Matrix Product State–Based Quantum Classifier

Bhatia, Amandeep Singh; Saggi, Mandeep Kaur; Kumar, Ajay; Jain, Sushma

doi:10.1162/neco_a_01202

Cited by 26 publications

(14 citation statements)

References 14 publications

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“…The first PQC type consists of circuits with a hierarchical architecture. Matrix Product State (MPS) (Bhatia et al 2019) and Tree Tensor Network (TTN) (Grant et al 2018) inspired circuits belong to this group. However, these PQCs measure only one qubit.…”

Section: The Hybrid Neural Networkmentioning

confidence: 99%

Hybrid quantum classical graph neural networks for particle track reconstruction

Tüysüz

Rieger

Novotny³

et al. 2021

Quantum Mach. Intell.

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The Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) will be upgraded to further increase the instantaneous rate of particle collisions (luminosity) and become the High Luminosity LHC (HL-LHC). This increase in luminosity will significantly increase the number of particles interacting with the detector. The interaction of particles with a detector is referred to as “hit”. The HL-LHC will yield many more detector hits, which will pose a combinatorial challenge by using reconstruction algorithms to determine particle trajectories from those hits. This work explores the possibility of converting a novel graph neural network model, that can optimally take into account the sparse nature of the tracking detector data and their complex geometry, to a hybrid quantum-classical graph neural network that benefits from using variational quantum layers. We show that this hybrid model can perform similar to the classical approach. Also, we explore parametrized quantum circuits (PQC) with different expressibility and entangling capacities, and compare their training performance in order to quantify the expected benefits. These results can be used to build a future road map to further develop circuit-based hybrid quantum-classical graph neural networks.

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Section: The Hybrid Neural Networkmentioning

confidence: 99%

Hybrid quantum classical graph neural networks for particle track reconstruction

Tüysüz

Rieger

Novotny³

et al. 2021

Quantum Mach. Intell.

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show abstract

“…Since the pioneering work of [98], great effort has been made to apply TN in the field of machine learning. TN-based methods have been utilized for applications, such as classification [98][99][100][101][102][103][104], generative modeling [105][106][107] and sequence modeling [108]. It has also been shown that TN-based architectures have deep connections to the building of QML models [109].…”

Section: Tensor Networkmentioning

confidence: 99%

Variational quantum reinforcement learning via evolutionary optimization

Chen

Huang

Hsing

et al. 2022

Mach. Learn.: Sci. Technol.

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Recent advance in classical reinforcement learning (RL) and quantum computation (QC) points to a promising direction of performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in modern quantum devices. Here we present two frameworks of deep quantum RL tasks using a gradient-free evolution optimization: First, we apply the amplitude encoding scheme to the Cart-Pole problem, where we demonstrate the quantum advantage of parameter saving using the amplitude encoding; Second, we propose a hybrid framework where the quantum RL agents are equipped with a hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs of dimensions exceeding the number of qubits. This allows us to perform quantum RL on the MiniGrid environment with 147-dimensional inputs. The hybrid TN-VQC architecture provides a natural way to perform efficient compression of the input dimension, enabling further quantum RL applications on noisy intermediate-scale quantum devices.

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“…< l a t e x i t s h a 1 _ b a s e 6 4 = " objects appearing in the TN description are not required to correspond to physically realizable quantum states, some proposals deal with truly quantum data structures, and some have tested TN-based approaches on NISQ hardware [30,49,55]. In the present work, we compare models with a tree tensor network (TTN) structure for classification that are constrained to be true quantum data structures with those that are unconstrained, using metrics of performance and interpretability.…”

Section: Quantum Embeddingmentioning

confidence: 99%

Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

Wall,

D'Aguanno

2021

Preprint

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We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree tensor network (TTN) topology, which acts as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion, analogous to coarse-graining strategies used in renormalization group methodologies from statistical physics. This unsupervised feature extractor then feeds a supervised linear classifier together with a set of truth labels for the data type, and encodes the output in a small-dimensional quantum register. In contrast to previous work on quantum-inspired TTN classifiers, in which the embedding map and class decision weights did not map the data to well-defined quantum states, we present an approach that can be implemented on gate-based quantum computing devices. In particular, we identify an embedding map with accuracy similar to the recently defined exponential machines (Novikov et al., arXiv:1605.03795), but which produces valid quantum state embeddings of classical data vectors, and utilize manifoldbased gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights, and may produce models that are less susceptible to adversarial perturbations. We demonstrate our methodologies in applications utilizing the MNIST handwritten digit dataset and a multivariate timeseries dataset of human activity recognition.

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Matrix Product State–Based Quantum Classifier

Cited by 26 publications

References 14 publications

Hybrid quantum classical graph neural networks for particle track reconstruction

Hybrid quantum classical graph neural networks for particle track reconstruction

Variational quantum reinforcement learning via evolutionary optimization

Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

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