Implement tensor multiplication and factorization to operate separately on qubit superpositions.

Currently an array of 3 qubits (thus a vector of 2^3 = 8 possible states) can only be used to apply three-qubit-gates (CCNOT or CSWAP), because the matrix representing the gate has to have the same side length as the superposition vector. To allow 1-qubit-gates (like the Pauli-X gate) to operate on multiple qubits, the tensor product is necessary to appropriately modify the gate matrix.

Still, the size of the superposition vector will grow exponentially to the amount of qubits. As long as these qubits are not entangled, they could be treated (and measured) separately. To implement this, tensor factorization is required.

Integrate this project with QuantumFlow and investigate support for other quantum computing toolkits like Q# or QISKit.

Below is some quick code I've put together while playing with this library. I've just started reading up on Quantum computing, so I'm not 100% clear on how the kronecker product is to be applied when working with a subset of qubits, but I've validated that it works properly for the spanning/parallel case. I.e. apply-qgate with H*H matrix works properly for the Hadamard to a two-qubit pair.

; More efficient construction of the superposition. On my test system constructing a 14-bit
; superposition takes 3.5 seconds with the original code. This code takes 3 milliseconds.
(defun superpos (bits &optional (zero 0))
(let ((outrep (make-list (expt 2 (length bits)) :initial-element zero))
(index (reduce (lambda (current previous) (+ (* current 2) previous)) bits)))
(setf (elt outrep index) (+ zero 1))
outrep))

; Kronecker / tensor product
(defun kronecker-product(A B)
(matrix-create
(lambda (i j)
(let ((p (matrix-row-count B))
(q (matrix-column-count B)))
(* (elt (elt A (floor i p)) (floor j q))
(elt (elt B (mod i p)) (mod j q)))))
(* (matrix-row-count A) (matrix-row-count B))
(* (matrix-column-count A) (matrix-column-count B))))