T8: A Practical Guide to Pauli-operator Based Quantum Computation

Pauli spin operators have existed for nearly as long as quantum mechanics. Moreover with the advent of quantum computing, their prominence has only grown as they represent the primary method for the quantization of Boolean variables. Despite this central role, it can often be the case that learnings and understandings which are found in one quantum computing discipline—be it algorithm development, language development, circuit optimization, quantum error correction, quantum control, and quantum hardware design and characterization—are not generally understood between these disciplines. This tutorial aims to aid in this cross-pollination by presenting a working knowledge about the theory behind Pauli-based quantum computation and practical methods for deploying that knowledge for students and practitioners alike. The tutorial features a range of speakers working in different disciplines of quantum computing research and development to provide their insights into the usefulness of the Pauli algebra and transformations on it.

Topics covered:

• A Practical Theory of the Pauli Algebra: intro to the Pauli algebra, use as an operator basis, Clifford group, Pauli Tableau, symplectic vector space, symplectic automorphisms

• Linear Quantum Error Correcting Codes: QEC basics, stabilizer codes, subsystem codes, fault-tolerant operation

• Pauli-based Representation and Optimization of Quantum Logic: Pauli-based representations, circuit manipulation and conversion, optimization and circuit synthesis

• Pauli-operator Methods for Hardware Design and Testing: Defining a qubit via Pauli operators, Clifford benchmarking, channel tomography, Clifford and non-Clifford gate design