



@article {2983,
	title = {Quantum computational advantage via high-dimensional Gaussian boson sampling},
	journal = {Science Advances},
	volume = {8},
	year = {2022},
	month = {1/5/2022},
	pages = {eabi7894},
	abstract = {<p>A programmable quantum computer based on fiber optics outperforms classical computers with a high level of confidence. Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.</p>},
	doi = {10.1126/sciadv.abi7894},
	url = {https://www.science.org/doi/abs/10.1126/sciadv.abi7894},
	author = {Abhinav Deshpande and Arthur Mehta and Trevor Vincent and Nicolas Quesada and Marcel Hinsche and Marios Ioannou and Lars Madsen and Jonathan Lavoie and Haoyu Qi and Jens Eisert and Dominik Hangleiter and Bill Fefferman and Ish Dhand}
}
@article {2773,
	title = {Quantum Computational Supremacy via High-Dimensional Gaussian Boson Sampling},
	year = {2021},
	month = {2/24/2021},
	abstract = {<p>Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.</p>},
	url = {https://arxiv.org/abs/2102.12474},
	author = {Abhinav Deshpande and Arthur Mehta and Trevor Vincent and Nicolas Quesada and Marcel Hinsche and Marios Ioannou and Lars Madsen and Jonathan Lavoie and Haoyu Qi and Jens Eisert and Dominik Hangleiter and Bill Fefferman and Ish Dhand}
}
@article {1434,
	title = {Quantum Tomography via Compressed Sensing: Error Bounds, Sample  Complexity, and Efficient Estimators
},
	journal = {New Journal of Physics},
	volume = {14},
	year = {2012},
	month = {2012/09/27},
	pages = {095022},
	abstract = {  Intuitively, if a density operator has small rank, then it should be easier
to estimate from experimental data, since in this case only a few eigenvectors
need to be learned. We prove two complementary results that confirm this
intuition. First, we show that a low-rank density matrix can be estimated using
fewer copies of the state, i.e., the sample complexity of tomography decreases
with the rank. Second, we show that unknown low-rank states can be
reconstructed from an incomplete set of measurements, using techniques from
compressed sensing and matrix completion. These techniques use simple Pauli
measurements, and their output can be certified without making any assumptions
about the unknown state.
  We give a new theoretical analysis of compressed tomography, based on the
restricted isometry property (RIP) for low-rank matrices. Using these tools, we
obtain near-optimal error bounds, for the realistic situation where the data
contains noise due to finite statistics, and the density matrix is full-rank
with decaying eigenvalues. We also obtain upper-bounds on the sample complexity
of compressed tomography, and almost-matching lower bounds on the sample
complexity of any procedure using adaptive sequences of Pauli measurements.
  Using numerical simulations, we compare the performance of two compressed
sensing estimators with standard maximum-likelihood estimation (MLE). We find
that, given comparable experimental resources, the compressed sensing
estimators consistently produce higher-fidelity state reconstructions than MLE.
In addition, the use of an incomplete set of measurements leads to faster
classical processing with no loss of accuracy.
  Finally, we show how to certify the accuracy of a low rank estimate using
direct fidelity estimation and we describe a method for compressed quantum
process tomography that works for processes with small Kraus rank.
},
	doi = {10.1088/1367-2630/14/9/095022},
	url = {http://arxiv.org/abs/1205.2300v2},
	author = {Steven T. Flammia and David Gross and Yi-Kai Liu and Jens Eisert}
}
@article {1432,
	title = {Quantum state tomography via compressed sensing},
	journal = {Physical Review Letters},
	volume = {105},
	year = {2010},
	month = {2010/10/4},
	abstract = {  We establish methods for quantum state tomography based on compressed
sensing. These methods are specialized for quantum states that are fairly pure,
and they offer a significant performance improvement on large quantum systems.
In particular, they are able to reconstruct an unknown density matrix of
dimension d and rank r using O(rd log^2 d) measurement settings, compared to
standard methods that require d^2 settings. Our methods have several features
that make them amenable to experimental implementation: they require only
simple Pauli measurements, use fast convex optimization, are stable against
noise, and can be applied to states that are only approximately low-rank. The
acquired data can be used to certify that the state is indeed close to pure, so
no a priori assumptions are needed. We present both theoretical bounds and
numerical simulations.
},
	doi = {10.1103/PhysRevLett.105.150401},
	url = {http://arxiv.org/abs/0909.3304v4},
	author = {David Gross and Yi-Kai Liu and Steven T. Flammia and Stephen Becker and Jens Eisert}
}
