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Photonics North (PN)

Seeding Gaussian Boson Samplers with Single Photons for Enhanced State Generation

Valerio Crescimanna, Aaron Z. Goldberg, Khabat Heshami

Published May 28, 2024• 0 citations
Publisher

Abstract

Usually, generation of non-Gaussian states involves tradeoffs between success probability and quality of the resultant state. For example, injecting squeezed light into a multimode interferometer and postselecting on certain patterns of photon-number outputs in all but one mode can herald the creation of these states. We consider the addition of a non-Gaussian resource state, particularly single photons to this configuration, and show how it improves the qualities and generation probabilities of desired states.

DOI
10.1109/pn62551.2024.10621820

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Usually, generation of non-Gaussian states involves tradeoffs between success probability and quality of the resultant state. For example, injecting squeezed light into a multimode interferometer and postselecting on certain patterns of photon-number outputs in all but one mode can herald the creation of these states. We consider the addition of a non-Gaussian resource state, particularly single photons to this configuration, and show how it improves the qualities and generation probabilities of desired states.
Non-Gaussian quantum states are crucial to fault-tolerant quantum computation with continuous-variable systems. Usually, generation of such states involves trade-offs between success probability and quality of the resultant state. For example, injecting squeezed light into a multimode interferometer and postselecting on certain patterns of photon-number outputs in all but one mode, a fundamentally probabilistic task, can herald the creation of cat states, Gottesman-Kitaev-Preskill (GKP) states, and more. We consider the addition of a non-Gaussian resource state, particularly single photons, to this configuration and show how it improves the qualities and generation probabilities of desired states. With only two modes, adding a single-photon source improves GKP-state fidelity from 0.68 to 0.95 and adding a second then increases the success probability eightfold; for cat states with a fixed target fidelity, the probability of success can be improved by factors of up to four by adding single-photon sources. These demonstrate the usefulness of additional commonplace non-Gaussian resources for generating desirable states of light.
We propose a heralded entanglement generation scheme based on Gaussian sources enhanced by photon addition and subtraction operations. By combining single-mode squeezing, linear interferometers, and conditional photon-number measurements on ancillary modes, our model can probabilistically generate dual-rail encoded Bell, GHZ, and W states. We systematically optimize the squeezing parameters and interferometer settings to maximize both the heralding success probability and the fidelity with the target states. Our results show that photon addition and subtraction significantly enhance the non-classicality of the output states and improve generation performance, while maintaining computational efficiency comparable to single-photon source models. We further analyze the robustness of the scheme under parameter perturbations and find that its performance remains stable under realistic experimental imperfections. This work provides a versatile and experimentally feasible framework for scalable heralded entanglement generation using Gaussian resources with non-Gaussian operations.
Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
Photonic quantum computing has gained significant interest in recent years due to its potential for scaling to large numbers of qubits. A critical requirement for fault-tolerant quantum computation is the reliable generation of non-Gaussian quantum states, typically achieved using Gaussian operations and photon-number-resolving detectors. However, the probabilistic nature of quantum measurement typically results in low success rates for state preparation. Conventionally, these circuits are optimized to herald a single specific target outcome, thereby disregarding the potential utility of alternative measurement patterns generated by the same physical setup. In this work, we propose and demonstrate a multi-outcome optimization strategy that increases the overall acceptance probability by allowing a single circuit to produce useful quantum states across several measurement patterns. To evaluate this approach, we apply the framework to the generation of Gottesman-Kitaev-Preskill core states, Schrodinger cat states, binomial codes, and cubic phase states using both two-mode and three-mode Gaussian circuits. We demonstrate that the success probability can be enhanced through two distinct mechanisms: first, by simultaneously targeting a diverse set of useful resource states, and second, by aggregating degenerate outcomes to maximize the production rate of a single target state.
Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study boson sampling from general, single-mode states using a scheme that can generate any such state by combining Gaussian states and photon number measurements. We derive a formula that can be used to calculate the output photon number probabilities of these states after they travel through a linear interferometer. This extends the Boson sampling protocol to the widest array of possible single-mode states and from this we show that the complexity scaling of all such states is similar and hence there is no complexity advantage of using complex input states over simpler ones.
The effects of optical loss and photon distinguishability on the heralded generation of entangled states based on Gaussian resources are quantitatively investigated. By incorporating mode-dependent loss and the statistical characteristics of partially distinguishable photons into a phase-space representation, an efficient numerical framework is established to optimize target-state fidelity and success probability, with a specific focus on the enhancement triggered by non-Gaussian operations such as photon addition and subtraction. The numerical optimization results indicate that a non-vacuum post-selection strategy within a dual-rail encoding framework, combined with the simultaneous tuning of squeezing parameters and the interferometer network, effectively suppresses vacuum noise, enabling the generation of high-fidelity Bell, GHZ, and W states under realistic experimental constraints. The results show that introducing non-Gaussian operations can successfully enhance the state generation performance under realistic imperfections analogous to the enhancements observed under ideal conditions. This study demonstrates that experimental imperfections primarily scale down the success probability rather than fundamentally compromising the state fidelity, providing practical design guidelines for scalable state engineering on integrated photonic platforms.