Support for applying measurements in a Circuit at a specific moment using delay instruction

[Kapabeta]

Describe the feature you'd like
There are two different requests but correlated.

1. The delay function in a quantum circuit yells the machine do nothing with a duration on the certain qubit. See Gates and Instructions: Delay for the more details.

2. The measurements can be opreated at different machine time if one specify the time order manually or via the circuit design. (See the Fig below.) This will let some bit are measured, but the others still keep coherence and are to be computed.

How would this feature be used? Please describe.
These functions may not be important in quantum computation since the circuit topology will be equivalent. However, in the quantum communication and related topic, it will be more realistic if the measurements of the final state are at the different runtime moments (with physical time interval). This issue is a key when one analyzes the fidelity of some specific protocals, or considers the effect of the delay-choise and the quantum eraser.

A concrete example is given as follows. Two users commuicate with each other via a Bell state. In general, they will Not measure the final state synchronic and in the same diraction. The following Fig shows that two user measure at different physical time. Futhermore, one observes the state on z axis and the other observes the state on x axis.

Additional context
As these functions is adopted by Qiskit but not by Braket, the error message will appear when one conver the quantum circuit containing delay gate via qiskit.braket.provider.

[christianbmadsen]

@Kapabeta Thank you so much for the detailed request. This is a reasonable ask and we will evaluate how it fits with our roadmap. When we have an answer we will circle back in this issue but for now we recommend holding off on implementation.

[zmohammad01]

Hey @Kapabeta - Thanks for you patience with us here. We have opened an internal ticket for the engineering team to brainstorm some solutions and will update you here with a resolution