Fault-tolerance on near-term quantum computers and subsystem quantum error correcting codes

Large-scale fault-tolerant quantum computers are supposed to provide exponential speedup over many classical algorithms for solving realistic computationally intensive problems. Given that practical quantum computers are extremely sensitive to noise, error correction protocols have to be employed in order to suppress noises in the quantum system and maintain the fidelity of computations. As quantum computing experiments are progressing into the regime where active quantum error correction can soon be implemented, it is becoming more important to understand the properties of small quantum error correcting codes and how to efficiently implement them in actual experiments given realistic near-term quantum device specifications. In this dissertation, we present our work on suppressing errors in quantum computing systems in two directions: realizing fault-tolerance with several small quantum error-correcting codes under realistic device assumptions, and developing large-scale code families with subsystem quantum error correcting codes. For small codes such as the Bare [[7,1,3]] code, the Bacon-Shor code, and the rotated 17-qubit surface code, we show designs for implementing them in realistic ion trap quantum computers while minimizing the amount of resources needed and optimizing fidelity of the logical system. For families of subsystem quantum error correcting codes, we investigate the compass codes, Bravyi-Bacon-Shor codes and subsystem hypergraph product codes, and show that these codes can be advantageous in terms of handling biased noises, having good code parameters, and exhibiting efficient decoding performance.Ph.D