



01826nas a2200169   4500008004100000245005800041210005800099260001500157490000700172520131900179100001901498700002401517700002001541700001701561700002401578856005401602       2017                        eng d00aHamiltonian Simulation with Optimal Sample Complexity0 aHamiltonian Simulation with Optimal Sample Complexity  c2017/03/310 v133 a<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>1 aKimmel, Shelby1 aLin, Cedric, Yen-Yu1 aLow, Guang, Hao1 aOzols, Maris1 aYoder, Theodore, J.  uhttps://www.nature.com/articles/s41534-017-0013-701534nas a2200157   4500008004100000245007200041210006900113260001500182300001100197490000700208520106200215100001901277700002001296700002401316856003601340       2015                        eng d00aRobust Single-Qubit Process Calibration via Robust Phase Estimation0 aRobust SingleQubit Process Calibration via Robust Phase Estimati  c2015/12/08  a0623150 v923 a  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)].
1 aKimmel, Shelby1 aLow, Guang, Hao1 aYoder, Theodore, J.  uhttp://arxiv.org/abs/1502.02677