First-order gauge-invariant error rates in quantum processors

Process matrix models for quantum gates operations contain non-physical “gauge” degrees of freedom.  These gauge freedoms wreak a surprising amount of havoc.  For example, they imply that commonly used error metrics, such as the process fidelity and diamond distance of a quantum gate, are not physically well-defined quantities but rather depend on an arbitrary choice of reference frame.  In this talk we present a partial solution to this problem by introducing error rates that are invariant under small gauge transformations to first order in the error strengths.  These rates are useful in the common context where a quantum processor’s operations are close to ideal.  We walk through a simple example, showing how first-order gauge-invariant rates can be associated with physically meaningful characteristics of a gate set and how they can be categorized into “intrinsic” errors associated with individual gates and “relational” errors that exist between sets of gates.

This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research Quantum Testbed Program. Sandia National Laboratories is operated by NTESS, a wholly owned subsidiary of Honeywell International, for the US Department of Energy’s NNSA under contract DE-NA0003525