Comparing Zero-Noise Extrapolation Models on a 6-Qubit Grover's Algorithm

Quantum computers have the potential to address computational problems beyond the practical capabilities of classical systems, but Noisy Intermediate-Scale Quantum (NISQ) processors remain limited by errors that accumulate during circuit execution. Quantum Error Mitigation (QEM), particularly Zero-Noise Extrapolation (ZNE), offers a way to reduce these errors without requiring additional physical qubits. However, ZNE has been studied extensively in relatively small or shallow circuits, leaving its effectiveness in deep, non-variational algorithms less explored. This project investigates whether combining readout mitigation and ZNE can mitigate errors in a deep, six-qubit Grover's search algorithm. The circuit was compiled onto IBM's 133-qubit FakeTorino simulated backend, reaching a depth of 1,118 and containing 369 entangling gates. Under simulated noise, the unmitigated probability of measuring the target state was 3.36%, compared with a uniform random-guessing probability of 1.5625%. Digital unitary gate folding and readout error mitigation were subsequently applied across four progressively increased noise-scaling sets (S1–S4), and scale factors. Four extrapolation models (Linear, Quadratic, Poly-Exponential, and Padé) were evaluated. The Poly-Exponential model achieved the highest average target-state probability, reaching 6.91% at S4, approximately 2.06 times the unmitigated probability. These results demonstrate that combining readout mitigation with ZNE can partially recover computational signals in deep quantum circuits under simulated hardware noise, suggesting the potential combined error mitigation techniques for improving the reliability of near-term quantum algorithms without active quantum error correction.