Wladimir Silva and colleagues at North Carolina State University have developed an adaptive quantum algorithm for matrix multiplication that reduces the complexity of inner product calculations to O (log N) by using Quantum Random Access Memory. Their new “Adaptive Stacking” framework dynamically adjusts the algorithm’s execution, enabling compatibility with both near-term and fault-tolerant quantum systems and offering a flexible range of time complexities. Validation through a Quantum Machine Learning simulation on the MNIST dataset shows 96% accuracy and suggests a pathway towards sharply more efficient high-dimensional linear algebra operations. Demonstrated numerical stability and MNIST classification accuracy with a dynamically adjusted AQ-Stacker, a new hybrid quantum-classical algorithm, achieves 96 per cent accuracy on the MNIST dataset, exceeding the performance of previous methods with improved numerical stability in a practical quantum machine learning simulation. Realising super-classical efficiency in high-dimensional linear algebra has long been hindered by the difficulty of reconciling quantum speedups with the limitations of current quantum hardware. The MNIST dataset, comprising 70,000 labelled images of handwritten digits, serves as a standard benchmark for evaluating machine learning algorithms, particularly those dealing with image recognition and classification. Achieving high accuracy on this dataset demonstrates the algorithm’s ability to handle complex data representations and perform meaningful computations. AQ-Stacker overcomes this challenge by dynamically adjusting its execution pattern to optimise performance. This dynamic adjustment is crucial because the performance of quantum algorithms is heavily influenced by the number and quality of available qubits, as well as the coherence time, the duration for which qubits maintain their quantum state. Quantum Random Access Memory reduces the complexity of computing vector inner products to O(log N), enabling a tunable time-complexity range potentially reaching O(N2) on fault-tolerant systems. The use of QRAM allows for the preparation of quantum states in O(log N) time, significantly reducing data loading bottlenecks