An Azure service that provides quantum computing and optimization solutions.
Hello Akita !
Thank you for posting on MS Learn Q&A.
You should not treat a NISQ transpiled circuit and a Clifford+T circuit as equivalent inputs because they represent different compilation assumptions so different results are expected.
In practice, I would recommend using algorithm level or logical QASM as the default input where you keep meaningful gates such as rx, ry, rz controlled ops and measurements...
Then let Azure QRE account for the fault tolerant cost using its target parameters, error budget, rotation synthesis assumptions, T-state requirements and QEC model.
Azure QRE is specifically intended to estimate resources for running a quantum algorithm on a fault tolerant quantum computer and not to simulate a NISQ backend gate set.
You can check about estimation here : https://learn.microsoft.com/en-us/azure/quantum/intro-to-resource-estimation
Or you can use a pre decomposed Clifford+T QASM only when you have intentionally performed a fault tolerant compilation yourself and you want QRE to estimate the resources for that exact decomposition. In that case, the T-count or the T-depth and synthesis precision are already baked into your input circuit.
The reason the results differ is that QRE reports and uses different logical quantities, including tCount, rotationCount, rotationDepth, numTstates, and numTsPerRotation. Arbitrary rotations are not the same as explicit T gates: QRE can estimate the T-state cost of rotations based on rotation synthesis assumptions, while a Clifford+T input directly fixes the number of T gates seen by the estimator.
https://learn.microsoft.com/en-us/azure/quantum/overview-resource-estimator-output-data