Efficient Verification of Ground States of Frustration-Free Hamiltonians

• URL: http://arxiv.org/abs/2206.15292v3
• Date: Thu, 4 Jan 2024 09:37:45 GMT
• Title: Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Authors: Huangjun Zhu, Yunting Li, and Tianyi Chen
• Abstract summary: We propose a recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. We derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma and quantum union bound. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.
• Score: 28.03059224016627
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a simple, but powerful recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. Moreover, we derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma (with improvement) and quantum union bound. Notably, the number of samples required does not increase with the system size when the underlying Hamiltonian is local and gapped, which is the case of most interest. As an application, we propose a general approach for verifying Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local spin measurements, which requires only a constant number of samples for AKLT states defined on various lattices. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.

Related papers

• Tower of Structured Excited States from Measurements [0.07673339435080445]
  We introduce a log-depth protocol leveraging quantum phase estimation to measure a global observable. We demonstrate its capability to prepare towers of structured excited states that are useful in quantum metrology. Our results expand the utility of measurement-based approaches to accessing highly entangled states in quantum many-body systems.
  arXiv  Detail & Related papers  (2024-11-26T01:07:46Z)
• Bounding the Sample Fluctuation for Pure States Certification with Local Random Measurement [4.923287660970805]
  Recent advancements in randomized measurement techniques have provided fresh insights in this area. We investigate the fundamental properties of schemes that certify pure quantum states through random local Haar measurements. Our results unveil the intrinsic interplay between operator complexity and the efficiency of quantum algorithms, serving as an obstacle to local certification of pure states with long-range entanglement.
  arXiv  Detail & Related papers  (2024-10-22T02:26:44Z)
• Arbitrary Ground State Observables from Quantum Computed Moments [0.0]
  We extend the quantum computed moments (QCM) method to estimate arbitrary ground state observables of quantum systems. We present preliminary results of using QCM to determine the ground state magnetisation and spin-spin correlations of the Heisenberg model.
  arXiv  Detail & Related papers  (2023-12-12T04:29:43Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Detection of Beyond-Quantum Non-locality based on Standard Local Quantum Observables [46.03321798937856]
  We show that device independent detection cannot distinguish beyond-quantum non-local states from standard quantum states. This paper gives a device dependent detection based on local observables to distinguish any beyond-quantum non-local state from all standard quantum states.
  arXiv  Detail & Related papers  (2023-01-10T20:19:34Z)
• The power of noisy quantum states and the advantage of resource dilution [62.997667081978825]
  Entanglement distillation allows to convert noisy quantum states into singlets. We show that entanglement dilution can increase the resilience of shared quantum states to local noise.
  arXiv  Detail & Related papers  (2022-10-25T17:39:29Z)
• Scalable approach to many-body localization via quantum data [69.3939291118954]
  Many-body localization is a notoriously difficult phenomenon from quantum many-body physics. We propose a flexible neural network based learning approach that circumvents any computationally expensive step. Our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.
  arXiv  Detail & Related papers  (2022-02-17T19:00:09Z)
• Experimental SWAP test of infinite dimensional quantum states [0.0]
  SWAP test measures the overlap of two motional states in a system of trapped $171mathrmYb+$ ions. We report the overlap measurement of a variety of quantum states: Fock states, coherent states, squeezed vacuum states, and cat states.
  arXiv  Detail & Related papers  (2021-03-18T12:43:12Z)
• Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices [68.8204255655161]
  Purifying entanglement resources after their imperfect generation is an indispensable step towards using them in quantum architectures. Here we depart from the typical purification paradigm for multipartite states explored in the last twenty years. We find that smaller sacrificial' states, like Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states.
  arXiv  Detail & Related papers  (2020-11-23T19:00:00Z)
• Sample-efficient learning of quantum many-body systems [17.396274240172122]
  We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs state. We give the first sample-efficient algorithm for the quantum Hamiltonian learning problem.
  arXiv  Detail & Related papers  (2020-04-15T18:01:59Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.