Experimental Loopback Boson Sampling Achieves Complexity Amplification with 25-mode Interferometers and Five Output Channels

Quantum computation seeks to solve problems intractable for classical computers, and a promising approach involves harnessing the unique properties of photons. Yu. A. Biriukov, R. D. Morozov, and K. I. Okhlopkov, alongside colleagues from M. V. Lomonosov Moscow State University and the Russian Quantum Center, now demonstrate a significant step forward with an enhanced boson sampling technique. Their experiment introduces optical feedback, creating temporal correlations that amplify the complexity of the quantum sampling process, a crucial factor in achieving a demonstrable quantum advantage. By reconstructing the chip’s behaviour and validating it through Bayesian analysis, the team confirms their system surpasses the capabilities of standard boson sampling, offering a resource-efficient pathway towards scalable quantum computation with single photons.

Demonstrating Quantum Advantage Via Boson Sampling

Scientists have achieved a significant milestone in quantum computation by demonstrating a sophisticated boson sampling experiment. Boson sampling is a specialized quantum computation task designed to be exceptionally difficult for classical computers to simulate, involving photons passing through a network of beam splitters. This experiment aimed to demonstrate a quantum advantage, proving that a quantum computer can perform a task beyond the reach of classical computation. The team focused on improving the complexity of the setup through demultiplexing, which creates multiple indistinguishable photon paths, and introducing a loopback mechanism, adding a temporal dimension to the computation.

Rigorous validation methods were employed to ensure the setup functioned correctly and produced genuine quantum behavior. The experiment utilized a source of single photons with specific characteristics, verified through precise measurements. A key component was a demultiplexer, which splits each photon into multiple indistinguishable paths, increasing the complexity of the network. This demultiplexer, combined with a 25-port interferometer, formed the core of the boson sampling circuit. Single-photon detectors and a time-tagging module were used to precisely measure the arrival times of photons, enabling the implementation of the temporal loopback.

The team successfully generated five photons at a specific rate, achieving high transmission efficiency and demonstrating the indistinguishability of photons from different paths. Researchers meticulously reconstructed the matrix describing the interferometer’s behavior, achieving high fidelity between the reconstruction and the actual device. A Bayesian inference approach was used to validate the loopback sampler, comparing its performance against standard boson samplers and confirming the impact of the temporal feedback. This validation process provided strong evidence that the setup was functioning correctly and producing genuine quantum behavior. The experiment represents a step towards demonstrating a quantum advantage for boson sampling, by increasing the difficulty of classical simulation and pushing the boundaries of quantum optical technology.

Loopback Boson Sampling Amplifies Complexity

Scientists engineered a novel boson sampling technique, termed loopback boson sampling, to amplify computational complexity by introducing temporal correlations among photons. The study pioneered an experimental setup employing a 25-mode femtosecond laser-written interferometer, strategically configured with five output channels connected to five input channels. This configuration creates a system where photons arriving at different times interact, effectively increasing the complexity of the sampling process without physically expanding the interferometer’s size. Researchers injected single photons periodically into the interferometer, leveraging the looped connections to encode information in the temporal degree of freedom.

The team meticulously reconstructed the matrix characterizing the chip’s behavior, enabling precise control and analysis of photon propagation. To validate the sampler and confirm its distinct behavior from standard boson sampling, scientists performed Bayesian analysis, rigorously assessing the system’s performance and confirming the impact of the temporal correlations. A theoretical description, based on transformations of annihilation operators, was developed to model the system’s evolution and deliver the structure of the transmission matrix. This model allowed researchers to quantify the complexity of their boson sampler in relation to conventional boson sampling approaches, demonstrating a resource-efficient method for increasing sampling complexity.

Experiments utilized femtosecond laser-written circuits to create the complex optical network, ensuring high precision and control over photon paths. The interferometer was designed to support 25 distinct modes, allowing for a high degree of complexity in the sampling process. Scientists characterized the system’s performance by analyzing the output distribution of photons, confirming that the looped connections successfully introduced the desired temporal correlations. This work demonstrates the feasibility of using optical feedback to enhance the complexity of boson sampling, paving the way for scalable demonstrations of quantum advantage with single photons and offering a promising path towards building more powerful quantum computing systems.

Optical Feedback Amplifies Boson Sampling Complexity

Scientists have demonstrated a significant advancement in boson sampling by incorporating optical feedback lines, a novel approach that amplifies complexity through the introduction of temporal correlations. The team utilized a 25-mode femtosecond laser-written interferometer, connecting five output channels to five input channels to establish correlations between consecutive photon arrival events. This configuration effectively expands the accessible computational space, resulting in more complex output statistics than those observed in standard boson sampling. Researchers meticulously reconstructed the matrix defining the chip’s behavior, validating the sampler and confirming its distinct behavior from conventional boson sampling methods.

The research team developed a theoretical framework describing the system based on transformations of annihilation operators, delivering the structure of the transmission matrix and quantifying the complexity of their boson sampler in terms equivalent to a conventional system. The setup achieves temporal synchronization without active stabilization, and the total transmission through the chip is approximately 30%, accounting for propagation and interface losses. Measurements confirm that the optical feedback loops expand the effective complexity of boson sampling without increasing the number of physical components. By reconnecting outputs to inputs, the team created temporal correlations between successive photon injections, allowing photons from preceding iterations to interfere with newly arriving photons.

Specifically, with 16 incoming photons, subsets of photons were observed to interfere, demonstrating the impact of the feedback mechanism. The system was designed to allow for three temporal iterations, matching the repetition rate of incoming photons, and the theoretical analysis shows the complexity scales linearly with the number of temporal iterations. This work demonstrates a resource-efficient method to increase sampling complexity, paving the way for scalable demonstrations of quantum advantage using single photons.

Temporal Feedback Amplifies Boson Sampling Complexity

This research demonstrates a significant advance in photonic quantum computing through the experimental realisation of boson sampling enhanced by optical feedback. By introducing temporal correlations between photons within a 25-mode interferometer, the team successfully amplified the complexity of the sampling process without increasing physical resources. Measurements align with theoretical predictions, confirming that the looped architecture operates distinctly from conventional boson sampling methods. This achievement establishes a scalable and resource-efficient pathway towards more complex photonic quantum processors, offering a foundation for future exploitation of temporal feedback as a computational tool.

The authors acknowledge that operating at larger photon numbers and exploring alternative statistical validation approaches could further improve device performance and facilitate large-scale implementations. Beyond complexity verification, the principles demonstrated may also find application in quantum simulations of systems exhibiting inherent temporal correlations, such as those found in non-Markovian dynamics or feedback-controlled quantum networks. This work represents a crucial step towards harnessing the power of temporal correlations to enhance quantum computational capabilities and broaden the scope of quantum simulation.