



@article {3315,
	title = {Page curves and typical entanglement in linear optics},
	journal = {Quantum},
	volume = {7},
	year = {2023},
	month = {5/18/2023},
	pages = {1017},
	abstract = {<p>Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the R{\'e}nyi-2 Page curve (the average R{\'e}nyi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the R{\'e}nyi-2 entropy by studying its variance. Using the aforementioned results for the R{\'e}nyi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.</p>},
	doi = {10.22331/q-2023-05-23-1017},
	url = {https://arxiv.org/abs/2209.06838},
	author = {Joseph T. Iosue and Adam Ehrenberg and Dominik Hangleiter and Abhinav Deshpande and Alexey V. Gorshkov}
}
@article {2827,
	title = {Precise Hamiltonian identification of a superconducting quantum processor},
	year = {2021},
	month = {8/18/2021},
	abstract = {<p>The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. Here, we develop a characterization technique to benchmark the implementation precision of a specific quantum simulation task. We infer all parameters of the bosonic Hamiltonian that governs the dynamics of excitations in a two-dimensional grid of nearest-neighbour coupled superconducting qubits. We devise a robust algorithm for identification of Hamiltonian parameters from measured times series of the expectation values of single-mode canonical coordinates. Using super-resolution and denoising methods, we first extract eigenfrequencies of the governing Hamiltonian from the complex time domain measurement; next, we recover the eigenvectors of the Hamiltonian via constrained manifold optimization over the orthogonal group. For five and six coupled qubits, we identify Hamiltonian parameters with sub-MHz precision and construct a spatial implementation error map for a grid of 27 qubits. Our approach enables us to distinguish and quantify the effects of state preparation and measurement errors and show that they are the dominant sources of errors in the implementation. Our results quantify the implementation accuracy of analog dynamics and introduce a diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.</p>},
	url = {https://arxiv.org/abs/2108.08319},
	author = {Dominik Hangleiter and Ingo Roth and Jens Eisert and Pedram Roushan}
}
