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Explore quantum computing advancements
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Module 6
Fault-Tolerant Quantum Computing
1
Clifford Gates, Gottesman-Knill, and Classical Simulability
Distinguish between Clifford and non-Clifford gates and analyze the implications of the Gottesman-Knill theorem for the classical simulability of quantum circuits
2
Transversal Gates and Logical Clifford Operations on CSS Codes
Analyze the fault-tolerant properties of transversal gates and identify which logical Clifford gates can be implemented transversally on a given CSS code
3
Magic State Distillation: Protocol, Overhead, and Fidelity
Analyze the protocol for magic state distillation, including the resource overhead and the achievable fidelity improvement per distillation round
4
Building the 7-Qubit Steane Code Encoder
Construct the encoding circuit for the 7-qubit Steane code using its properties as a CSS code
5
Steane Code Syndrome Measurement and Single-Qubit Error Correction
Implement syndrome measurement for the Steane code and demonstrate its ability to correct an arbitrary single-qubit error
6
Surface Code Stabilizers on a 2D Lattice
Define the surface code on a 2D lattice by specifying the stabilizer generators for plaquette and vertex operators
7
Surface Code Syndrome Measurement Circuits
Implement syndrome measurement circuits for X and Z stabilizers in the surface code
8
Decoding Error Chains on the Surface Code
Interpret syndrome measurement outcomes to identify error chains on the surface code lattice
9
Decoding Surface Codes with Minimum-Weight Perfect Matching
Formulate the surface code decoding problem as a minimum-weight perfect matching instance and analyze the mapping from syndromes to graph weights
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Quantum Error Correction Fundamentals
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Recent Advances in Quantum Error Correction