Spoofing cross entropy measure in boson sampling

Cross entropy measure is a widely used benchmarking to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling. In this work, we propose a heuristic classical algorithm that generates heavy outcomes of the ideal boson sampling distribution and consequently achieves a large cross entropy. The key idea is that there exist classical samplers that are efficiently simulable and correlate with the ideal boson sampling probability distribution and that the correlation can be used to post-select heavy outcomes of the ideal probability distribution, which essentially leads to a large cross entropy. As a result, our algorithm achieves a large cross entropy score by selectively generating heavy outcomes without simulating ideal boson sampling. We first show that for small-size circuits, the algorithm can even score a better cross entropy than the ideal distribution of boson sampling. We then demonstrate that our method scores a better cross entropy than the recent Gaussian boson sampling 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 our approach works for much larger system sizes in fermion sampling, where we can efficiently compute output probabilities.Comment: 14 pages, 11 figure

Information transmission with continuous variable quantum erasure channels

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 type 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 involving 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 quantum erasure channel in continuous variable settings and sheds light on the understanding of other type of continuous variable quantum channels

Classical simulation of bosonic linear-optical random circuits beyond linear light cone

Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine classical simulability of sampling from the output photon-number distribution of linear-optical circuits composed of random beam splitters with equally distributed squeezed vacuum states and single-photon states input. We provide efficient classical algorithms to simulate linear-optical random circuits and show that the algorithms' error is exponentially small up to a depth less than quadratic in the distance between sources using a classical random walk behavior of random linear-optical circuits. Notably, the average-case depth allowing an efficient classical simulation is larger than the worst-case depth limit, which is linear in the distance. Besides, our results together with the hardness of boson sampling give a lower-bound on the depth for constituting global Haar-random unitary circuits.Comment: 16 pages, 1 figur

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators XP+PX, i.e., a non-Gaussian measurement, is required to be fully optimal.Comment: 13 pages, 6 figure