From observations to complexity of quantum states via unsupervised learning

• URL: http://arxiv.org/abs/2102.11328v3
• Date: Wed, 27 Jul 2022 13:00:35 GMT
• Title: From observations to complexity of quantum states via unsupervised learning
• Authors: Markus Schmitt and Zala Lenar\v{c}i\v{c}
• Abstract summary: We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states by determining the minimal number of parameters needed to reproduce local observations. The latter can be used as a probe of thermalization, to assign the local complexity of density matrices in open setups and for the reconstruction of underlying Hamiltonian operators. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.

Related papers

• Universal learning of nonlocal entropy via local correlations in non-equilibrium quantum states [8.415573546527419]
  Characterizing the nonlocal nature of quantum states is a central challenge in the practical application of large-scale quantum computation and simulation.<n>We employ a multilayer perceptron (MLP) to establish a universal mapping between the QMI and local correlations only up to second order for nonequilibrium states generated by quenches in a one-dimensional disordered XXZ model.
  arXiv  Detail & Related papers  (2025-11-23T07:34:25Z)
• Certifying localizable quantum properties with constant sample complexity [1.5334952984692285]
  We introduce a highly general certification framework based on a physical phenomenon that we call localizable quantumness.<n>We develop certification protocols that certify global properties by witnessing them on a small, accessible subsystem.<n>Our method dramatically reduces experimental cost by relying solely on local Pauli measurements.
  arXiv  Detail & Related papers  (2025-09-22T11:06:20Z)
• QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning [48.12231190677108]
  Quantum Annealing Multi-Head Attention (QAMA) is proposed, a novel drop-in operator that reformulates attention as an energy-based Hamiltonian optimization problem.<n>In this framework, token interactions are encoded into binary quadratic terms, and quantum annealing is employed to search for low-energy configurations.<n> Empirically, evaluation on both natural language and vision benchmarks shows that, across tasks, accuracy deviates by at most 2.7 points from standard multi-head attention.
  arXiv  Detail & Related papers  (2025-04-15T11:29:09Z)
• Quantum Gibbs states are locally Markovian [1.9643748953805944]
  We show that for any Hamiltonian with a bounded interaction degree, the quantum Gibbs state is locally Markov at arbitrary temperature. We introduce a regularization scheme for imaginary-time-evolved operators at arbitrarily low temperatures.
  arXiv  Detail & Related papers  (2025-04-03T01:54:42Z)
• Comparing quantum complexity and quantum fidelity [0.0]
  We show that complexity provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions. We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics.
  arXiv  Detail & Related papers  (2025-03-12T13:04:57Z)
• The complexity of entanglement embezzlement [0.0]
  We study the circuit complexity of embezzlement using sequences of states that enable arbitrary precision for the process. Our results imply that circuit complexity acts as a physical obstruction to perfect embezzlement.
  arXiv  Detail & Related papers  (2024-10-24T18:00:33Z)
• Bounding the Sample Fluctuation for Pure States Certification with Local Random Measurement [4.923287660970805]
  Recent advancements in randomized measurement techniques have provided fresh insights in this area. We investigate the fundamental properties of schemes that certify pure quantum states through random local Haar measurements. Our results unveil the intrinsic interplay between operator complexity and the efficiency of quantum algorithms, serving as an obstacle to local certification of pure states with long-range entanglement.
  arXiv  Detail & Related papers  (2024-10-22T02:26:44Z)
• Observation of disorder-free localization and efficient disorder averaging on a quantum processor [117.33878347943316]
  We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions.
  arXiv  Detail & Related papers  (2024-10-09T05:28:14Z)
• Emergence of global receptive fields capturing multipartite quantum correlations [0.565473932498362]
  In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations. We show that monitoring the neural network weight space while learning quantum statistics allows to develop physical intuition about complex multipartite patterns. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns.
  arXiv  Detail & Related papers  (2024-08-23T12:45:40Z)
• 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)
• Solving reaction dynamics with quantum computing algorithms [42.408991654684876]
  We study quantum algorithms for response functions, relevant for describing different reactions governed by linear response.<n>We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations.
  arXiv  Detail & Related papers  (2024-03-30T00:21:46Z)
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement [41.94295877935867]
  We introduce and develop the framework of Gibbs-preserving local operations and classical communication. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation.
  arXiv  Detail & Related papers  (2023-11-20T14:58:31Z)
• Detection of Beyond-Quantum Non-locality based on Standard Local Quantum Observables [46.03321798937856]
  We show that device independent detection cannot distinguish beyond-quantum non-local states from standard quantum states. This paper gives a device dependent detection based on local observables to distinguish any beyond-quantum non-local state from all standard quantum states.
  arXiv  Detail & Related papers  (2023-01-10T20:19:34Z)
• Real-Time Krylov Theory for Quantum Computing Algorithms [0.0]
  New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information. We develop the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. We discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.
  arXiv  Detail & Related papers  (2022-08-01T18:00:48Z)
• Quantum state tomography with tensor train cross approximation [84.59270977313619]
  We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
  arXiv  Detail & Related papers  (2022-07-13T17:56:28Z)
• Quantum Causal Unravelling [44.356294905844834]
  We develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography.
  arXiv  Detail & Related papers  (2021-09-27T16:28:06Z)
• 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)
• Entanglement Structure Detection via Machine Learning [0.0]
  We propose an efficient machine learning based approach for predicting the entanglement intactness and depth simultaneously. In particular, the learned classifier can discover the entanglement intactness and depth bounds for the noised GHZ state.
  arXiv  Detail & Related papers  (2020-12-01T14:37:56Z)

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.