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I am trying to perform OTOC for my 7 qubit protocol. I need to carefully control and use only 7 qubits but after making measurement in the 16 qubit Melbourne system (ibmq_16_melbourne) my protocol gets transpiled in all of the 16 qubits.

Is there any way (some codes in qiskit) to use only 7 qubits of the 16 qubits in IBMQ Melbourne, so that it uses only 7 qubits which I have used in the protocol for transpiling and measurement and not more? Or is there any other quantum computer available on which I can do this?

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The transpiler always expands the input circuits to the size of the target device. This is different than saying you are using all the qubits. This tutorial may be of help: Using the Transpiler

It shows you how to visually check which qubits you are using on a device

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