Generative machine learning with tensor networks: benchmarks on near-term quantum computers

Abstract

Noisy, intermediate-scale quantum (NISQ) computing devices have become an industrial reality in the last few years, and cloud-based interfaces to these devices are enabling exploration of near-term quantum computing on a range of problems. As NISQ devices are too noisy for many of the algorithms with a known quantum advantage, discovering impactful applications for near-term devices is the subject of intense research interest. We explore quantum-assisted machine learning (QAML) on NISQ devices through the perspective of tensor networks (TNs), which offer a robust platform for designing resource-efficient and expressive machine learning models to be dispatched on quantum devices. In particular, we lay out a framework for designing and optimizing TN-based QAML models using classical techniques, and then compiling these models to be run on quantum hardware, with demonstrations for generative matrix product state (MPS) models. We put forth a generalized canonical form for MPS models that aids in compilation to quantum devices, and demonstrate greedy heuristics for compiling with a given topology and gate set that outperforms known generic methods in terms of the number of entangling gates, e.g., CNOTs, in some cases by an order of magnitude. We present an exactly solvable benchmark problem for assessing the performance of MPS QAML models, and also present an application for the canonical MNIST handwritten digit dataset. The impacts of hardware topology and day-to-day experimental noise fluctuations on model performance are explored by analyzing both raw experimental counts and statistical divergences of inferred distributions. We also present parametric studies of depolarization and readout noise impacts on model performance using hardware simulators.

arXiv comment31 pages. 18+49 figures

References in corpus (59)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Supervised learning with quantum enhanced feature spaces
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum machine learning in feature Hilbert spaces
• Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
• Superconducting Qubits: Current State of Play
• Parameterized quantum circuits as machine learning models
• Circuit-centric quantum classifiers
• Entanglement and quantum computation with ions in thermal motion
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Roads towards fault-tolerant universal quantum computation
• Classical simulation of quantum many-body systems with a tree tensor network
• Tensor networks for complex quantum systems
• Quantum machine learning: a classical perspective
• Optimal Quantum Circuits for General Two-Qubit Gates
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• ProjectQ: An Open Source Software Framework for Quantum Computing
• Sequential generation of entangled multi-qubit states
• Robust data encodings for quantum classifiers
• Variational quantum algorithms for nonlinear problems
• Reconstructing quantum states with generative models
• Hierarchical quantum classifiers
• Towards Quantum Machine Learning with Tensor Networks
• Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Unsupervised Generative Modeling Using Matrix Product States
• Equivalence of restricted Boltzmann machines and tensor network states
• Natural two-qubit gate for quantum computation using the XY interaction
• Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Quantum Circuits for Isometries
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Entanglement in Deep Learning Architectures
• Challenges and Opportunities of Near-Term Quantum Computing Systems
• A Software Methodology for Compiling Quantum Programs
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• ScaffCC: Scalable Compilation and Analysis of Quantum Programs
• Overview and Comparison of Gate Level Quantum Software Platforms
• Sequential Generation of Matrix-Product States in Cavity QED
• Tree Tensor Networks for Generative Modeling
• Machine learning of noise-resilient quantum circuits
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Machine Learning Phase Transitions with a Quantum Processor
• Efficient quantum circuits for one-way quantum computing
• staq -- A full-stack quantum processing toolkit
• TensorNetwork for Machine Learning
• Matrix Product Operators for Sequence to Sequence Learning
• Tensor-based algorithms for image classification
• Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning
• Modeling Sequences with Quantum States: A Look Under the Hood
• Quantum Machine Learning Tensor Network States
• Anomaly Detection with Tensor Networks
• Heuristics for Quantum Compiling with a Continuous Gate Set
• Tangent-Space Gradient Optimization of Tensor Network for Machine Learning
• Number-State Preserving Tensor Networks as Classifiers for Supervised Learning

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• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
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• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK
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