qit.utils.op_list

qit.utils.op_list(G, dim)

Operator consisting of k-local terms, given as a list.

Parameters

• G (list[list[tuple]]) – list of k-local operator terms

• dim (Sequence[int]) – vector of subsystem dimensions

Returns

matrix defined by G

Return type

array[complex]

G is a list of lists, $G=[c_1,c_2,...,c_n]$. Each list $c_i$ corresponds to a term in the operator, and consists of k two-tuples: $c_i$ = [(A1, s1), (A2, s2), … , (Ak, sk)]. Aj are arrays and sj subsystem indices, corresponds to the k-local term given by the tensor product

$$A_1^{(s_1)}{A}_2^{(s_2)}\cdots A_k^{(s_k)}.$$

The dimensions of all operators acting on subsystem sj must match dim[sj].

Alternatively one can think of G as defining a hypergraph, where each subsystem corresponds to a vertex and each array c_i in the list describes a hyperedge connecting the vertices {s1, s2, …, sk}.

Example: The connection list

::

G = [[(sz,1)], [(sx,1), (sx,3)], [(sy,1), (sy,3)], [(sz,1), (sz,3)], [(sz,2)], [(A,2), (B+C,3)], [(2*sz,3)]]

corresponds to the operator

$${\sigma }_{z1}+{\sigma }_{z2}+2{\sigma }_{z3}+{\sigma }_{x1}{\sigma }_{x3}+{\sigma }_{y1}{\sigma }_{y3}+{\sigma }_{z1}{\sigma }_{z3}+A_2(B+C{)}_3.$$