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I have a quantum ciruit, a qiskit application, that uses four qubits and has a depth of a few dozen operations (unitary transformation). It gives correct results when run on the simulator backend but not when run on, for example, IBMQ-Lima. I suspect I need a better processor but I don't know how to get access. I set up an account for qiskit runtime, but that doesn't seem to give me counts back. I am wondering how to get access to a better processor? I am willing to pay.

Well, except for Nairobi, all of my backends have low volume. What can I do to purchase access to one of the larger machines? I contacted the general IBM support chat and they didn't know.

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You need a processor with a better quantum volume. This page contains all IBM Quantum systems. For each system, it displays number of qubits and quantum volume.

To get a list of the backends available to your Qiskit runtime account, you can query them using QiskitRuntimeService.backends() method as follows:

service = QiskitRuntimeService()
backends = service.backends(filters = lambda b: not b.configuration().simulator
    and b.configuration().n_qubits > 5
    and b.configuration().quantum_volume > 16)

for backend in backends:
    print(backend.name, '\t# Qubits:', backend.n_qubits, '\tQV:', backend.configuration().quantum_volume)

The result should be something like:

ibm_nairobi     # Qubits: 7     QV: 32
ibm_oslo        # Qubits: 7     QV: 32
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