%0 Journal Article %J npj Quantum Information %D 2017 %T Hamiltonian Simulation with Optimal Sample Complexity %A Shelby Kimmel %A Cedric Yen-Yu Lin %A Guang Hao Low %A Maris Ozols %A Theodore J. Yoder %X
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.
 
 
%B npj Quantum Information %V 13 %8 2017/03/31 %G eng %U https://www.nature.com/articles/s41534-017-0013-7 %N 3 %R 10.1038/s41534-017-0013-7 %0 Journal Article %J Physical Review A %D 2015 %T Robust Single-Qubit Process Calibration via Robust Phase Estimation %A Shelby Kimmel %A Guang Hao Low %A Theodore J. Yoder %X 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)]. %B Physical Review A %V 92 %P 062315 %8 2015/12/08 %G eng %U http://arxiv.org/abs/1502.02677 %N 6 %R 10.1103/PhysRevA.92.062315