Scalable and Flexible Classical Shadow Tomography with Tensor Networks

• URL: http://arxiv.org/abs/2209.02093v3
• Date: Thu, 25 May 2023 07:13:41 GMT
• Title: Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• Authors: Ahmed A. Akhtar, Hong-Ye Hu, Yi-Zhuang You
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the single-qubit (local) Pauli measurement, which is well suited for predicting local operators but inefficient for large operators; and the global Clifford measurement, which is efficient for low-rank operators but infeasible on near-term quantum devices due to the extensive gate overhead. In this work, we demonstrate a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits, which interpolates between the limits of Pauli and Clifford measurements. The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction map and evaluating various physical properties. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum (NISQ) devices. We show that the shallow-circuit measurement protocol provides immediate, exponential advantages over the Pauli measurement protocol for predicting quasi-local operators. It also enables a more efficient fidelity estimation compared to the Pauli measurement.

Related papers

• Holographic Classical Shadow Tomography [1.9818805908789396]
  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.
  arXiv  Detail & Related papers  (2024-06-17T17:40:59Z)
• Efficient Classical Shadow Tomography through Many-body Localization Dynamics [4.923287660970805]
  We introduce an alternative approach founded on the dynamics of many-body localization. We demonstrate that our scheme achieves remarkable efficiency comparable to shallow circuits.
  arXiv  Detail & Related papers  (2023-09-03T19:50:28Z)
• A quantum advantage over classical for local max cut [48.02822142773719]
  Quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. Results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical.
  arXiv  Detail & Related papers  (2023-04-17T16:42:05Z)
• Closed-form analytic expressions for shadow estimation with brickwork circuits [0.4997673761305335]
  Properties of quantum systems can be estimated using classical shadows. We derive analytical expressions for shadow estimation using brickwork circuits. We find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
  arXiv  Detail & Related papers  (2022-11-17T19:01:15Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• 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)
• Neural network enhanced measurement efficiency for molecular groundstates [63.36515347329037]
  We adapt common neural network models to learn complex groundstate wavefunctions for several molecular qubit Hamiltonians. We find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables.
  arXiv  Detail & Related papers  (2022-06-30T17:45:05Z)
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables [0.0]
  We introduce a method for performing a single joint measurement that can be implemented locally. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy.
  arXiv  Detail & Related papers  (2022-06-17T17:42:54Z)
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics [0.0]
  We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles. We numerically demonstrate our approach for finite-depth local unitary circuits and finite-time local-Hamiltonian generated evolutions.
  arXiv  Detail & Related papers  (2021-07-10T11:34:51Z)

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.