Foundational Concepts in Quantum Error Correction
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Quantum Error Correction
Here I outline the motivation for QEC, beginning with Richard Feynman’s observation that simulating quantum systems requires machines governed by quantum mechanics. We review Shor’s 9-qubit code, which protects against arbitrary single-qubit errors, and extend the discussion to fault-tolerant quantum computation (FTQC), where circuits are constructed to minimize error propagation. Early experimental demonstrations, including the 1998 NMR-based implementation by David Cory and collaborators, are discussed. Finally, we examine topological codes, as a viable framework for building robust quantum systems. These developments follow the evolution of QEC from theoretical constructs to experimental proof-of-concept and toward scalable, fault-tolerant quantum computation.
Please the full paper on the Foundational Concepts in Quantum Error Correction below. This work was done for a class during my PhD. Taught by Dr. Swati Singh at the University of Delaware.