![]() EncodeOp user defined type = ((Qubit, Qubit) => LogicalRegister): Denotes that an operation takes qubits representing data along with fresh auxiliary qubits in order to produce a code block of an error-correcting code.RecoveryFn user defined type = (Syndrome -> Pauli): Denotes that a classical function should be used to interpret a syndrome and return a correction that should be applied.Syndrome user defined type = Result: Denotes that an array of measurement results should be interpreted as the syndrome measured on a code block.LogicalRegister user defined type = Qubit: Denotes that a register of qubits should be interpreted as the code block of an error-correcting code.To help specify error correcting codes, the Q# canon provides several distinct user-defined types: Representing Error Correcting Codes in Q# We refer readers interested in learning more to Gottesman 2009. In particular, we emphasize that recovery is a classical inference procedure which takes as its input the syndrome which occurred, and returns a prescription for how to fix any errors that may have occurred.Ī full introduction to the stabilizer formalism is beyond the scope of this section. We call these results a syndrome, and refer to the process of mapping a syndrome back to the error that caused it as recovery. Thus, the results of the two measurements uniquely determines which bit-flip error occurred, but without revealing any information about which state we encoded. ![]() We denote the results of each measurement by the sign of the eigenvalue that is observed, either $+$ or $-$, corresponding to the Q# Result values of Zero and One, respectively. To emphasize this, we repeat the table above, but add the results of measuring $Z_0 Z_1$ and $Z_1 Z_2$ on each row. In classical computing, if one wants to protect a bit against errors, it can often suffice to represent that bit by a logical bit by repeating the data bit.įor instance, let $\overline$, so the result of measuring $Z_0 Z_1$ reveals useful information about which error occurred.
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