33 research outputs found
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