Reliable confidence regions for quantum tomography using distribution moments

• URL: http://arxiv.org/abs/2307.12823v2
• Date: Tue, 19 Mar 2024 09:52:33 GMT
• Title: Reliable confidence regions for quantum tomography using distribution moments
• Authors: D. O. Norkin, E. O. Kiktenko, A. K. Fedorov,
• Abstract summary: We suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We benchmark our approach for a number of quantum tomography protocols using both simulation and demonstration with the use of a cloud-accessible quantum processor.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum states with reliable confidence intervals. In this work we suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We approximate the probability distribution of the Hilbert-Schmidt distance between the target state and the estimation, which is given by the linear inversion, by calculating its two moments. We also present a generalization of this approach for quantum process tomography and deriving confidence intervals for affine functions. We benchmark our approach for a number of quantum tomography protocols using both simulation and demonstration with the use of a cloud-accessible quantum processor. The obtained results pave the way for the use of the suggested scheme for the complete characterization of quantum systems of various natures.

Related papers

• Exploring quantum localization with machine learning [39.58317527488534]
  We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model.
  arXiv  Detail & Related papers  (2024-06-01T08:50:26Z)
• Disentanglement Provides a Unified Estimation for Quantum Entropies and Distance Measures [2.14566083603001]
  This paper introduces a unified approach using Disentangling Quantum Neural Networks (DEQNN) for estimating quantum entropies and distances. Our mathematical proof demonstrates that DEQNN can preserve quantum entropies and distances in smaller partial states. This method is scalable to an arbitrary number of quantum states and is particularly effective for less complex quantum systems.
  arXiv  Detail & Related papers  (2024-01-15T14:33:03Z)
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements [17.38734393793605]
  An efficient representation of quantum states enables realizing quantum state tomography with minimal measurements. We propose an alternative approach to state tomography that uses tensor network representations of mixed states through locally purified density operators. Our study opens avenues in quantum state tomography for two-dimensional systems using tensor network formalism.
  arXiv  Detail & Related papers  (2023-07-31T03:14:31Z)
• Arbitrary coherent distributions in a programmable quantum walk [9.037302699507409]
  coherent superposition of position states in a quantum walk (QW) can be precisely engineered towards the desired distributions to meet the need of quantum information applications. We experimentally demonstrate that the rich dynamics featured with arbitrary coherent distributions can be obtained by introducing different sets of the time- and position-dependent operations. Our results contribute to the practical realization of quantum-walk-based quantum computation, quantum simulations and quantum information protocols.
  arXiv  Detail & Related papers  (2022-02-19T15:56:45Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Learning Temporal Quantum Tomography [0.0]
  Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. We develop a practical and approximate tomography method using a recurrent machine learning framework. We demonstrate our algorithms for quantum learning tasks followed by the proposal of a quantum short-term memory capacity to evaluate the temporal processing ability of near-term quantum devices.
  arXiv  Detail & Related papers  (2021-03-25T17:01:24Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Facial Expression Recognition on a Quantum Computer [68.8204255655161]
  We show a possible solution to facial expression recognition using a quantum machine learning approach. We define a quantum circuit that manipulates the graphs adjacency matrices encoded into the amplitudes of some appropriately defined quantum states.
  arXiv  Detail & Related papers  (2021-02-09T13:48:00Z)
• Estimation of pure quantum states in high dimension at the limit of quantum accuracy through complex optimization and statistical inference [0.0]
  Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices. In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar. Here we present an adaptive tomographic method and show through numerical simulations, that it is difficult to approach the fundamental accuracy of pure quantum states in high dimension.
  arXiv  Detail & Related papers  (2020-07-02T21:33:16Z)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.