



@article {1812,
	title = {Hamiltonian Simulation with Optimal Sample Complexity},
	journal = {npj Quantum Information},
	volume = {13},
	year = {2017},
	month = {2017/03/31},
	abstract = {<blockquote class="abstract mathjax" style="line-height: 20.16px; margin-bottom: 1.5em; color: rgb(0, 0, 0); font-family: \&quot;Lucida Grande\&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.</blockquote><div>\&nbsp;</div><div class="metatable" style="font-size: 12.96px; margin: 0px 0px 1.5em 20px; color: rgb(0, 0, 0); font-family: \&quot;Lucida Grande\&quot;, helvetica, arial, verdana, sans-serif;">\&nbsp;</div>},
	doi = {10.1038/s41534-017-0013-7},
	url = {https://www.nature.com/articles/s41534-017-0013-7},
	author = {Shelby Kimmel and Cedric Yen-Yu Lin and Guang Hao Low and Maris Ozols and Theodore J. Yoder}
}
@article {1513,
	title = {Robust Single-Qubit Process Calibration via Robust Phase Estimation},
	journal = {Physical Review A},
	volume = {92},
	year = {2015},
	month = {2015/12/08},
	pages = {062315},
	abstract = {  An important step in building a quantum computer is calibrating
experimentally implemented quantum gates to produce operations that are close
to ideal unitaries. The calibration step involves estimating the error in gates
and then using controls to correct the implementation. Quantum process
tomography is a standard technique for estimating these errors, but is both
time consuming, (when one only wants to learn a few key parameters), and
requires resources, like perfect state preparation and measurement, that might
not be available. With the goal of efficiently estimating specific errors using
minimal resources, we develop a parameter estimation technique, which can gauge
two key parameters (amplitude and off-resonance errors) in a single-qubit gate
with provable robustness and efficiency. In particular, our estimates achieve
the optimal efficiency, Heisenberg scaling. Our main theorem making this
possible is a robust version of the phase estimation procedure of Higgins et
al. [B. L. Higgins, New J. Phys. 11, 073023 (2009)].
},
	doi = {10.1103/PhysRevA.92.062315},
	url = {http://arxiv.org/abs/1502.02677},
	author = {Shelby Kimmel and Guang Hao Low and Theodore J. Yoder}
}
