  Entanglement, a direct consequence of elementary quantum gates such as
controlled-NOT or Toffoli gates, is a key resource that leads to quantum
advantages. In this work, we establish the framework of certifying entanglement
generation in cloud-based quantum computing services. Namely, we present the
construction of quantum circuits that certify entanglement generation in a
circuit-based quantum computing model. The framework relaxes the assumption of
the so-called qubit allocation, which is the step in a cloud service to relate
physical qubits in hardware to a circuit proposed by a user. Consequently, the
certification is valid no matter how unsuccessful qubit allocations may be in
cloud computing or how untrustful the service may be in qubit allocations. We
then demonstrate the certification of entanglement generation on two and three
qubits in the IBMQ and IonQ services. Remarkably, entanglement generation is
successfully certified in the IonQ service that does not provide a command of
qubit allocations. The capabilities of entanglement generation in the circuits
of IBMQ and IonQ are also quantified. We envisage that the proposed framework
is applied when cloud-based quantum computing services are exploited for
practical computation and information tasks, for which our results would find
if it is possible to achieve quantum advantages.
