Question about rotationDepth vs. circuitDepth in Azure Quantum Resource Estimator

rotationDepth in the Azure Quantum resource estimator is a logical-level metric that counts how many layers of single-qubit rotation gates are applied sequentially in the algorithm, before any layout or hardware mapping is considered.

From the documentation:

• rotationDepth (in logicalCounts) is defined as the pre-layout rotation depth.
• It is a logical-counts quantity, alongside rotationCount, tCount, cczCount, etc.
• The formatted output logicalCountsRotationDepth is the same quantity, but as a string with a metric suffix.

This depth is specific to rotation gates (for example, the single-qubit rotations described in the qubit concepts documentation such as (R_x(\theta), R_y(\theta), R_z(\theta))) and measures how many such rotation layers must be executed one after another, assuming all possible parallelism between rotations has already been exploited at the logical level.

By contrast, circuitDepth is a more general notion (not explicitly defined in the provided context) that usually refers to the total number of sequential gate layers in a circuit, counting all gate types (Clifford, T, rotations, multi-qubit gates, etc.). In other words:

• rotationDepth ⊆ circuitDepth: it focuses only on the portion of the depth contributed by rotation gates, before layout and hardware constraints.
• circuitDepth would encompass the full logical schedule of all gate types, while rotationDepth isolates the depth of rotation operations, which is especially relevant for resource estimation because rotations are ultimately compiled into discrete gate sequences (for example, involving T gates) and strongly influence T-state and distillation requirements.

The Q# standard library function Std.ResourceEstimation.RotationDepth(amount : Int) : (Int, Int) exists specifically to feed a rotation-depth value into the resource estimator via AccountForEstimates, reinforcing that rotationDepth is a distinct, trackable metric separate from a generic circuit depth.

References:

• Retrieve the output of the Microsoft Quantum resource estimator
• What is the Microsoft Quantum resource estimator?
• RotationDepth function
• The qubit in quantum computing