Quantum splines for non-linear approximations

Macaluso, Antonio; Clissa, Luca; Lodi, Stefano; Sartori, Claudio

doi:10.1145/3387902.3394032

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…However, the main challenge to tackle in the near future for qSLP-MAQA is still the design of a proper activation function-in the sense of the Universal Approximation Theorem-which is one of the significant issues for building a complete quantum neural network. Yet, a recent proposal of QSplines [13] opened the possibility of approximating non-linear activation functions via a quantum algorithm. Even so, QSplines use the HHL as a subroutine, a fault-tolerant quantum algorithm that cannot be adopted in hybrid computation on NISQ devices.…”

Section: Maqa As Quantum-classical Hybrid Algorithmmentioning

confidence: 99%

“…For this purpose, a rich collection of quantum algorithms for basic linear algebra subroutines have been proposed in literature [9][10][11]. Some popular examples of this approach are QSVM [12] and QSplines [13], which obtain an exponential speed-up with respect to their classical counterparts. However, the protocols within this category usually assume the availability of a fault-tolerant quantum computer.…”

Section: Introductionmentioning

confidence: 99%

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MAQA: a quantum framework for supervised learning

Macaluso

Klusch

Lodi

et al. 2023

Quantum Inf Process

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Quantum machine learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources to solve pattern recognition tasks are still to be demonstrated. This work proposes a universal, efficient framework that can reproduce the output of a plethora of classical supervised machine learning algorithms exploiting quantum computation’s advantages. The proposed framework is named Multiple Aggregator Quantum Algorithm (MAQA) due to its capability to combine multiple and diverse functions to solve typical supervised learning problems. In its general formulation, MAQA can be potentially adopted as the quantum counterpart of all those models falling into the scheme of aggregation of multiple functions, such as ensemble algorithms and neural networks. From a computational point of view, the proposed framework allows generating an exponentially large number of different transformations of the input at the cost of increasing the depth of the corresponding quantum circuit linearly. Thus, MAQA produces a model with substantial descriptive power to broaden the horizon of possible applications of quantum machine learning with a computational advantage over classical methods. As a second meaningful addition, we discuss the adoption of the proposed framework as hybrid quantum–classical and fault-tolerant quantum algorithm.

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Section: Maqa As Quantum-classical Hybrid Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

MAQA: a quantum framework for supervised learning

Macaluso

Klusch

Lodi

et al. 2023

Quantum Inf Process

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“…[23,24] In ref. [19], in the context of fault-tolerant quantum computing, the quantum splines to realize nonlinear approximation is proposed, in which Harrow Hassidim Lloyd (HHL) quantum algorithm is utilized. The classical activation functions popular in classical neural network has been realized in the quantum manner.…”

Section: Non-linearity Mapping Between the Input And Outputmentioning

confidence: 99%

“…In the classical computer, this nonlinear effect can be realized by bringing in various nonlinear activation functions. It deserves a deep study DOI: 10.1002/andp.202200546 how to realize the nonlinear activation function in the quantum manner, [14][15][16][17][18][19][20] serving quantum neural networks. [21] In this work, we propose to simulate the activation of the neuron and realize the nonlinearity by the quantum operation.…”

Section: Introductionmentioning

confidence: 99%

Quantum Simulation of Tunable Neuron Activation

et al. 2023

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The activation of the neuron is simulated by a quantum circuit. When the circuit is deep enough, the output qubit is deterministically in the state if the probability of the input qubit in the designated state is larger than the threshold value. Conversely, the output qubit is deterministically in the state if the probability is smaller than the threshold value. The threshold value is adjustable. When the depth of the circuit is limited, the nonlinear relations between the input and the output can also be realized.

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“…Notably, the idea of identifying specific classes of problems where the sparsity affects the computational complexity of a quantum algorithm has shown good results in the context of fault-tolerant quantum machine learning [14].…”

Section: Solving Csgp Using Qaoamentioning

confidence: 99%

BILP-Q: Quantum Coalition Structure Generation

Venkatesh,

Macaluso,

Klusch

2022

Preprint

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Quantum AI is an emerging field that uses quantum computing to solve typical complex problems in AI. In this work, we propose BILP-Q, the first-ever general quantum approach for solving the Coalition Structure Generation problem (CSGP), which is notably NP-hard. In particular, we reformulate the CSGP in terms of a Quadratic Binary Combinatorial Optimization (QUBO) problem to leverage existing quantum algorithms (e.g., QAOA) to obtain the best coalition structure. Thus, we perform a comparative analysis in terms of time complexity between the proposed quantum approach and the most popular classical baselines. Furthermore, we consider standard benchmark distributions for coalition values to test the BILP-Q on small-scale experiments using the IBM Qiskit environment. Finally, since QUBO problems can be solved operating with quantum annealing, we run BILP-Q on medium-size problems using a real quantum annealer (D-Wave).

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Quantum splines for non-linear approximations

Cited by 8 publications

References 10 publications

MAQA: a quantum framework for supervised learning

MAQA: a quantum framework for supervised learning

Quantum Simulation of Tunable Neuron Activation

BILP-Q: Quantum Coalition Structure Generation

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