feat: implemented expectation for non diagonal observbales

src/qibo/hamiltonians/expectation.py

@@ -0,0 +1,26 @@
+from math import prod
+
+from qibo import Circuit, gates, symbols
+from qibo.config import raise_error
+from qibo.hamiltonians import SymbolicHamiltonian
+
+
+def Expectation(circuit: Circuit, observable: SymbolicHamiltonian) -> float:
+    if len(circuit.measurements) > 0:
+        raise_error(RuntimeError)
+    exp_val = 0.0
+    for term in observable.terms:
+        Z_observable = SymbolicHamiltonian(
+            prod([symbols.Z(q) for q in term.target_qubits]),
+            nqubits=circuit.nqubits,
+            backend=observable.backend,
+        )
+        measurements = [
+            gates.M(factor.target_qubit, basis=factor.gate.__class__)
+            for factor in term.factors
+        ]
+        circ_copy = circuit.copy(True)
+        [circ_copy.add(m) for m in measurements]
+        freq = observable.backend.execute_circuit(circ_copy).frequencies()
+        exp_val += Z_observable.expectation_from_samples(freq)
+    return exp_val