Supercomputer simulations of transmon quantum computers
We develop a simulator for quantum computers composed of superconducting
transmon qubits. The simulation model supports an arbitrary number of transmons
and resonators. Quantum gates are implemented by time-dependent pulses.
Nontrivial effects such as crosstalk, leakage to non-computational states,
entanglement between transmons and resonators, and control errors due to the
pulses are inherently included. The time evolution of the quantum computer is
obtained by solving the time-dependent Schr\"odinger equation. The simulation
algorithm shows excellent scalability on high-performance supercomputers. We
present results for the simulation of up to 16 transmons and resonators.
Additionally, the model can be used to simulate environments, and we
demonstrate the transition from an isolated system to an open quantum system
governed by a Lindblad master equation. We also describe a procedure to extract
model parameters from electromagnetic simulations or experiments. We compare
simulation results to experiments on several NISQ processors of the IBM Q
Experience. We find nearly perfect agreement between simulation and experiment
for quantum circuits designed to probe crosstalk in transmon systems. By
studying common gate metrics such as the fidelity or the diamond distance, we
find that they cannot reliably predict the performance of repeated gate
applications or practical quantum algorithms. As an alternative, we find that
the results from two-transmon gate set tomography have an exceptional
predictive power. Finally, we test a protocol from the theory of quantum error
correction and fault tolerance. We find that the protocol systematically
improves the performance of transmon quantum computers in the presence of
characteristic control and measurement errors.
Dennis Willsch