Why Lower Circuit Depth Did Not Guarantee Better Physical Fidelity

1. The Depth Reduction Hypothesis

In quantum circuit compilation, long-range entangling operations typically require linear chains of SWAP gates, expanding two-qubit gate depth as \(O(D)\) where \(D\) is the physical distance on the processor lattice. Dynamic feed-forward circuits, by contrast, use mid-circuit measurement and classical feed-forward to execute teleportation-style routing in constant \(O(1)\) two-qubit gate depth regardless of distance.

We tested whether this constant-depth advantage translates to superior physical Bell-state fidelity on IBM Quantum's 156-qubit Heron architecture (ibm_marrakesh, 18,432 shots).

2. Empirical Findings Across 3 Distances

3. Physical Takeaway: Measurement & Reset Latency

Mid-circuit measurement and qubit reset on superconducting hardware are significantly slower and noisier than single-qubit microwave gates. On IBM Heron r2, the error penalty of dynamic ancilla operations exceeded the cumulative decoherence of up to 7 SWAP gates.

Q-Psi's pre-QPU calibration cost model correctly predicted both conclusive outcomes (2/2 confirmed).