Quantum machine learning achieves 93.9% accuracy despite 93% signal loss

Wladimir Silva and colleagues at North Carolina State University have characterized the “Kingston constant,” which describes the critical 93% signal amplitude decay on the ibm_kingston processor. Despite this attenuation, the Hadamard test perceptron still achieves MNIST accuracy of 93.9%, supporting the proposed Hadamard resiliency law. At a feature depth of 256, a “coherence gap” of approximately 0.91 appears. This indicates that coherent phase error rather than depolarization noise currently limits the scaling of the quantum linear layer. This discovery provides a predicted boundary for a strong quantum linear layer on current NISQ devices and highlights a “wall of coherence” at a circuit depth of approximately 10,000 gates.

Hadamard test perceptron maintains accuracy despite severe signal loss at ibm_kingston

Despite a 93% signal amplitude decay, quantified as the “Kingston constant” of 0.07, the Hadamard test perceptron maintained an MNIST accuracy of 93.9%, demonstrating remarkable durability not previously observed in short-term quantum devices. This performance validates Hadamard’s law of resiliency and suggests that the quantum classifier can function despite significant signal degradation, calling into question the previous assumption that such losses would render the algorithm unusable. The MNIST dataset consists of 70,000 labeled grayscale images of handwritten digits and served as the benchmark for this evaluation. The Hadamard Test Perceptron, a quantum machine learning algorithm that utilizes the Hadamard test for efficient feature extraction, was implemented and tested on an ibm_kingston quantum processor, a superconducting transmon qubit device. The observed 93.9% accuracy represents the classification rate achieved on the MNIST test set, indicating robust performance despite significant signal attenuation. Analysis of the ibm_kingston processor reveals a “coherence gap” of approximately 0.91 at a feature depth of 256, identifying coherent phase error as the primary limitation rather than depolarization noise.

At a feature depth of 256, the processor reached the “wall of coherence” and exceeded the hardware endurance limit of 3,500 gates at a circuit depth of approximately 10,000 quantum gates. This discovery isolated coherent phase error and crosstalk as the main limitations. Taking into account this coherence-induced signal attenuation, a sophisticated hardware-enabled model was developed to establish predictive bounds for a strong quantum linear layer. The concept of “feature depth” refers to the number of consecutive quantum linear layers applied to the input data. Each layer contains a series of quantum gates, contributing to the overall depth of the circuit. The observed coherence wall marks the point at which the accumulation of phase errors overwhelms the signal, leading to a significant reduction in performance. The development of hardware-aware models is important to accurately predict the performance of quantum algorithms on a given device, taking into account the inherent characteristics and limitations of the hardware. Currently, these results are focused on the MNIST dataset, and demonstrating comparable durability across more complex real-world datasets remains a key challenge to practical application.

Coherent phase errors define the limits of practical quantum machine learning

Mapping of the boundaries of what is achievable with today’s quantum computers is underway, shifting the focus from theoretical possibilities to practical limits. This work confirms remarkable durability in quantum machine learning, maintaining accuracy despite significant signal loss, but also reveals a significant disconnect between simulation and reality. The key discovery is that the main obstacle to large-scale, complex quantum computations is the accumulation of coherent phase errors within quantum circuits, rather than just random errors. Traditionally, quantum error mitigation strategies have focused on dealing with depolarization noise that randomly flips the state of a qubit. However, this study shows that coherent phase errors resulting from imperfections in gate operation and qubit control play a major role in limiting the performance of quantum algorithms, especially at high circuit depths. These phase errors accumulate over time, leading to systematic drift of quantum states and reduced signal fidelity.

Realistic expectations require recognizing that there are significant differences between simulated and physical quantum performance. Identifying coherent phase errors as the primary cause challenges common noise models, enables model refinement, and establishes clear boundaries for what is currently achievable in near-term quantum devices. Verification of Hadamard’s law of resiliency demonstrates that quantum classifiers can maintain accuracy despite significant signal loss, which is a surprising result. The “Kingston Constant” of 0.07 and the “Coherence Gap” of 0.91 provide quantitative metrics to characterize the performance limitations of the ibm_kingston processor. These metrics can be used to benchmark the performance of other quantum devices or to guide the development of more robust quantum algorithms. Further research will focus on extending these findings to more complex datasets and addressing important challenges toward practical application. Future research will explore techniques to reduce coherent phase errors, such as dynamic decoupling and optimal control, to improve the performance of quantum machine learning algorithms in short-term quantum devices. The ultimate goal is to develop quantum algorithms that can outperform classical algorithms for real-world problems despite the limitations of current quantum hardware.

This study reveals a significant difference between the predicted and actual performance of quantum classifiers on ibm_kingston processors. We now show that coherent phase errors, rather than random noise, limit the scaling of the quantum linear layer, forming a “wall of coherence” at feature depth 256. This discovery calls into question existing quantum error mitigation strategies that primarily deal with depolarization noise and establish robust quantum computation boundaries on current hardware. The researchers demonstrated 93.9% MNIST accuracy despite 93% signal decay to validate Hadamard’s resiliency law, and plan to extend these findings to more complex datasets.