One of the most exciting potential applications of a quantum computer is the ability

to efficiently simulate quantum systems, a task that is out of the reach of even the

largest classical supercomputers. Such simulations require a quantum algorithm capable

of efficiently representing and manipulating a quantum system, as well as a device with

sufficient coherence to execute it. In this work, we describe experiments advancing both

of these goals. First, we discuss dephasing—currently a leading cause of decoherence

in superconducting qubits—and present measurements accurately quantifying both low-

and high-frequency phase noise sources. We then discuss two quantum algorithms for

the simulation of chemical Hamiltonians, and experimentally contrast their performance.

These results show that with continuing improvement in quantum devices we may soon

be able to apply quantum computers to practical chemistry problems.