qrisp.qaoa.controlled_RX_mixer_gen#

controlled_RX_mixer_gen(predicate)[source]#

Generate a controlled RX mixer for a given predicate function.

Parameters:

predicatefunction: A function receiving a QuantumVariable and an index $i$ . This function returns a QuantumBool indicating if the predicate is satisfied for qv[i], that is, if the element qv[i] should be swapped in.

Returns:

controlled_RX_mixerfunction: A function receiving a QuantumVariable and a real parameter $β$ . This function performs the application of the mixing operator.

Examples

We define the predicate function for the MaxIndepSet problem. It returns True for the index (node) $i$ if all neighbors $j$ of the node $i$ in the graph $G$ are not selected, and False otherwise.

from qrisp import QuantumVariable, QuantumBool, h, mcx, auto_uncompute, multi_measurement
import networkx as nx

G = nx.Graph()
G.add_edges_from([(0, 1), (1, 2), (2, 0)])  
neighbors_dict = {node: list(G.adj[node]) for node in G.nodes()}

def predicate(qv,i):
    qbl = QuantumBool()
    if len(neighbors_dict[i])==0:
        x(qbl)
    else:
        mcx([qv[j] for j in neighbors_dict[i]],qbl,ctrl_state='0'*len(neighbors_dict[i]))
    return qbl

qv = QuantumVariable(3)
h(qv)
qbl = predicate(qv,0)
multi_measurement([qv,qbl])
# Yields: {('000', True): 0.125,('100', True): 0.125,('010', False): 0.125,('110', False): 0.125,('001', False): 0.125,('101', False): 0.125,('011', False): 0.125,('111', False): 0.125}

The resulting controlled_RX_mixer then only swaps the node $i$ in if all neighbors $j$ in the graph $G$ are not selected.