# Boson sampling with Gaussian measurements

@article{Chakhmakhchyan2017BosonSW,
title={Boson sampling with Gaussian measurements},
author={L. Chakhmakhchyan and Nicolas J. Cerf},
journal={Physical Review A},
year={2017},
volume={96},
pages={032326}
}
• Published 15 May 2017
• Physics
• Physical Review A
We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a twofold version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states… Expand

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#### References

SHOWING 1-10 OF 52 REFERENCES
Exact boson sampling using Gaussian continuous-variable measurements
• Physics
• 2017
Boson sampling is a quantum mechanical task involving Fock basis state preparation and detection and evolution using only linear interactions. A classical algorithm for producing samples from thisExpand
Sufficient Conditions for Efficient Classical Simulation of Quantum Optics
• Physics
• 2015
We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output.Expand
BosonSampling with Lost Photons
• Computer Science, Physics
• ArXiv
• 2015
It is shown that, if k out of n photons are lost, then BosonSampling cannot sample classically from a distribution that is 1/n^Theta(k)-close to the ideal distribution, unless a $\text{BPP}^{\text{NP}}$ machine can estimate the permanents of Gaussian matrices in $n^{O(k)}$ time. Expand
Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
• Physics
• 2017
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suitedExpand
The computational complexity of linear optics
• Computer Science, Physics
• STOC '11
• 2011
A model of computation in which identical photons are generated, sent through a linear-optical network, then nonadaptively measured to count the number of photons in each mode is defined, giving new evidence that quantum computers cannot be efficiently simulated by classical computers. Expand
What can quantum optics say about complexity theory?
• Medicine, Physics
• Physical review letters
• 2015
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, a general formula is derived for calculating the output probabilities, and by considering input thermal states, it is shown that theoutput probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. Expand
Error tolerance of the boson-sampling model for linear optics quantum computing
• Physics
• 2012
Linear optics quantum computing is a promising approach to implementing scalable quantum computation. However, this approach has very demanding physical resource requirements. Recently, Aaronson andExpand
Scalable implementation of boson sampling with trapped ions.
• Physics, Medicine
• Physical review letters
• 2014
This work proposes a scalable implementation of boson sampling using local transverse phonon modes of trapped ions to encode the bosons, which would outperform the most powerful classical computers and constitute an effective disproof of the famous extended Church-Turing thesis. Expand
Spin models and boson sampling
• Mathematics, Physics
• 2015
In this work we proof that boson sampling with $N$ particles in $M$ modes is equivalent to short-time evolution with $N$ excitations in an XY model of $2N$ spins. This mapping is efficient wheneverExpand
Compact Gaussian quantum computation by multi-pixel homodyne detection
• Computer Science, Physics
• 2013
This method is based on a multi-pixel homodyne detection system recently demonstrated experimentally, which includes classical data post-processing and allows the incorporation of the linear optics network in the stage of the measurement. Expand