Characterizing and Mitigating Errors in Quantum Computers

This thesis aims to present methods for characterizing and mitigating errors in quantum computers. We begin by providing a historical overview of computing devices and the evolution of quantum information. The basics of characterizing noise in quantum computers and the utilization of quantum control and error mitigation techniques to reduce the impact of noise on performance are also discussed. In the initial part of the thesis, we focus on a particularly detrimental type of time-dependent errors and derive theoretical limits of a closed-loop feedback based quantum control protocol for their mitigation. Two different protocols, one suitable for fault-tolerant systems and another for near-term devices, are presented and their performance is demonstrated through numerical simulations. Additionally, we explore the mitigation of coherent noise at the circuit level through the use of the hidden inverses protocol with results from experiments conducted at Duke University, Sandia National Laboratories, and IBM. Finally, we propose a scalable error characterization procedure for large quantum systems, which is tested through numerical simulations to highlight its sensitivity to various sources of noise. Crucially, this protocol does not require access to ideal classical simulation of quantum circuits unlike other benchmarks such as quantum volume or cross entropy benchmarks.