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I am designing a quantum circuit which uses one qubit as the control of many $\text{CSWAP}$ operations. And then, this qubit will be measured.

Will the result be more prone to noise since all the information is on the same qubit? See the picture below.

The bottom qubit will be measured.

enter image description here

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    $\begingroup$ More prone to noise with respect to which other circuit? What would you want to compare your circuit to? $\endgroup$
    – Tristan Nemoz
    Apr 9 at 14:59
  • $\begingroup$ @TristanNemoz I tried to run this circuit using IBM's fake backend as well as real backend. On the fake backend, the results were expected. On the real backend, it was much much more noise. IBM claims fake backend noise would behave similarly to the real ones. So I wonder if it is my design that make it too much prone to error. $\endgroup$
    – Deren Liu
    Apr 9 at 17:08
  • $\begingroup$ In that case, it would be more efficient to include in your other post the information you provided in this one, you'd be more likely to get an answer by doing so. $\endgroup$
    – Tristan Nemoz
    Apr 9 at 18:34

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The reason why you are seeing inaccurate results on a real backend is because of the SWAP gates. In the current quantum computing hardware that IBM uses, the dominant source of noise is because of multi-qubit gates like CX and SWAP (also CSWAP). This is because the multi-qubit gates that act on multiple qubits suffer from errors and noise that depend on all the physical qubits being used for that gate. So noise and error rates for multi-qubit gates are typically higher than those of single-qubit gates, so a circuit consisting of multi-qubit gates will experience more noise than a circuit of the same number of single qubit gates. And due to this reason the transpilers in qiskit will try to avoid using multi-qubit gates as much as possible.

So if you redesign your circuit (or use a pass manager in qiskit) to have less number of CSWAP gates then your circuit will be less prone to errors and noise.

Now coming to your concern of why you are seeing different results between a fake backend and a real backend. This is what qiskit documentation says about fake backend:

Fake backends: The fake backends in qiskit_ibm_runtime.fake_provider mimic the behaviors of IBM Quantum™ systems by using system snapshots. The system snapshots contain important information about the quantum system, such as the coupling map, basis gates, and qubit properties, which are useful for testing the transpiler and performing noisy simulations of the system. The noise model from the snapshot is automatically applied during simulation.

This means that the error rates and noise that are programmed into a fake backend only represent a snapshot of what you would actually see on a real device, whereas on a real device the error rates and noise can dynamically change and also the qubits experience more cross-talk due to the interference with other qubits in close vicinity. So if you have more number of multi-qubit gates then your circuit will be more prone to error.

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  • $\begingroup$ Thank you for you answer. So multi-qubit gates are nowhere near reliable across all IBM hardwares. Is it the situation we're in? $\endgroup$
    – Deren Liu
    May 20 at 7:33
  • $\begingroup$ Multi-qubit gates are to some extent reliable. It's just that they are more prone to error and for this you can specify error mitigation techniques to use with your quantum circuit. But adding too many error mitigation techniques will slow the execution of the circuit. $\endgroup$ May 20 at 13:46

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