Quantum Error Correction

Quantum fault-tolerance is one of the core reasons we believe there can be a general-purpose quantum computer. In this course, we will cover fundamentals (error correction criteria; Pauli stabilizer/additive codes; symplectic spaces and chain complexes; concatenation), well-known codes (5-qubit code, Steane code, toric/surface codes, color codes), aspects of decoding (hardness and efficiency, statistical mechanics of decoding, clustering phenomena), more recent advances (LDPC and Floquet), codes for non-qubits (bosonic and non-Pauli stabilizer), and problems inherent to quantum settings (measurement errors, propagation of errors in circuits, logical operations, magic state distillation), and will glimpse at physically motivated constructions (thermal self-correction and bulk-boundary correspondence). Prerequisite: thorough linear algebra, PHYSICS 130, and basic probability. This course is restricted to graduate students only. Undergraduates may enroll in the class only with a permission number.