Gabriele Agliardi

Tommaso Fioravanti, Brian Quanz, Gabriele Agliardi et al.

Quantum Machine Learning (QML) holds the promise of enhancing machine learning modeling in terms of both complexity and accuracy. A key challenge in this domain is the encoding of input data, which plays a pivotal role in determining the performance of QML models. In this work, we tackle a largely unaddressed aspect of encoding that is unique to QML modeling -- rather than adjusting the ansatz used for encoding, we consider adjusting how data is conveyed to the ansatz. We specifically implement QML pipelines that leverage classical data manipulation (i.e., ordering, selecting, and weighting features) as a preprocessing step, and evaluate if these aspects of encoding can have a significant impact on QML model performance, and if they can be effectively optimized to improve performance. Our experimental results, applied across a wide variety of data sets, ansatz, and circuit sizes, with a representative QML approach, demonstrate that by optimizing how features are encoded in an ansatz we can substantially and consistently improve the performance of QML models, making a compelling case for integrating these techniques in future QML applications. Finally we demonstrate the practical feasibility of this approach by running it using real quantum hardware with 100 qubit circuits and successfully achieving improved QML modeling performance in this case as well.

Gabriele Agliardi, Enrico Prati

There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around $90\%$ reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.

Gabriele Agliardi, Giorgio Cortiana, Anton Dekusar et al.

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.