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arXiv:2603.22427

Predictive supremacy of informationally-restricted quantum perceptron

Shubhayan Sarkar

quant-phSubmitted Mar 23, 2026• Announced Mar 25, 2026• 0 citations
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Abstract

In the current world, the use of artificial intelligence is penetrating every aspect of human life. The basic element of any artificial intelligence is a digital neuron, called a perceptron, while its quantum analogue is called a quantum perceptron. Here, we introduce a model of perceptron called the informationally-restricted measurement-based perceptron (IMP), where each input is composed of two bits, while at the node, depending on a free input variable, the perceptron decides which bit to evaluate. Additionally, the states transmitted from the input to the node are restricted to a bit (qubit). We establish that under this restriction, the quantum IMP predicts better than a classical IMP. This means that under dimensional restriction of the transmitted states, when both the classical and quantum perceptrons learn the same, the quantum perceptron predicts better than the classical perceptron. For our purpose, we find specific learned values of the perceptron that can display the advantage of a quantum perceptron over its classical counterpart. Restricting to discrete binary inputs, we establish that the observed quantum advantage is universal, that is, for any non-trivial function implementable by both the quantum and classical IMP, one can always find a quantum implementation that outperforms the predictive capability of every classical one. This points to the fact that, given identical learning and resources, a quantum perceptron would predict better than any classical one.

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5+4 pages, 2 Figures, Comments are appreciated :)

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In the current world, the use of artificial intelligence is penetrating every aspect of human life. The basic element of any artificial intelligence is a digital neuron, called a perceptron, while its quantum analogue is called a quantum perceptron. Here, we introduce a model of perceptron called the informationally-restricted measurement-based perceptron (IMP), where each input is composed of two bits, while at the node, depending on a free input variable, the perceptron decides which bit to evaluate. Additionally, the states transmitted from the input to the node are restricted to a bit (qubit). We establish that under this restriction, the quantum IMP predicts better than a classical IMP. This means that under dimensional restriction of the transmitted states, when both the classical and quantum perceptrons learn the same, the quantum perceptron predicts better than the classical perceptron. For our purpose, we find specific learned values of the perceptron that can display the advantage of a quantum perceptron over its classical counterpart. Restricting to discrete binary inputs, we establish that the observed quantum advantage is universal, that is, for any non-trivial function implementable by both the quantum and classical IMP, one can always find a quantum implementation that outperforms the predictive capability of every classical one. This points to the fact that, given identical learning and resources, a quantum perceptron would predict better than any classical one.
Abstract Artificial neural networks are the heart of machine learning algorithms and artificial intelligence. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt’s “perceptron”, but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a binary-valued perceptron, which shows exponential advantage in storage resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives answers consistent with the expected results. We show that this quantum model of a perceptron can be trained in a hybrid quantum-classical scheme employing a modified version of the perceptron update rule and used as an elementary nonlinear classifier of simple patterns, as a first step towards practical quantum neural networks efficiently implemented on near-term quantum processing hardware.
A Perceptron is a fundamental building block of a neural network. The flexibility and scalability of perceptron make it ubiquitous in building intelligent systems. Studies have shown the efficacy of a single neuron in making intelligent decisions. Here, we examined and compared two perceptron’s with distinct mechanisms, and developed a quantum version of one of those perceptron’s. As a part of this modelling, we implemented the quantum circuit for an artificial perception, generated a dataset, and simulated the training. Through these experiments, we show that there is an exponential growth advantage and test different qubit versions. Our findings show that this quantum model of an individual perceptron can be used as a pattern classifier. For the second type of model, we provide an understanding to design and simulate a spike-dependent quantum perceptron. Our code is available at https://github.com/ashutosh1919/quantum-perceptron
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
Quantum information and quantum computers have enabled us to write algorithms, - quantum algorithms - that in some cases display a speedup with respect to their classical counterpart. As machine learning is becoming of upmost importance not only for our every-day-life and for scientific research, it is natural to inquire if we could use methods from quantum information to speed up machine learning’s processes. In this Thesis, we review a model of a quantum perceptron, a key component for modern neural networks, and simulate its time evolution to characterize behavior.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a quadratic improvement over the classical perceptron algorithm using Grover's search have been proposed by Wiebe et al. arXiv:1602.04799 . While the first model reduces the complexity with respect to the size of the training set, the second one improves the bound on the number of mistakes made by the perceptron. In this paper, we introduce a hybrid quantum-classical perceptron algorithm with lower complexity and better generalization ability than the classical perceptron. We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile.