Information recoverability of noisy quantum states

• URL: http://arxiv.org/abs/2203.04862v3
• Date: Sat, 8 Apr 2023 06:08:03 GMT
• Title: Information recoverability of noisy quantum states
• Authors: Xuanqiang Zhao, Benchi Zhao, Zihan Xia, Xin Wang
• Abstract summary: We introduce a systematic framework to study how well we can retrieve information from noisy quantum states. We fully characterize the range of recoverable classical information. We also resolve the minimum information retrieving cost, which, along with the corresponding optimal protocol, is efficiently computable by semidefinite programming.
• Score: 5.526775342940154
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Extracting classical information from quantum systems is an essential step of many quantum algorithms. However, this information could be corrupted as the systems are prone to quantum noises, and its distortion under quantum dynamics has not been adequately investigated. In this work, we introduce a systematic framework to study how well we can retrieve information from noisy quantum states. Given a noisy quantum channel, we fully characterize the range of recoverable classical information. This condition allows a natural measure quantifying the information recoverability of a channel. Moreover, we resolve the minimum information retrieving cost, which, along with the corresponding optimal protocol, is efficiently computable by semidefinite programming. As applications, we establish the limits on the information retrieving cost for practical quantum noises and employ the corresponding protocols to mitigate errors in ground state energy estimation. Our work gives the first full characterization of information recoverability of noisy quantum states from the recoverable range to the recovering cost, revealing the ultimate limit of probabilistic error cancellation.

Related papers

• Quantum information scrambling in adiabatically-driven critical systems [49.1574468325115]
  Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution.
  arXiv  Detail & Related papers  (2024-08-05T18:00:05Z)
• Corrupted sensing quantum state tomography [0.0]
  We propose the concept of corrupted sensing quantum state tomography which enables the simultaneous reconstruction of quantum states and structured noise. It is envisaged that the techniques can become a practical tool to greatly reduce the cost and computational effort for quantum tomography in noisy quantum systems.
  arXiv  Detail & Related papers  (2024-05-23T10:13:59Z)
• Topological rejection of noise by quantum skyrmions [0.0]
  We show that quantum skyrmions and their nonlocal topological observables remain resilient to noise even as typical entanglement witnesses and measures of the state decay. This allows us to introduce the notion of digitization of quantum information based on our new discrete topological quantum observables.
  arXiv  Detail & Related papers  (2024-03-04T13:36:40Z)
• Retrieving non-linear features from noisy quantum states [11.289924445850328]
  In this paper, we analyze the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.
  arXiv  Detail & Related papers  (2023-09-20T15:28:18Z)
• Efficient information recovery from Pauli noise via classical shadow [6.689075863602204]
  We introduce an efficient algorithm that can recover information from quantum states under Pauli noise. For a local and bounded-degree observable, only partial knowledge of the channel is required to recover the ideal information. As a notable application, our method can be severed as a sample-efficient error mitigation scheme for Clifford circuits.
  arXiv  Detail & Related papers  (2023-05-06T23:34:13Z)
• Potential and limitations of quantum extreme learning machines [55.41644538483948]
  We present a framework to model QRCs and QELMs, showing that they can be concisely described via single effective measurements. Our analysis paves the way to a more thorough understanding of the capabilities and limitations of both QELMs and QRCs.
  arXiv  Detail & Related papers  (2022-10-03T09:32:28Z)
• Efficient algorithms for quantum information bottleneck [64.67104066707309]
  We propose a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck.
  arXiv  Detail & Related papers  (2022-08-22T14:20:05Z)
• Quantum Noise-Induced Reservoir Computing [0.6738135972929344]
  We propose a framework called quantum noise-induced reservoir computing. We show that some abstract quantum noise models can induce useful information processing capabilities for temporal input data. Our study opens up a novel path for diverting useful information from quantum computer noises into a more sophisticated information processor.
  arXiv  Detail & Related papers  (2022-07-16T12:21:48Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Quantum noise protects quantum classifiers against adversaries [120.08771960032033]
  Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. We show that by taking advantage of depolarisation noise in quantum circuits for classification, a robustness bound against adversaries can be derived. This is the first quantum protocol that can be used against the most general adversaries.
  arXiv  Detail & Related papers  (2020-03-20T17:56:14Z)

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.