Optimal Trotterization in universal quantum simulators under faulty control
Abstract
Universal quantum simulation may provide insights into those manybody systems that cannot be described classically and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary time evolution of the simulator into a stroboscopic sequence of repeated elementary evolutions, is a key algorithmic component which makes quantum simulation of dynamics tractable. The Trotter number n sets the time scale on which a computer running this algorithm is switched from one elementary evolution to another. In the ideal case, the precision of the simulation can be arbitrarily controlled by increasing n . We study a more realistic scenario where each gate is applied imperfectly. The resultant tradeoff in errors leads to an ultimate limit on the precision of the simulation. We calculate the optimum Trotter number n^{*} that achieves this limit, which is the minimum statistical distance from the actual simulation to the ideal one.
 Publication:

Physical Review A
 Pub Date:
 May 2015
 DOI:
 10.1103/PhysRevA.91.052327
 arXiv:
 arXiv:1502.04536
 Bibcode:
 2015PhRvA..91e2327K
 Keywords:

 03.67.Lx;
 03.67.Ac;
 Quantum computation;
 Quantum algorithms protocols and simulations;
 Quantum Physics
 EPrint:
 13pp. The distance to the published version has been reduced