Reaching beyond the horizon of classical computation: how to measure and improve the quantum capacity for computation

I will present some recent breakthrough theoretical results to identify and suppress errors across a quantum computer in an efficient and practical manner. I will also present preliminary results on the implementation of these methods on a 10 qubit ion trap quantum computer. Coupled with the simplified form for the error model that is achievable via randomized compiling, I will describe how these diagnostic tests, which we call ‘cycle benchmarking’ , enable a scalable approach to measuring several critical error characterizations, such as spatial and temporal error correlations and a practical bound on the cumulative error rate for an arbitrary quantum computation on an arbitrarily large number of qubits. We call this new experimentally measurable bound the ‘quantum capacity’ for computation. This implies that we now have a definitive test for quantum advantage, aka quantum supremacy, for *any* application on both small and large scale quantum computers, as well as the means for quantitatively assessing the degree of quantum advantage as control and hardware design improves.

Joint work with Joel Wallman, Alexander Erhart, Roman Stricker,
Esteban A. Martinez, Daniel Nigg, Philipp Schindler, Thomas Monz, and Rainer Blatt