally demonstrate scalable, optimal photon distillation as a substantially more resource-efficient strategy to reduce indistinguishability errors in a way that is compatible with fault-tolerant operation. Photon distillation is an intrinsically bosonic, coherent error-mitigation technique which exploits quantum interference to project single photons into purified internal states, thereby reducing indistinguishability errors at both a higher efficiency and higher threshold than quantum error correction. We observe unconditional error reduction (i.e., below-threshold behaviour) consistent with theoretical predictions, even when accounting for noise introduced by the distillation gate, thereby achieving actual net-gain error mitigation under conditions relevant for fault-tolerant quantum computing. We anticipate photon distillation will find uses in large-scale quantum computers. We also expect this work to inspire the search for additional intrinsically bosonic error-reduction strategies, even for fault-tolerant architectures.
A reliable source of identical (indistinguishable) photons is a prerequisite for exploiting interference effects, which is a necessary component for linear optical based quantum computing, and applications thereof such as Boson sampling. Generally speaking, the degree of distinguishability will determine the efficacy of the particular approach, for example by limiting the fidelity of constructed resource states, or reducing the complexity of an optical circuits output distribution. It is therefore of great practical relevance to engineer heralded sources of highly pure and indistinguishable photons. Inspired by magic state distillation, we present a protocol using standard linear optics which can be used to increase the indistinguishability of a photon source, to arbitrary accuracy. In particular, in the asymptotic limit of small error ε, to reduce the error to ε^{'}<ε requires O((ε/ε^{'})^{2}) photons. We demonstrate the scheme is robust to detection and control errors in the optical components, and discuss the effect of other error sources.
Several photonic quantum technologies rely on the ability to generate multiple indistinguishable photons. Benchmarking the level of indistinguishability of these photons is essential for scalability. The Hong-Ou-Mandel dip provides a benchmark for the indistinguishability between two photons, and extending this test to the multi-photon setting has so far resulted in a protocol that computes the genuine n-photon indistinguishability (GI). However, this protocol has a sample complexity that increases exponentially with the number of input photons for an estimation of GI up to a given additive error. To address this problem, we introduce new theorems that strengthen our understanding of the relationship between distinguishability and the suppression laws of the quantum Fourier transform interferometer (QFT). Building on this, we propose a protocol using the QFT for benchmarking GI that achieves constant sample complexity for the estimation of GI up to a given additive error for prime photon numbers, and sub-polynomial scaling otherwise, representing an exponential improvement over the state of the art. We prove the optimality of our protocol in many relevant scenarios and validate our approach experimentally on Quandela's reconfigurable photonic quantum processor, where we observe a clear advantage in runtime and precision over the state of the art. We therefore establish the first scalable method for computing multi-photon indistinguishability, which applies naturally to current and near-term photonic quantum hardware.