Overlapped grouping measurement: A unified framework for measuring quantum states

• URL: http://arxiv.org/abs/2105.13091v2
• Date: Thu, 12 Jan 2023 10:58:45 GMT
• Title: Overlapped grouping measurement: A unified framework for measuring quantum states
• Authors: Bujiao Wu, Jinzhao Sun, Qi Huang, and Xiao Yuan
• Abstract summary: We propose a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. Our numerical result shows significant improvements over existing schemes.
• Score: 2.1166716158060104
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable compatibility, or classical shadows of quantum states, different advanced measurement schemes have been proposed to greatly reduce the large measurement cost. Yet, the underline cost reduction mechanisms seem distinct from each other, and how to systematically find the optimal scheme remains a critical challenge. Here, we address this challenge by proposing a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. Our framework allows us to introduce a general scheme~ -- ~overlapped grouping measurement, which simultaneously exploits the advantages of most existing methods. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. We provide explicit grouping strategies and numerically verify its performance for different molecular Hamiltonians with up to 16 qubits. Our numerical result shows significant improvements over existing schemes. Our work paves the way for efficient quantum measurement and fast quantum processing with current and near-term quantum devices.

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)
• Entanglement measurement based on convex hull properties [0.0]
  We will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states. Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment.
  arXiv  Detail & Related papers  (2024-11-08T08:03:35Z)
• A universal scheme to self-test any quantum state and extremal measurement [41.94295877935867]
  quantum network considered in this work is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.
  arXiv  Detail & Related papers  (2023-12-07T16:20:28Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping [55.47824411563162]
  Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. We develop a practical, efficient estimation strategy, which we call ShadowGrouping.
  arXiv  Detail & Related papers  (2023-01-09T14:41:07Z)
• 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)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• 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)
• Efficient estimation of multipartite quantum coherence [3.948541278345575]
  We propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements. We experimentally implement various multi-qubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherence are efficiently inferred from measuring few observables.
  arXiv  Detail & Related papers  (2020-10-06T10:45:43Z)

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.