Quantum Circuit Pruning: Improving Fidelity via Compilation-Aware Circuit Approximation

TL;DR

The paper tackles fidelity losses on NISQ devices caused by routing overhead from qubit movement during compilation. It introduces routing-aware pruning, which evaluates each parametric two-qubit gate by comparing its inherent fidelity impact $F_{R_{\hat{n}}(\theta)}$ against routing-induced fidelity loss $F_{\texttt{swap}}$, pruning gates when routing costs outweigh contributions to computation. Simulations on grid-based architectures using realistic noise models show reductions of up to $48.6\%$ in two-qubit gates and fidelity improvements up to $47.7\%$, especially for larger circuits where routing is more expensive. The approach generalizes across circuit families (e.g., QFT, QAOA) and aligns with or surpasses compilation-agnostic approximations, highlighting its potential for practical, scalable improvements in quantum compiler design for NISQ devices. The work underscores the benefit of integrating routing costs into pruning decisions to boost reliability on near-term quantum hardware, with future work including real-device validation.

Abstract

This work presents a routing-aware pruning strategy for quantum circuits executed on Noisy Intermediate-Scale Quantum (NISQ) devices. We propose a method to remove parametric controlled rotations whose small rotation angles do not justify the routing overhead required for their implementation. By selectively pruning such gates, the method mitigates fidelity loss arising from additional SWAP operations introduced during compilation. Our approach evaluates whether executing a gate leads to greater fidelity loss than omitting it. Simulations on benchmark circuits with realistic noise models show that the method reduces two-qubit gate counts (up to 48.6%) while improving final state fidelity (up to 47.7%), especially for larger circuits where routing costs dominate.

Figures (5)

• Figure 1: Before applying a conditional rotation $\theta$, the compiler assesses the distance between the two interacting qubits (blue and red paths). The probability of pruning increases with path length. The values shown correspond to a $p_2 = 0.005$ ($F_{\texttt{swap}}$ from Equation (\ref{['eq:f_swap']})) and a $\theta = \pi/6$ rotation ($F_{R_{\hat{n}}(\theta)}$ from Equation (\ref{['eq:theo_op']})). In this example, a $\frac{\pi}{6}$-rotation between the blue qubits is pruned, while the same rotation between the red qubits is not.
• Figure 2: Considered nearest-neighbor topologies ranging from 4 to 14 qubits.
• Figure 3: Two-qubit gate count (top row) and circuit fidelity (bottom row) for the selected benchmarks containing between 4 and 14 qubits. The percentage improvement in fidelity achieved by the pruning methodology is indicated above each corresponding bar.
• Figure 4: Fidelity's relative improvement when pruning the circuit (blue) and relative reduction of two-qubit gates (orange) for an increasing circuit size.
• Figure 5: Fidelities for the noiseless and noisy approximation (blue and orange lines, respectively), and this work's proposed pruned circuit (red), for QFT circuit sizes between 4 and 14 qubits. The percentage improvement in fidelity for the best approx. degree and the pruned circuit is indicated above each corresponding bar.

Theorems & Definitions (2)

• Theorem 1
• proof