Pattern-Dependent Performance of the Bernstein-Vazirani Algorithm

TL;DR

This study investigates how the structure of problems affects the performance of the Bernstein-Vazirani quantum algorithm on real hardware, revealing significant pattern-dependent fidelity drops and highlighting current noise model limitations.

Contribution

It provides the first comprehensive hardware-aware benchmarking of the Bernstein-Vazirani algorithm across diverse patterns, demonstrating the critical impact of problem structure on quantum performance.

Findings

Performance drops from 100% to 26.4% success on real hardware.

Pattern density correlates strongly with fidelity degradation.

Current noise models fail to capture structure-dependent errors.

Abstract

Quantum computers promise to redefine the boundaries of computational science, offering the potential for exponential speedups in solving complex problems across chemistry, optimization, and materials science. Yet, their practical utility remains constrained by unpredictable performance degradation under real-world noise conditions. A key question is how problem structure itself influences algorithmic resilience. In this work, we present a comprehensive, hardware-aware benchmarking study of the Bernstein-Vazirani algorithm across 11 diverse test patterns on multiple superconducting quantum processors, revealing that algorithmic performance is exquisitely sensitive to problem structure. Our results reveal average success rates of 100.0\% (ideal simulation), 85.2\% (noisy emulation), and 26.4\% (real hardware), representing a dramatic 58.8\% average performance gap between noisy emulation and real hardware execution. With quantum state tomography confirming corresponding average state fidelities of 0.993, 0.760, and a 0.234 fidelity drop to hardware. Performance degrades dramatically from 75.7\% success for sparse patterns to complete failure for high-density 10-qubit patterns. Most strikingly, quantum state tomography reveals a near-perfect correlation between pattern density and state fidelity degradation, providing the fundamental explanation for observed performance patterns. The catastrophic fidelity collapse observed in real hardware measurements -- dropping to 0.111 compared to the predicted 0.763 -- underscores severe limitations in current noise models for capturing structure-dependent error mechanisms. Our work establishes pattern-dependent performance as a critical consideration for quantum algorithm deployment and provides a quantitative framework for predicting algorithm feasibility in practical applications.