Semi-device-dependent blind quantum tomography

• URL: http://arxiv.org/abs/2006.03069v2
• Date: Thu, 6 Jul 2023 06:05:41 GMT
• Title: Semi-device-dependent blind quantum tomography
• Authors: Ingo Roth, Jadwiga Wilkens, Dominik Hangleiter, Jens Eisert
• Abstract summary: Current schemes typically require measurement devices for tomography that are a priori calibrated to high precision. We show that exploiting the natural low-rank structure of quantum states of interest suffices to arrive at a highly scalable blind' tomography scheme. We numerically demonstrate that robust blind quantum tomography is possible in a practical setting inspired by an implementation of trapped ions.
• Score: 1.3075880857448061
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Extracting tomographic information about quantum states is a crucial task in the quest towards devising high-precision quantum devices. Current schemes typically require measurement devices for tomography that are a priori calibrated to high precision. Ironically, the accuracy of the measurement calibration is fundamentally limited by the accuracy of state preparation, establishing a vicious cycle. Here, we prove that this cycle can be broken and the dependence on the measurement device's calibration significantly relaxed. We show that exploiting the natural low-rank structure of quantum states of interest suffices to arrive at a highly scalable `blind' tomography scheme with a classically efficient post-processing algorithm. We further improve the efficiency of our scheme by making use of the sparse structure of the calibrations. This is achieved by relaxing the blind quantum tomography problem to the de-mixing of a sparse sum of low-rank matrices. We prove that the proposed algorithm recovers a low-rank quantum state and the calibration provided that the measurement model exhibits a restricted isometry property. For generic measurements, we show that it requires a close-to-optimal number of measurement settings. Complementing these conceptual and mathematical insights, we numerically demonstrate that robust blind quantum tomography is possible in a practical setting inspired by an implementation of trapped ions.

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)
• Multi-qubit State Tomography with Few Pauli Measurements [8.611891055029076]
  A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. This is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. We build an efficient framework that requires fewer measurements but yields an expected accuracy.
  arXiv  Detail & Related papers  (2023-05-31T14:10:26Z)
• Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer [0.2621730497733947]
  We implement these measurements on a superconducting quantum computer. Our experiment produces sufficiently low error to allow the saturation of the theoretical limits. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.
  arXiv  Detail & Related papers  (2023-02-10T09:44:58Z)
• 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)
• 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)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Quantum verification and estimation with few copies [63.669642197519934]
  The verification and estimation of large entangled systems represents one of the main challenges in the employment of such systems for reliable quantum information processing. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity) and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography.
  arXiv  Detail & Related papers  (2021-09-08T18:20:07Z)
• Quantum tomography of noisy ion-based qudits [0.0]
  We show that it is possible to construct a quantum measurement protocol that contains no more than a single quantum operation in each measurement circuit. The measures described can significantly improve the accuracy of quantum tomography of real ion-based qudits.
  arXiv  Detail & Related papers  (2020-11-09T04:10:32Z)
• Fast and robust quantum state tomography from few basis measurements [65.36803384844723]
  We present an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
  arXiv  Detail & Related papers  (2020-09-17T11:28:41Z)
• High-accuracy adaptive quantum tomography for high-dimensional quantum systems [0.0]
  We introduce an adaptive tomographic method that is characterized by a precision that is better than half that of the Gill-Massar bound for any finite dimension. We demonstrate the high-accuracy of our method by estimating the state of 10-dimensional quantum systems.
  arXiv  Detail & Related papers  (2020-09-10T11:46:51Z)

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.