A
quantum computing method is provided. The
quantum computing method includes providing a physical
quantum system (1) comprising components (2). The quantum computing method includes performing an encoded quantum computation (7) on the physical
quantum system (1), including: preparing at least a portion of the physical
quantum system (1) in an initial
quantum state; evolving the physical
quantum system (1) to a final
quantum state; measuring at least a portion of the physical quantum
system (1) to provide a readout value; and determining the output of the encoded quantum computation (7) based on the readout value. During at least a portion of the encoded quantum computation (7), the
quantum state of at least a subset of the components (2) is an encoded quantum state according to the encoding. Evolving the physical quantum
system (1) to the final quantum state includes performing: a plurality of encoded evolution steps (105) for changing the encoding of the components (2), and a plurality of algorithmic evolution steps (106) for at least a portion of the action of at least one of a plurality of instructions (61, 62) for physically implementing a
quantum algorithm (6) under the current encoding. At least some of the multiple coding evolution steps (105) and at least some of the multiple
algorithm evolution steps (106) are performed according to an alternation sequence, which alternates between the coding evolution steps (105) and the
algorithm evolution steps (106). At least one coding evolution step (105) in the alternation sequence includes performing a set of parity coding operations (75). Each parity coding operation (75) in the set of parity coding operations (75) is performed on a corresponding subset comprising at least two components (2). Each parity coding operation (75) in the set of parity coding operations (75) encodes the parity of all components (2) in the corresponding subset comprising at least two components (2) into at least one component (2) of the subset. At least one algorithmic evolution step (106) in the alternating sequence includes performing at least one algorithmic action operation (74) on at least one component (2), wherein the at least one algorithmic action operation (74) physically implements at least a portion of the action of at least one of the multiple instructions (61, 62) of the
quantum algorithm (6) under the current encoding of the component (2).