Fault-Tolerant Quantum Measurement of Error Syndromes and Logical Operators

Fault-tolerant quantum computation requires the measurements of error syndromes and logical operators in a way that minimizes undesired correlated errors on the quantum data. This thesis explores possible forms for performing these measurements. Our first result aims at minimizing the number of ancilla qubits for syndrome measurement. We show that on a generalized surface code family known as 2D compass codes, each stabilizer check can be fault-tolerantly measured witha single ancilla qubit, regardless of the weight of the check. Our result infers that large ancilla blocks are not always necessary for performing stabilizer measure- ments of high weight. We then look at another regime where ancilla size is less of a concern. We show a simple framework that bridges Shor- and Steane-style ancillas, which are arguably the smallest and biggest ancilla constructions for syndrome measurements respectively. Our framework enables intermediate-size ancillas whose preparations are easier than Steane-style ancilla, while being more robust against measurement errors compared to Shor’s construction. We further show that our new constructions could be useful for future quantum computers with long coherence time. Our final result look at how the framework for constructing syndrome measurement circuits can be modified to perform logical operator measurements. While Shor- and Steane-style ancilla can be used for logical measurements, they have impractical time and space overhead when applied to large quantum codes. We show that on a quantum low-density-parity-check code family called hyperbolic surface codes, intermediate ancilla can be constructed such that no repetitive logical measurements are required for boosting the accuracy. In addition, these ancilla blocks can be directly prepared without postselection or state distillation.