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If we have for example a gate $U^{\otimes2}$, then within superconducting hardware, is the $U$ applied onto the first qubit and then the second or is a pulse corresponding to a composite gate (tensor product matrix) created which is applied onto both?

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  • $\begingroup$ are you asking whether one should think of $A\otimes B$ as $A$ being applied (to first qubit) before or after $B$ is applied to the second qubit (rather than the two gates being applied simultaneously)? $\endgroup$
    – glS
    Sep 8 at 9:05
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    $\begingroup$ I'm asking that in hardware, are the gates applied simultaneously as a single pulse, or individually as separate pulses? $\endgroup$
    – At2005
    Sep 8 at 10:13
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    $\begingroup$ Is $H$ the Hadamard gate? $\endgroup$
    – Mark S
    Sep 8 at 11:02
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    $\begingroup$ If you want specifically to know what happens on the hardware level, you need to specify what hardware you are thinking of. Moreover, you might even need to specify what systems you are thinking of (e.g. those of IBM, or those of Google, or a specific chip of, let's say, Rigetti). Also realize that in pretty much all cases a Hadamard gate will never be implemented itself, but compiled to some other native gates. $\endgroup$
    – JSdJ
    Sep 8 at 12:16
  • $\begingroup$ Ok, I've changed the question to deal with an arbitrary native gate $U$, and have specified superconducting QCs $\endgroup$
    – At2005
    Sep 8 at 14:43
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Typically superconducting qubits can be controlled independently, eg. due to having separate control wires. So you'd have independent pulses in each control wire applying a gate to the respective qubits. The gates can be done at the same time.

Due to crosstalk, it can matter if operations are done at the same time or one after the other. Doing them at the same time may have higher error. But doing them one after another means qubits have to live longer while the computation runs, which is probably worse than crosstalk.

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Case 1: Composite gate Given that your composite gate will be a 4x4 matrix, which will be multiplied to some wavevector, your question is not a valid question in terms of which qubit it gets applied to first or last. In this case, it is applied "together" in some vague sense of matrix vector multiplication.

Case 2: Applied separetely Since your two qubits are not entangled, and you are only applying one gate on each qubit, it does not matter which one is applied first as long as you measure after applying both.

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    $\begingroup$ Re case 2: does it matter whether the qubits are entangled? $H$ applied to one qubit will commute with $H$ applied to another qubit, even if the qubits are entangled. $\endgroup$
    – Mark S
    Sep 8 at 11:02
  • $\begingroup$ Sorry if I was unclear, but I don't mean $U^{\otimes2}$ mathematically, I'm asking how real devices implement composite gates $\endgroup$
    – At2005
    Sep 8 at 14:46

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