Decoding errors using quantum subspace expansion

An apparatus comprising:

• quantum hardware;
• and
• one or more classical processors;
• wherein the apparatus is configured to perform operations for correcting a result of a quantum computation, the operations comprising:
• selecting, by the one or more classical processors, a quantum error correcting code to perform the quantum computation, wherein the quantum error correcting code is defined by a respective set of stabilizer generators;
• determining, by the one or more classical processors, a set of symmetry operators, comprising:
• selecting a subset of the set of stabilizer generators, the subset comprising a plurality of stabilizer generators;
• determining, for each stabilizer generator in the selected subset, a sum between an identity operator and the stabilizer generator;
• and
• multiplying the determined sums together to form a summation of terms, wherein each term in the summation is equal to a respective symmetry operator;
• measuring, using the quantum hardware, a projective correction of a physical observable over an output quantum state of the quantum computation using the determined set of symmetry operators, wherein the physical observable corresponds to the result of the quantum computation;
• and
• determining, by the one or more classical processors, a corrected result of the quantum computation using the measured projective correction of the physical observable.