1202.1536 (Andrew T. Sornborger)

Quantum Simulation of Tunneling in Small Systems    [PDF]

Andrew T. Sornborger

A number of quantum algorithms have been performed on small quantum
computers; these include Shor's prime factorization algorithm, error
correction, Grover's search algorithm and a number of analog and digital
quantum simulations. Because of the number of gates and qubits necessary,
however, digital quantum particle simulations remain untested. A contributing
factor to the system size required is the number of ancillary qubits needed to
implement matrix exponentials of the potential operator. Here, we show that a
set of tunneling problems may be investigated with no ancillary qubits and a
cost of one single-qubit operator per time step for the potential evolution. We
show that physically interesting simulations of tunneling using 2 qubits (i.e.
on 4 lattice point grids) may be performed with 40 single and two-qubit gates.
Approximately 70 to 140 gates are needed to see interesting tunneling dynamics
in three-qubit (8 lattice point) simulations.

View original: http://arxiv.org/abs/1202.1536