Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory

• URL: http://arxiv.org/abs/2311.12596v2
• Date: Wed, 22 Nov 2023 13:48:39 GMT
• Title: Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Authors: Carlos L. Benavides-Riveros, Tomasz Wasak, Alessio Recati
• Abstract summary: Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation. Here we combine ideas from functional theories and quantum information to develop a novel functional framework for the QFI of fermionic and bosonic ground states. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation, detect quantum phase transitions, witness genuine multipartite entanglement, or probe nonlocality. Despite this widespread range of applications, computing the QFI value of quantum many-body systems is, in general, a very demanding task. Here we combine ideas from functional theories and quantum information to develop a novel functional framework for the QFI of fermionic and bosonic ground states. By relying upon the constrained-search approach, we demonstrate that the QFI matricial values can universally be determined by the one-body reduced density matrix (1-RDM), avoiding thus the use of exponentially large wave functions. Furthermore, we show that QFI functionals can be determined from the universal 1-RDM functional by calculating its derivatives with respect to the coupling strengths, becoming thus the generating functional of the QFI. We showcase our approach with the Bose-Hubbard model and present exact analytical and numerical QFI functionals. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information.

Related papers

• How to harness high-dimensional temporal entanglement, using limited interferometry setups [62.997667081978825]
  We develop the first complete analysis of high-dimensional entanglement in the polarization-time-domain. We show how to efficiently certify relevant density matrix elements and security parameters for Quantum Key Distribution. We propose a novel setup that can further enhance the noise resistance of free-space quantum communication.
  arXiv  Detail & Related papers  (2023-08-08T17:44:43Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• QSAN: A Near-term Achievable Quantum Self-Attention Network [73.15524926159702]
  Self-Attention Mechanism (SAM) is good at capturing the internal connections of features. A novel Quantum Self-Attention Network (QSAN) is proposed for image classification tasks on near-term quantum devices.
  arXiv  Detail & Related papers  (2022-07-14T12:22:51Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum Federated Learning with Quantum Data [87.49715898878858]
  Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner.
  arXiv  Detail & Related papers  (2021-05-30T12:19:27Z)
• Quantum Fisher information from randomized measurements [0.0]
  The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas. We use measurements of the density matrix to construct lower bounds that converge to the QFI. We present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
  arXiv  Detail & Related papers  (2021-05-27T14:16:14Z)
• Experimental estimation of the quantum Fisher information from randomized measurements [9.795131832414855]
  The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. Here, we explore how the QFI can be estimated via randomized measurements. We experimentally validate this approach using two platforms: a nitrogen-vacancy center spin in diamond and a 4-qubit state provided by a superconducting quantum computer.
  arXiv  Detail & Related papers  (2021-04-01T15:12:31Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning [0.0]
  We study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN) We employ a statistical and differential geometric approach to study the learning theory of QNN.
  arXiv  Detail & Related papers  (2020-11-16T10:41:47Z)
• Variational Quantum Algorithm for Estimating the Quantum Fisher Information [0.0]
  We present a variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing.
  arXiv  Detail & Related papers  (2020-10-20T17:44:55Z)
• Quantum restricted Boltzmann machine universal for quantum computation [4.3411599646551196]
  Quantum neural network provides a powerful tool to represent the large-scale wave function. A significant open problem is what exactly the representational power boundary of the single-layer quantum neural network is.
  arXiv  Detail & Related papers  (2020-05-25T08:25:22Z)

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.