A Diary of a Faulty Logical Qubit: Logical Gate Set Tomography

The field of quantum characterization, verification, and validation (QCVV) is designed to assess the performance of quantum processors by analyzing their qubits and logic operations. One can construct a comprehensive model of quantum processor operations via tomographic reconstruction methods, using data from many individual experiments designed to probe the operations. One such tomographic method is gate set tomography (GST), which reconstructs the process matrices for all quantum operations based on data collected through carefully constructed quantum programs executed on the quantum processor. As we transition from the NISQ era of quantum computers to fault-tolerant, error-corrected machines, quantum computers will contain thousands of qubits, and characterizing each physical qubit will become infeasible. Therefore, to reduce the amount of computational and experimental resources, we can instead characterize logical qubits. There are a variety of logical characterization techniques in literature, such as logical randomized benchmarking and logical process tomography; however, existing methods are not complete in their characterization or make strong assumptions about SPAM. Our work investigates the performance of logical gate set tomography (LoGST) on logical qubits running five-qubit and seven-qubit quantum error correcting codes.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This research was funded, in part, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA). All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the U.S. Government