Tutorial: Quantum Error Correcting Codes and Circuits: Algorithm-Architecture Codesign

Engineering practical and reliable quantum computers and communication systems requires: (a) protection of quantum states from decoherence, and (b) overcoming the reliability issues due to faulty gates. The half-day tutorial will provide a detailed overview of the new developments related to quantum ECCs and fault tolerant computing. Specific topics include: (a) Introduction to quantum gates and circuits, (b) Shor’s 9-qubit ECC and stabilizer formalism for quantum ECCs (c) Systematic method for construction of quantum ECC circuits, (d) Optimization of quantum ECC circuits in terms of number of multiple-qubit gates, and (e) Nearest neighbor compliant (NNC) quantum ECC circuits. Descriptions of the topics are listed below. Introduction to quantum gates and circuits. Shor’s 9-qubit code and stabilizer formalism – Bit flip codes, phase flip codes, Shor’s 9-qubit code, Stabilizer formalism. Systematic method for construction of quantum ECC circuits – Encoder circuit, Syndrome measurement circuit, 5-qubit code encoder and decoder circuit, Steane code encoder and decoder circuit. Optimization of quantum ECC circuits in terms of number of multiple-qubit gates – Circuit equivalence rules, Optimization of circuits using circuit equivalence rules, Optimization using group theoretic matrix equivalence. Nearest-neighbor compliant quantum circuits – Various IBM architectures, nearest neighbor compliance, swap gates, minimization of swap gates for NNC circuits.