Parameter-dependent decomposition rules cannot specialize on constant parameters under capture

Summary

Under qml.qjit(capture=True), Catalyst's graph-based decomposition compiles a single, generic decomposition rule per operator type, traced with an abstract parameter, and applies it uniformly via the MLIR decompose-lowering pass. As a result, decomposition rules whose structure depends on the concrete value of a parameter cannot specialize, i.e. the parameter is always abstract at rule-compile time.

The concrete motivating case is the adaptive-precision RZ phase-gradient decomposition here: https://github.com/PennyLaneAI/pennylane/pull/10098. It truncates the SemiAdder width (and drops angles that round to zero) based on the concrete angle bits, guarded by:

if adaptive_precision and not math.is_abstract(phi):
    ...  # truncate angle_wires / phase_grad_wires to the significant width

Under capture=True, phi is always abstract when the rule is compiled, so this branch is dead code: the adder is always full width and the Toffoli/T counts are identical for adaptive_precision=True and False. The large (~70%) Toffoli/T reduction that this rule produces under capture=False silently vanishes under capture.

Why "the angles are constants" does not help

Even when the circuit has no arguments and the angles are compile-time constants, the concreteness is not exploited. The angles are concrete literals in the captured plxpr:

import numpy as np, pennylane as qml, jax
qml.capture.enable()

angles = [f * 2 * np.pi for f in (1/2, 1/4, 3/4, 1/64, 7/8, 2.0**-7)]

def circuit():
    for a in angles:
        qml.RZ(a, 0)
    return qml.expval(qml.Z(0))

print(jax.make_jaxpr(circuit)())
# ... operator[op_cls=RZ ...] 3.141592653589793:f32[] 0:i32[]
# ... operator[op_cls=RZ ...] 1.5707963267948966:f32[] 0:i32[]
# ... operator[op_cls=RZ ...] 0.09817477042468103:f32[] 0:i32[]  (etc.)

But the decomposition rule is compiled once, generically, keyed by op-name + wire-count rather than by the concrete angle. The concrete value flows into the compiled rule as a runtime SSA operand (the emitted MLIR computes binary_decimals(phi) at "rule runtime"), so the per-angle structural truncation has nowhere to happen.

The rule still produces correct results, just without the optimization, so this is a silent performance regression relative to capture=False.

Environment

• catalyst 0.16.0-dev86
• pennylane 0.46.0-dev88
• jax 0.7.1
• macOS arm64

written with the help of genAI

Start with the graph-based decomposition path and the MLIR decompose-lowering pass, then compare how the adaptive-precision RZ decomposition behaves under capture=True and capture=False. Done means concrete constant parameters can enable the intended structural specialization under capture while preserving correct results.