Quantum Earth Mover's Distance: A New Approach to Learning Quantum Data

• URL: http://arxiv.org/abs/2101.03037v1
• Date: Fri, 8 Jan 2021 14:33:19 GMT
• Title: Quantum Earth Mover's Distance: A New Approach to Learning Quantum Data
• Authors: Bobak Toussi Kiani, Giacomo De Palma, Milad Marvian, Zi-Wen Liu, Seth Lloyd
• Abstract summary: We show that the quantum earth's (EM) or Wasserstein-1 distance possesses unique properties, not found in other commonly used quantum distance metrics. We propose a quantum Wasserstein generative adversarial network (qWGAN) which takes advantage of the quantum EM distance and provides an efficient means of performing learning on quantum data.
• Score: 12.109551561313706
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such as poor local minima and exponentially decaying gradients. As a new approach, we consider here the quantum earth mover's (EM) or Wasserstein-1 distance, recently proposed in [De Palma et al., arXiv:2009.04469] as a quantum analog to the classical EM distance. We show that the quantum EM distance possesses unique properties, not found in other commonly used quantum distance metrics, that make quantum learning more stable and efficient. We propose a quantum Wasserstein generative adversarial network (qWGAN) which takes advantage of the quantum EM distance and provides an efficient means of performing learning on quantum data. Our qWGAN requires resources polynomial in the number of qubits, and our numerical experiments demonstrate that it is capable of learning a diverse set of quantum data.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Preparation of Entangled Many-Body States with Machine Learning [0.06768558752130309]
  Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state, have been prepared, but fundamental difficulties in systems with many qubits remain. Here, we provide one algorithm with an implementation of a deep learning process and achieve to prepare the target ground states with many qubits.
  arXiv  Detail & Related papers  (2023-07-27T05:03:57Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators [0.0]
  Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model. We propose quantum machine learning with Kerrnon Parametric Hilberts (KPOs) as another promising quantum computing device.
  arXiv  Detail & Related papers  (2023-05-01T07:01:45Z)
• Quantum Machine Learning: from physics to software engineering [58.720142291102135]
  We show how classical machine learning approach can help improve the facilities of quantum computers. We discuss how quantum algorithms and quantum computers may be useful for solving classical machine learning tasks.
  arXiv  Detail & Related papers  (2023-01-04T23:37:45Z)
• Wasserstein Complexity of Quantum Circuits [10.79258896719392]
  Given a unitary transformation, what is the size of the smallest quantum circuit that implements it? This quantity, known as the quantum circuit complexity, is a fundamental property of quantum evolutions. We show that our new measure also provides a lower bound for the experimental cost of implementing quantum circuits.
  arXiv  Detail & Related papers  (2022-08-12T14:44:13Z)
• A Theoretical Framework for Learning from Quantum Data [15.828697880068704]
  We propose a theoretical foundation for learning classical patterns from quantum data. We present a quantum counterpart of the well-known PAC framework. We establish upper bounds on the quantum sample complexity quantum concept classes.
  arXiv  Detail & Related papers  (2021-07-13T21:39:47Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Finding Quantum Critical Points with Neural-Network Quantum States [0.0]
  We present an approach to finding the quantum critical points of the quantum Ising model using neural-network quantum states. We analytically constructed innate restricted Boltzmann machines, transfer learning and unsupervised learning.
  arXiv  Detail & Related papers  (2020-02-07T04:39:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.