Classification with Quantum Neural Networks on Near Term Processors

By Edward Farhi, Hartmut Neven. 2018

1,024 citations recorded by the source corpus.

We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network’s predictor of the binary label of the input state. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/5240a3531cd2f628bfe23425b1dd8ff89c15dc34

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Citations in the corpus

Quantum Natural Gradient (2019, methodology): “Applications include the Variational Quantum Eigensolver (VQE) [20], Quantum Approximate Optimization Algorithm (QAOA) [5] and Quantum Neural Networks (QNNs) [6, 10, 23].”
Transfer learning in hybrid classical-quantum neural networks (2019, background): “One of the possible quantum generalizations of feedforward neural networks can be given in terms of variational quantum circuits [17, 24, 30, 30, 33, 34, 39, 41, 43].”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “[29] Edward Farhi and Hartmut Neven, “Classification with quantum neural networks on near term processors,” arXiv preprint arXiv:1802.”
Parameterized quantum circuits as machine learning models (2019, methodology): “Farhi and Neven [46] propose a VQM binary classiﬁer for bit-strings.”
Barren plateaus in quantum neural network training landscapes (2018, methodology): “These approaches have even been extended to both quantum machine learning and error correction [6, 7, 20–23].”
Evaluating analytic gradients on quantum hardware (2018, background): “[7] Edward Farhi and Hartmut Neven, “Classification with quantum neural networks on near term processors,” (2018), arxiv:1802.”
PennyLane: Automatic differentiation of hybrid quantum-classical computations (2018, background): “Recent advances in the quantum machine learning literature [8, 10, 11, 41] have suggested ways to estimate analytic derivatives by computing linear combinations of different quantum circuits.”
Variational Quantum Circuits for Deep Reinforcement Learning (2019, background): “Previous works [26, 20, 27] have demonstrated that the variational circuits can model any function approximators, classiﬁers and even quantum-many-body physics that are intractable on classical computers.”
Hierarchical quantum classifiers (2018, neutral): “For networks that cannot be efficiently contracted a finite-difference method or an approximation to the true gradient must be used.(27) These strategies introduce additional noise due to finite-sampling error, and intrinsic noise of near-term quantum devices.”
Data re-uploading for a universal quantum classifier (2019, methodology): “This is similar to previous proposals of binary multiqubit classifiers [7], although we add the possibility of multiclass classification by introducing several thresholds (see Section 2).”