Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

Abstract

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

18 pages, 6 figures, Close to the published version, The first three authors (MS, SL, JL) contributed equally to this work

References in corpus (35)

• Variational Quantum Algorithms
• Topological entanglement entropy
• Barren plateaus in quantum neural network training landscapes
• Quantum Circuit Learning
• Parameterized quantum circuits as machine learning models
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• Quantum entanglement in condensed matter systems
• Efficient quantum state tomography
• Probing entanglement entropy via randomized measurements
• Quantum autoencoders for efficient compression of quantum data
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Modified Friedmann Equations from Tsallis Entropy
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
• Quantum Variational Autoencoder
• Nonadditive entropy: the concept and its use
• Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies
• Renyi Entropy and Free Energy
• Subadditivity of q-entropies for q>1
• Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
• Quantum algorithm for estimating Renyi entropies of quantum states
• Quantum Algorithm for Fidelity Estimation
• Entanglement Rényi $\alpha$-entropy
• Measuring Quantum Entropy
• Quantum algorithms for estimating quantum entropies
• New Quantum Algorithms for Computing Quantum Entropies and Distances
• Is the Tsallis entropy stable?
• Fast Quantum Algorithms for Trace Distance Estimation
• Estimating Quantum Mutual Information Through a Quantum Neural Network
• Quantum Neural Estimation of Entropies
• Sharp Continuity Bounds for Entropy and Conditional Entropy
• Quantum state tomography with disentanglement algorithm