Physics / research
Protect and control quantum information
Develop error-correcting codes and fault-tolerant reasoning from physical noise models, syndrome extraction, logical operations, and hardware constraints.
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Inside this module
Module 01 research
Protect and control quantum information
Develop error-correcting codes and fault-tolerant reasoning from physical noise models, syndrome extraction, logical operations, and hardware constraints.
- 01
Pauli errors and error-basis expansion
Expand physical qubit noise in an operator basis while distinguishing coherent rotations, stochastic channels, and leakage.
30 min - 02
Three-qubit repetition and phase-flip codes
Protect one restricted error type by parity measurements that preserve the unknown logical amplitudes.
30 min - 03
Knill–Laflamme error-correction conditions
Test exact correctability by comparing error-overlap matrices throughout a code subspace.
30 min - 04
Stabilizer formalism and syndromes
Use commuting Pauli checks to define codes, diagnose errors, and separate stabilizers from logical operators.
30 min - 05
CSS codes and classical-code relations
Construct complementary bit and phase checks from binary parity matrices and verify their compatibility.
30 min - 06
Surface-code checks and logical operators
Relate local checks, error-chain endpoints, and noncontractible logical strings in an explicit periodic lattice code.
30 min - 07
Decoding and measurement-error models
Decode syndrome histories using explicit data and readout error models rather than trusting a single round.
30 min - 08
Fault tolerance and threshold assumptions
Connect error propagation and fault-tolerant gadgets to conditional suppression bounds for long computations.
30 min - 09
Transversal gates and magic-state distillation
Explain limited error propagation from transversal gates and the conditional resource tradeoff of magic-state preparation.
30 min - 10
Coherent control errors and dynamical decoupling
Derive rotation signs and ideal echo cancellation while identifying calibration, bandwidth, leakage, and feedback limits.
30 min