Optimising shadow tomography with generalised measurements

• URL: http://arxiv.org/abs/2205.08990v2
• Date: Sat, 26 Nov 2022 07:04:47 GMT
• Title: Optimising shadow tomography with generalised measurements
• Authors: H. Chau Nguyen, Jan Lennart B\"onsel, Jonathan Steinberg and Otfried G\"uhne
• Abstract summary: Quantum technology requires scalable techniques to efficiently extract information from a quantum system. Traditional tomography is limited to a handful of qubits and shadow tomography has been suggested as a scalable replacement for larger systems. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalised measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analysed based on outcomes of ideal projective measurements on the system upon application of randomised unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalised measurements, or positive operator valued measures. Based on the idea of the least-square estimator, shadow tomography with generalised measurements is both more general and simpler than the traditional formulation with randomisation of unitaries. In particular, this formulation allows us to analyse theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Shadow tomography with generalised measurements is also indispensable in realistic implementation of quantum mechanical measurements, when noise is unavoidable. Moreover, we also demonstrate how the optimisation of measurements for shadow tomography tailored toward a particular set of observables can be carried out.

Related papers

• Optimal Quantum Overlapping Tomography [2.555222031881788]
  Partial tomography has emerged as a promising approach for characterizing complex quantum systems. We introduce a unified framework for optimal overlapping tomography by mapping the problem to clique cover model. We experimentally validate the feasibility of our schemes on practical nuclear spin processor.
  arXiv  Detail & Related papers  (2024-10-17T12:03:43Z)
• 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)
• Shadow tomography on general measurement frames [37.69303106863453]
  We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. We show that the formalism of measurement frames offers a natural framework for shadow tomography. We demonstrate that a sought-after target of shadow tomography can be achieved for the entire class of tight rank-1 measurement frames.
  arXiv  Detail & Related papers  (2023-01-30T19:00:17Z)
• 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)
• Solving Inverse Problems in Medical Imaging with Score-Based Generative Models [87.48867245544106]
  Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) Existing solutions based on machine learning typically train a model to directly map measurements to medical images. We propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models.
  arXiv  Detail & Related papers  (2021-11-15T05:41:12Z)
• 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)
• 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)
• Operational, gauge-free quantum tomography [0.18374319565577155]
  We introduce and implement efficient operational tomography. It addresses a problem of ambiguity in representation that arises in current tomographic approaches. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios.
  arXiv  Detail & Related papers  (2020-07-03T03:02:34Z)
• Semi-device-dependent blind quantum tomography [1.3075880857448061]
  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.
  arXiv  Detail & Related papers  (2020-06-04T18:00:04Z)
• OAM tomography with Heisenberg-Weyl observables [58.720142291102135]
  We apply a recent tomography protocol to simplify the measurement and characterisation of OAM states. Our scheme for OAM tomography in $d$ dimensions requires only a set of measurements on a mode qubit, i.e., a 2-dimensional system. This replaces the current complexity of OAM measurements by the ability to perform generalized Pauli operators $X_d, Z_d$ on OAM states.
  arXiv  Detail & Related papers  (2020-03-19T10:36:46Z)

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.