Classical Simulation of Quantum Adiabatic Algorithms using Mathematica on GPUs

Simulation of quantum computers is what allows us to test quantum software on a limited scale. Therefore this recent paper by Díaz-Pier, Venegas-Andraca, and Gómez-Muñoz, Classical Simulation of Quantum Adiabatic Algorithms using Mathematica on GPUs is of interest. The abstract:

In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a high-level user interface developed on Mathematica\copyright which is connected to C++ code in order to make our platform capable of communicating with a Graphics Processing Unit. We introduce the reader to the behavior of our proposal by simulating a quantum adiabatic algorithm designed for solving hard instances of the 3-SAT problem. We show that our simulator is capable of significantly increasing the number of qubits that can be simulated using classical hardware. Finally, we present a review of currently available classical simulators of quantum systems together with some justifications, based on our willingness to further understand processing properties of Nature, for devoting resources to building more powerful simulators.

(Image is figure 1 from the paper.)

Quantum Computing for Molecular Energy Simulations

Another one from arXiv: Quantum Computing for Molecular Energy Simulations by Whitfield, Biamonte, and Aspuru-Guzik. Another way quantum computers can be put to use besides the often cited factoring.

The abstract:

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, to obtain the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule, of how a chemical Hamiltonian can be simulated using a quantum computer.