Other than Z observables

Currently the observables passed to methods in QCut are always Z observables. If one wants to calculate expectation values in some other basis, like the X basis for example, this needs to be done by manually modifying the circuit.

Further, if one wants to calculate expectation values on multiple bases for a single qubit, multiple experiment runs with different circuit are needed.

This may change in a future release.

1: X observable expectation values

circuit_x = QuantumCircuit(3)
circuit_x.h(0)
circuit_x.cx(0,1)
circuit_x.cx(1,2)
circuit_x.h(2)
circuit_x.measure_all()

circuit_x.draw("mpl")

cut_circuit_x = QuantumCircuit(4)
cut_circuit_x.h(0)
cut_circuit_x.cx(0,1)
cut_circuit_x.append(cut_wire, [1,2])
cut_circuit_x.cx(2,3)
cut_circuit_x.h(3)

cut_circuit_z.draw("mpl")

observables = [0, 1, 2]

We have manually transformed qubit 2 to the X basis so now the expectation value returned by QCut will also be the X observable expectation value. The other qubits are stull in the Z basis so the expectation value will be the Z observable expectation value.

2: Z and X observable expectation values for a single qubit

In addition to the circuits above let’s define the “normal” Z basis circuits.

circuit_z = QuantumCircuit(3)
circuit_z.h(0)
circuit_z.cx(0,1)
circuit_z.cx(1,2)
circuit_z.measure_all()

circuit_z.draw("mpl")

cut_circuit_z = QuantumCircuit(4)
cut_circuit_z.h(0)
cut_circuit_z.cx(0,1)
cut_circuit_z.append(cut_wire, [1,2])
cut_circuit_z.cx(2,3)

cut_circuit_z.draw("mpl")

observables_x = [2]

Now to get expectation values for both X and Z basis for qubit 2 the QCut circuit knitting sequence can be executed on both Z and X basis circuits.