Doubly controlled iX circuit

A method for use with a quantum computing device that includes a doubtly controlled iX (CCiX) circuit and a measuremnet device, the method comprising:

• at the (CCiX) circuit:
• in a preparation stage, preparing a plurality of magic states;
• receiving a plurality of input qubit states including a first control qubit state, a second control qubit state, and a target qubit state;
• and
• in an execution stage, performing a CCiX operation on the target qubit state at least in part by:
• with the measurement device, performing a plurality of local joint measurements, wherein at least a subset of the plurality of local joint measurements are performed between the plurality of magic states and a plurality of auxiliary qubits;
• and
• with the measurement device, performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.

A quantum computing device comprising:

• a doubly controlled iX (CCiX) circuit configured to:
• in a preparation stage, prepare a plurality of |Sx states and a plurality of |T states at least in part by:
• in a first preparation sub-stage, preparing a first |Sx state, a second |Sx state, a first |T state, and a second |T state in parallel;
• and
• in a second preparation sub-stage subsequent to the first preparation sub-stage, preparing a third |Sx, a fourth |Sx state, a third |T state, and a fourth |T state in parallel;
• and
• in an execution stage, perform a CCiX operation on the target qubit state at least in part by:
• in a first execution sub-stage, performing a plurality of local joint ZZ measurements of respective first subsets of the |Sx states, the |T states, and the auxiliary qubits;
• in a second execution sub-stage, performing a plurality of local joint XZ measurements of respective second subsets of the |Sx states, the |T states, and the auxiliary qubits;
• and
• during each of the first execution sub-stage and the second execution sub-stage, performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.