Bernstein-vazirani Algorithm Performance Declines to 26.4% on Real Quantum Hardware, Revealing Pattern Sensitivity

Quantum computers hold the promise of revolutionising computational science, offering potential speedups for complex problems in fields such as optimisation and materials science, yet their real-world performance often falls short of expectations. Muhammad AbuGhanem from Faculty of Science, Ain Shams University and Zewail City of Science, Technology and Innovation, and colleagues, now demonstrate that the structure of a computational problem significantly impacts the reliability of quantum algorithms. The team conducted a detailed study of the Bernstein-Vazirani algorithm on superconducting processors, revealing a dramatic sensitivity to problem structure and a substantial performance gap between simulations, emulations and real hardware execution. Their results show that success rates plummet from nearly 100% in ideal simulations to just 26. 4% on actual quantum hardware, and crucially, that this degradation correlates strongly with the density of the computational pattern, highlighting a fundamental limitation in current noise models and establishing pattern-dependent performance as a critical factor for future algorithm deployment.

This work investigates the performance of the Bernstein-Vazirani algorithm, a fundamental quantum algorithm for determining a hidden bitstring, under varying input patterns. Researchers systematically varied the Hamming weight and autocorrelation properties of the hidden bitstring, measuring the resulting success probability and query complexity. Results demonstrate that the algorithm exhibits significantly enhanced performance when the hidden bitstring possesses low autocorrelation, meaning its elements are less correlated with their neighbours.

Conversely, performance deteriorates for bitstrings with high autocorrelation, such as those containing long runs of consecutive identical bits. This finding has important implications for the design of quantum algorithms and the selection of appropriate input data, suggesting that pre-processing data to reduce autocorrelation may improve algorithmic efficiency. The research provides a valuable benchmark for evaluating the performance of quantum algorithms on structured data, and contributes to a deeper understanding of the interplay between input data characteristics and quantum computational complexity.

Bernstein-Vazirani Algorithm on Superconducting Quantum Processors

This study meticulously investigated the performance of the Bernstein-Vazirani algorithm on superconducting quantum processors, employing a comprehensive benchmarking strategy to reveal the impact of problem structure on algorithmic resilience. Researchers implemented the algorithm across multiple 127-qubit devices, systematically testing it with diverse test patterns. To quantify performance, scientists measured success rates and leveraged quantum state tomography, a technique that reconstructs the quantum state of the system to assess fidelity. The team meticulously collected data across all patterns and devices, establishing a baseline performance and then systematically introducing single-bit errors and more complex patterns.

This allowed for a detailed analysis of how pattern complexity correlated with both success rates and state fidelity, revealing a pronounced performance hierarchy. Researchers explored patterns ranging from simple alternating sequences to high-density configurations, carefully monitoring entanglement load as a key indicator of structural complexity. Crucially, the study went beyond simple performance metrics, employing quantum state tomography to directly correlate pattern density with state fidelity degradation, establishing a near-perfect correlation between these two factors. This detailed analysis revealed a catastrophic fidelity collapse in real hardware measurements, underscoring limitations in current noise models. The team validated their findings through cross-device performance consistency checks, ensuring the observed patterns were not specific to individual hardware platforms.

Problem Structure Dictates Quantum Algorithm Performance

This research establishes a critical link between problem structure and algorithmic performance on near-term quantum computers, demonstrating that the Bernstein-Vazirani algorithm’s success is exquisitely sensitive to the patterns encoded within the computational problem. Scientists achieved 100. 0% success rates in ideal simulations, but real hardware execution yielded an average success rate of only 26. 4%, representing a dramatic performance gap between emulation and actual results. Quantum state tomography confirmed corresponding average state fidelities of 0.

993 for ideal simulations, 0. 760 for noisy emulation, and a substantial drop to 0. 234 on the hardware, highlighting the impact of real-world noise. Performance degraded significantly as pattern density increased, falling from 75. 7% success for sparse patterns to complete failure for high-density 10-qubit patterns.

Remarkably, quantum state tomography revealed a near-perfect correlation (r = 0. 972) between pattern density and state fidelity degradation, providing a fundamental explanation for the observed performance variations. The catastrophic fidelity collapse observed on real hardware underscores severe limitations in current noise models, which fail to capture structure-dependent error mechanisms. These findings suggest that problem formulations should minimise entanglement density and avoid symmetric encodings to achieve viable performance on current quantum hardware. The 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, paving the way for more robust and efficient quantum computations.

Input Pattern Density Impacts Quantum Performance

This research establishes a strong link between problem structure and algorithmic performance on near-term quantum computers. The team conducted a comprehensive benchmarking study of the Bernstein-Vazirani algorithm, employing diverse test patterns on multiple superconducting processors. Results demonstrate a substantial performance gap between simulations, emulations, and actual hardware execution, with average success rates declining dramatically from 100% in ideal simulations to 26. 4% on real hardware. Crucially, the study reveals that this performance degradation is not random; it correlates directly with the density of the input pattern, with sparser patterns exhibiting significantly higher success rates than dense ones.

State tomography confirmed this relationship, demonstrating a near-perfect correlation between pattern density and state fidelity, providing a fundamental explanation for the observed performance differences. The research highlights a critical limitation of current noise models, which often fail to account for the influence of problem-specific structure on error rates. Future work should focus on developing noise models that incorporate structural vulnerabilities, enabling more accurate predictions of algorithm feasibility and guiding the design of noise-resilient quantum algorithms.