arXiv subjects

Gabriele Agliardi

Publications and source records attributed to Gabriele Agliardi.

10 recordsLinked to original sources

arXiv2026

Hybrid quantum floating-point method for sharp arithmetic

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.

quant-ph↗

arXiv2025

Quantum feature encoding optimization

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.

quant-ph↗

arXiv2025

Portfolio construction using a sampling-based variational quantum scheme

The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variational Quantum Algorithm (VQA), combined with a local-search post-processing, for solving problem instances that beyond a certain size become classically hard. We also propose a problem formulation that is suited for sampling-based VQA. Our utility-scale experiments on IBM Heron processors involve 109 qubits and up to 4200 gates, achieving a relative solution error of 0.49%. Results indicate that a combined quantum-classical workflow achieves better accuracy compared to purely classical local search, and that hard-to-simulate quantum circuits may lead to better convergence than simpler circuits. Our work paves the path to further explore portfolio construction with quantum computers.

quant-ph↗

arXiv2024

Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

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.

quant-ph↗

arXiv2024

Quantum data encoding as a distinct abstraction layer in the design of quantum circuits

Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of quantum data encoding has never been addressed systematically so far. We formalize the concept of quantum data encoding, namely the format providing a representation of a data set through a quantum state, as a distinct abstract layer with respect to the associated data loading circuit. We survey existing encoding methods and their respective strategies for classical-to-quantum exact and approximate data loading, for the quantum-to-classical extraction of information from states, and for quantum-to-quantum encoding conversion. Next, we show how major quantum algorithms find a natural interpretation in terms of data loading. For instance, the Quantum Fourier Transform is described as a quantum encoding converter, while the Quantum Amplitude Estimation as an extraction routine. The new conceptual framework is exemplified by considering its application to quantum-based Monte Carlo simulations, thus showcasing the power of the proposed formalism for the description of complex quantum circuits. Indeed, the approach clarifies the structure of complex quantum circuits and enables their efficient design.

cs.ET↗

arXiv2024

A Machine Learning Approach to Boost the Vehicle-2-Grid Scheduling

Electric Vehicles (EVs) are emerging as battery energy storage systems (BESSs) of increasing importance for different power grid services. However, the unique characteristics of EVs makes them more difficult to operate than dedicated BESSs. In this work, we apply a data-driven learning approach to leverage EVs as a BESS to provide capacity-related services to the grid. The approach uses machine learning to predict how to charge and discharge EVs while satisfying their operational constraints. As a paradigm application, we use flexible energy commercialization in the wholesale markets, but the approach can be applied to a broader range of capacity-related grid services. We evaluate the proposed approach numerically and show that when the number of EVs is large, we can obtain comparable objective values to CPLEX and approximate dynamic programming, but with shorter run times. These reduced run times are important because they allow us to (re)optimize frequently to adapt to the time-varying system conditions.

math.OC↗

arXiv2024

Conditions for a quadratic quantum speedup in nonlinear transforms with applications to energy contract pricing

Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum-classical algorithm based on polynomial approximation of nonlinear functions, computed through Quantum Hadamard Products, and we rigorously assess the conditions for its end-to-end speedup for different implementation variants against classical algorithms. In our setting, a quadratic quantum speedup, up to polylogarithmic factors, can be proven only when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.

quant-ph↗

arXiv2023

Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling

We generalize the Approximate Quantum Compiling algorithm into a new method for CNOT-depth reduction, which is apt to process wide target quantum circuits. Combining this method with state-of-the-art techniques for error mitigation and circuit compiling, we present a 10-qubit experimental demonstration of Iterative Amplitude Estimation on a quantum computer. The target application is the derivation of the Expected Value of contract portfolios in the energy industry. In parallel, we also introduce a new variant of the Quantum Amplitude Estimation algorithm which we call Dynamic Amplitude Estimation, as it is based on the dynamic circuit capability of quantum devices. The algorithm achieves a reduction in the circuit width in the order of the binary precision compared to the typical implementation of Quantum Amplitude Estimation, while simultaneously decreasing the number of quantum-classical iterations (again in the order of the binary precision) compared to the Iterative Amplitude Estimation. The calculation of the Expected Value, VaR and CVaR of contract portfolios on quantum hardware provides a proof of principle of the new algorithm.

quant-ph↗

arXiv2022

Quantum integration of elementary particle processes

We apply quantum integration to elementary particle-physics processes. In particular, we look at scattering processes such as ${\rm e}^+{\rm e}^- \to q \bar q$ and ${\rm e}^+{\rm e}^- \to q \bar q' {\rm W}$. The corresponding probability distributions can be first appropriately loaded on a quantum computer using either quantum Generative Adversarial Networks or an exact method. The distributions are then integrated sing the method of Quantum Amplitude Estimation which shows a quadratic speed-up with respect to classical techniques. In simulations of noiseless quantum computers, we obtain per-cent accurate results for one- and two-dimensional integration with up to six qubits. This work paves the way towards taking advantage of quantum algorithms for the integration of high-energy processes.

hep-ph↗

arXiv2021

Optimized compiler for Distributed Quantum Computing

Practical distributed quantum computing requires the development of efficient compilers, able to make quantum circuits compatible with some given hardware constraints. This problem is known to be tough, even for local computing. Here, we address it on distributed architectures. As generally assumed in this scenario, telegates represent the fundamental remote (inter-processor) operations. Each telegate consists of several tasks: i) entanglement generation and distribution, ii) local operations, and iii) classical communications. Entanglement generations and distribution is an expensive resource, as it is time-consuming and fault-prone. To mitigate its impact, we model an optimization problem that combines running-time minimization with the usage of that resource. Specifically, we provide a parametric ILP formulation, where the parameter denotes a time horizon (or time availability); the objective function count the number of used resources. To minimize the time, a binary search solves the subject ILP by iterating over the parameter. Ultimately, to enhance the solution space, we extend the formulation, by introducing a predicate that manipulates the circuit given in input and parallelizes telegates' tasks.

quant-ph↗