Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits

• URL: http://arxiv.org/abs/2408.12199v1
• Date: Thu, 22 Aug 2024 08:21:28 GMT
• Title: Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
• Authors: Yuxuan Du, Min-Hsiu Hsieh, Dacheng Tao,
• Abstract summary: 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.
• Score: 63.733312560668274
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. However, recent progress in quantum learning theory invokes a crucial question: 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 using new classical inputs, after learning from data obtained by incoherently measuring states generated by the same circuit but with different classical inputs? In this work, 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. Building upon these derived complexity bounds, we further harness the concept of classical shadow and truncated trigonometric expansion to devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to polynomial scaling in many practical settings. Our results advance two crucial realms in quantum computation: the exploration of quantum algorithms with practical utilities and learning-based quantum system certification. We conduct numerical simulations to validate our proposals across diverse scenarios, encompassing quantum information processing protocols, Hamiltonian simulation, and variational quantum algorithms up to 60 qubits.

Related papers

• Quantum Simulation of Dissipative Energy Transfer via Noisy Quantum Computer [0.40964539027092917]
  We propose a practical approach to simulate the dynamics of an open quantum system on a noisy computer. Our method leverages gate noises on the IBM-Q real device, enabling us to perform calculations using only two qubits. In the last, to deal with the increasing depth of quantum circuits when doing Trotter expansion, we introduced the transfer tensor method(TTM) to extend our short-term dynamics simulation.
  arXiv  Detail & Related papers  (2023-12-03T13:56:41Z)
• 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)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Analog quantum variational embedding classifier [8.445680783099196]
  We propose a gate-based variational embedding classifier based on an analog quantum computer. We find the performance of our classifier can be increased by increasing the number of qubits until the performance saturates and fluctuates. Our algorithm presents the possibility of using current quantum annealers for solving practical machine-learning problems.
  arXiv  Detail & Related papers  (2022-11-04T20:58:48Z)
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer [0.0]
  We introduce an amplitude-based implementation for approximating non-linearity in the form of the unit step function on a quantum computer. We describe two distinct circuit types which receive their input either directly from a classical computer, or as a quantum state when embedded in a more advanced quantum algorithm.
  arXiv  Detail & Related papers  (2022-06-07T07:14:12Z)
• Quantum variational learning for entanglement witnessing [0.0]
  This work focuses on the potential implementation of quantum algorithms allowing to properly classify quantum states defined over a single register of $n$ qubits. We exploit the notion of "entanglement witness", i.e., an operator whose expectation values allow to identify certain specific states as entangled. We made use of Quantum Neural Networks (QNNs) in order to successfully learn how to reproduce the action of an entanglement witness.
  arXiv  Detail & Related papers  (2022-05-20T20:14:28Z)
• Low-rank tensor decompositions of quantum circuits [14.531461873576449]
  We show how MPOs can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers.
  arXiv  Detail & Related papers  (2022-05-19T22:09:15Z)
• 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)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)

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.