Wolfram reposted this
How do you correct an error without reading the information you are trying to protect? What information the classical controller should retain for that purpose? Quantum error correction depends on learning about errors without revealing the encoded quantum state. Continuous measurements make this a problem of inference and control: the signals are noisy, and errors keep occurring while the controller responds. I've drafted a notebook (see comments) where I work through this process using three physical qubits that encode one logical qubit. Starting from the stochastic master equation, I build the measurement model, derive the syndrome filter, and implement feedback in Wolfram Mathematica. I track the physical state separately from the controller’s estimate to examine how uncertainty about the initial state and incorrect assumptions about detector efficiency affect correction. The calculations also expose a crucial limitation: the qubits can pass the stabilizer checks even though the stored logical state has changed. Assessing correction therefore requires looking beyond the error checks to the information actually preserved. I finish by comparing two measurement and feedback schemes as detector efficiency varies. I welcome any feedback ;) #QEC #Wolfram #Mathematica #Quantum