Holographic Classical Shadow Tomography

• URL: http://arxiv.org/abs/2406.11788v1
• Date: Mon, 17 Jun 2024 17:40:59 GMT
• Title: Holographic Classical Shadow Tomography
• Authors: Shuhan Zhang, Xiaozhou Feng, Matteo Ippoliti, Yi-Zhuang You,
• Abstract summary: We introduce "holographic shadows", a new class of randomized measurement schemes for classical shadow tomography. "holographic shadows" achieves the optimal scaling of sample complexity for learning geometrically local Pauli operators at any length scale.
• Score: 1.9818805908789396
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce "holographic shadows", a new class of randomized measurement schemes for classical shadow tomography that achieves the optimal scaling of sample complexity for learning geometrically local Pauli operators at any length scale, without the need for fine-tuning protocol parameters such as circuit depth or measurement rate. Our approach utilizes hierarchical quantum circuits, such as tree quantum circuits or holographic random tensor networks. Measurements within the holographic bulk correspond to measurements at different scales on the boundary (i.e. the physical system of interests), facilitating efficient quantum state estimation across observable at all scales. Considering the task of estimating string-like Pauli observables supported on contiguous intervals of $k$ sites in a 1D system, our method achieves an optimal sample complexity scaling of $\sim d^k\mathrm{poly}(k)$, with $d$ the local Hilbert space dimension. We present a holographic minimal cut framework to demonstrate the universality of this sample complexity scaling and validate it with numerical simulations, illustrating the efficacy of holographic shadows in enhancing quantum state learning capabilities.

Related papers

• Measuring entanglement without local addressing via spiral quantum state tomography [0.0]
  Quantum state tomography serves as a key tool for identifying quantum states generated in quantum computers and simulators. Here, we present a tomography scheme that scales far more efficiently and eliminates the need for local addressing of single constituents. The results of the numerical simulations demonstrate a high degree of tomographic efficiency and accuracy.
  arXiv  Detail & Related papers  (2024-11-25T17:37:29Z)
• 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)
• Optimal overlapping tomography [0.814548016007804]
  Overlapping tomography is a scheme which allows to obtain all the information contained in specific subsystems of quantum systems. We present protocols for optimal overlapping tomography with respect to different figures of merit. Results will find applications in learning noise and interaction patterns in quantum computers as well as characterising fermionic systems in quantum chemistry.
  arXiv  Detail & Related papers  (2024-08-11T08:59:08Z)
• Learning topological states from randomized measurements using variational tensor network tomography [0.4818215922729967]
  Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. We implement and study a tomographic method that combines variational optimization on tensor networks with randomized measurement techniques. We demonstrate its ability to learn the ground state of the surface code Hamiltonian as well as an experimentally realizable quantum spin liquid state.
  arXiv  Detail & Related papers  (2024-05-31T21:05:43Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Operator relaxation and the optimal depth of classical shadows [0.0]
  We study the sample complexity of learning the expectation value of Pauli operators via shallow shadows'' We show that the shadow norm is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing circuit.
  arXiv  Detail & Related papers  (2022-12-22T18:46:46Z)
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
  We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
  arXiv  Detail & Related papers  (2022-10-27T11:37:14Z)
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks [0.0]
  We show a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead.
  arXiv  Detail & Related papers  (2022-09-05T18:42:53Z)
• 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)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)

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.