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Plausible claims for quantum advantage have been made using sampling problems such as random circuit sampling in superconducting qubit devices, and Gaussian boson sampling in quantum optics experiments. Now, the major next step is to channel the potential quantum advantage to solve practical applications rather than proof-of-principle experiments. It has recently been proposed that a Gaussian boson sampler can efficiently generate molecular vibronic spectra, which are an important tool for analysing chemical components and studying molecular structures. The best-known classical algorithm for calculating the molecular spectra scales super-exponentially in the system size. Therefore, an efficient quantum algorithm could represent a computational advantage. However, here we propose an efficient quantum-inspired classical algorithm for molecular vibronic spectra with harmonic potentials. Using our method, the zero-temperature molecular vibronic spectra problems that correspond to Gaussian boson sampling can be exactly solved. Consequently, we demonstrate that those problems are not candidates for quantum advantage. We then provide a more general molecular vibronic spectra problem, which is also chemically well motivated, for which our method does not work and so might be able to take advantage of a boson sampler. 

We investigate a resource-efficient distributed quantum sensing (DQS) scheme using phase-sensitive optical parametric amplifiers and linear optics, achieving sensitivity levels close to the optimal limit determined by the quantum Fisher information of the resource state. 

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the Nout ~ \sqrt(N) scaling of the number of surviving photons Nout in the number of input photons N. We numerically verify this result using a tensor network algorithm with U(1) symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks. 

Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling (BS). We present a heuristic classical algorithm that attains a better XE than the current BS experiments in a verifiable regime and is likely to attain a better XE score than the near-future BS experiments in a reasonable running time. The key idea behind the algorithm is that there exist distributions that correlate with the ideal BS probability distribution and that can be efficiently computed. The correlation and the computability of the distribution enable us to postselect heavy outcomes of the ideal probability distribution without computing the ideal probability, which essentially leads to a large XE. Our method scores a better XE than the recent Gaussian BS experiments when implemented at intermediate, verifiable system sizes. Much like current state-of-the-art experiments, we cannot verify that our spoofer works for quantum-advantage-size systems. However, we demonstrate that our approach works for much larger system sizes in fermion sampling, where we can efficiently compute output probabilities. Finally, we provide analytic evidence that the classical algorithm is likely to spoof noisy BS efficiently. 

Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels.