Abstract: A decoder apparatus for decoding syndrome data of a quantum error correction code is disclosed. The decoder apparatus is configured to receive position data representing the respective location of defects from the syndrome data in a decoding graph. The decoder apparatus also receives dimension data of the decoding graph and determines the respective location of each of the plurality of defects in the decoding graph based on the position data and the dimension data. The decoder apparatus then decodes the syndrome data using the determined respective location of each of the plurality of defects.

Abstract: A computer-implemented postselection-free method of initializing qubits in a quantum computer, comprising: preparing at least one data qubit and a plurality of auxiliary qubits in respective initial states, wherein each of the at least one data qubit and the plurality of auxiliary qubits has a respective probability of being prepared with an error; and, performing a plurality of non-measurement multi-qubit quantum logic operations that propagate errors between the at least one data qubit and the plurality of auxiliary qubits so as to reduce the probability of an error affecting the at least one data qubit.

Abstract: A computer-implemented postselection-free method of initializing qubits in a quantum computer, comprising: preparing at least one data qubit and a plurality of auxiliary qubits in respective initial states, wherein each of the at least one data qubit and the plurality of auxiliary qubits has a respective probability of being prepared with an error; and, performing a plurality of non-measurement multi-qubit quantum logic operations that propagate errors between the at least one data qubit and the plurality of auxiliary qubits so as to reduce the probability of an error affecting the at least one data qubit.