Photonic Boson Sampling in a Tunable Circuit (1212.2234v3)

Abstract: Quantum computers are unnecessary for exponentially-efficient computation or simulation if the Extended Church-Turing thesis---a foundational tenet of computer science---is correct. The thesis would be directly contradicted by a physical device that efficiently performs a task believed to be intractable for classical computers. Such a task is BosonSampling: obtaining a distribution of n bosons scattered by some linear-optical unitary process. Here we test the central premise of BosonSampling, experimentally verifying that the amplitudes of 3-photon scattering processes are given by the permanents of submatrices generated from a unitary describing a 6-mode integrated optical circuit. We find the protocol to be robust, working even with the unavoidable effects of photon loss, non-ideal sources, and imperfect detection. Strong evidence against the Extended Church-Turing thesis will come from scaling to large numbers of photons, which is a much simpler task than building a universal quantum computer.

• The paper presents a novel experimental verification of BosonSampling by showing that three-photon amplitudes are characterized by the permanents of submatrix elements.
• It employs single- and dual-mode coherent states for circuit characterization, achieving an L1-norm of 0.027 for two-photon and 0.122 for three-photon experiments.
• The study underscores BosonSampling's scalability potential to challenge classical computation and refute the Extended Church-Turing thesis.

An Analysis of Photonic Boson Sampling in a Tunable Circuit

The paper "Photonic Boson Sampling in a Tunable Circuit" presents an experimental analysis of BosonSampling, a non-universal quantum computing task with implications for computational complexity theory and quantum mechanics. This research evaluates the feasibility of BosonSampling as a means to challenge the Extended Church-Turing Thesis (ECT), which posits that any computation feasible on a realistic physical device can be efficiently performed on a probabilistic Turing machine.

Experimental Focus

The authors experimentally verify the premise that the amplitudes of three-photon scattering events are characterized by the permanents of submatrices derived from a unitary matrix describing a six-mode integrated optical circuit. This experiment provides evidence for the computational complexity of BosonSampling, suggesting that it is infeasible for classical computers to efficiently sample from the same distribution, thus potentially contradicting the ECT thesis.

Methodology and Results

An efficient characterization method using single- and dual-mode coherent states measures the unitary transformation within the photonic circuit. The experimental setup includes two pairs of single photons produced via spontaneous parametric downconversion, which are then input into the BosonSampling circuit. The experiment tested both non-colliding and colliding output configurations, measuring the non-classical interference visibility to ensure robust results despite photon loss and detection imperfections.

Numerically, the experiment shows a strong match between predicted and measured distributions. The average $L_{1}$-norm distance between the predicted and measured visibilities for the two-photon experiment was $0.027$, indicating excellent agreement. For the three-photon case, the $L_{1}$-norm was $0.122$, suggesting a higher deviation due to technical limitations such as higher-order photon emissions and slight photon distinguishability.

Implications and Future Directions

This paper strongly indicates the potential for BosonSampling to act as a harbinger of quantum computational advantage, potentially disproving the ECT thesis for particular tasks. Given the experimental robustness demonstrated with imperfect components, the work provides optimistic prospects for scalability. Achieving practical BosonSampling on a larger scale—i.e., with 20 to 30 photons—would intensify the evidence against ECT in classical computational complexity theory.

Future advancements will necessitate higher-efficiency photon-number-resolving detectors and integrated circuits paired with advanced, triggered photon sources. The development of loss-tolerant BosonSampling experiments is crucial, given the absence of error correction for intermediate quantum computing models like BosonSampling. Notably, the research implies statistical sampling can still be effective amidst noise, an important factor for real-world application considerations.

Broader Impact and Conclusion

The research contributes to the theoretical and practical considerations surrounding quantum computational models. It addresses a prevalent challenge in demonstrating quantum advantage without the need for full-scale quantum computers, which remain a considerable engineering hurdle. Moreover, the methods and insights from this paper can inform other quantum computational paradigms and bolster confidence in non-universal quantum computing's capacity to solve specific classes of problems beyond classical capabilities.

This paper delineates critical developments in our understanding of computational complexity and quantum mechanics while providing a roadmap for future explorations of quantum advantage in computation. The successful demonstration of BosonSampling foretells not just an experimental triumph but a shift in addressing long-standing theoretical conjectures in computer science.