- Multi-qubit quantum gate matrices for arbitrary number of qubits:
I found this formula from a PDF that I’ve since been unable to find. It’s used to make arbitrary multi-qubit quantum gate matrices. It’s clearly a fairly hard-to-find formula, since I’ve never found it in this representation in any place since.
For an N-qubit system, where the, say, 2 operators, say K and M acts on 2 qubits, the k’th and the m’th, the formula for the matrix of the full operator is:
I_{full} is an identity matrix of dimensions equal to the vector space (2^N square matrix), and Each of the 1-bit operators are 2×2 matrices. The subscript is the qubit on which they act on. C is a ‘control’ gate, with zeros everywhere except the (2,2) position, where it has a 1. B is the operator matrix.
Latex code doesn’t render on BU-provided blogs, but one makes do with what one has.
Reasonably close link: https://cs.stackexchange.com/questions/48834/applying-a-multi-qubit-quantum-gate-to-specific-qubits