Optimizing local Hamiltonians for the best metrological performance

• URL: http://arxiv.org/abs/2206.02820v1
• Date: Mon, 6 Jun 2022 18:01:03 GMT
• Title: Optimizing local Hamiltonians for the best metrological performance
• Authors: \'Arp\'ad Luk\'acs, R\'obert Tr\'enyi, Tam\'as V\'ertesi, G\'eza T\'oth
• Abstract summary: We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. We present the quantum Fisher information in a bilinear form and maximize it by iterating a see-saw. We consider a number of other problems in quantum information theory that can be solved in a similar manner.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable states the most from the point of view of quantum metrology. We show that this problem can be reduced to maximize the quantum Fisher information over a certain set of Hamiltonians. We present the quantum Fisher information in a bilinear form and maximize it by iterating a see-saw, in which each step is based on semidefinite programming. We also solve the problem with the method of moments that works very well for smaller systems. We consider a number of other problems in quantum information theory that can be solved in a similar manner. For instance, we determine the bound entangled quantum states that maximally violate the Computable Cross Norm-Realignment (CNNR) criterion.

Related papers

• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics [42.29248343585333]
  We benchmark quantum hardware and error mitigation techniques on up to 133 qubits. We show reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates. Results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning.
  arXiv  Detail & Related papers  (2024-04-11T18:00:05Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• Truncation technique for variational quantum eigensolver for Molecular Hamiltonians [0.0]
  variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for noisy quantum devices. We propose a physically intuitive truncation technique that starts the optimization procedure with a truncated Hamiltonian. This strategy allows us to reduce the required number of evaluations for the expectation value of Hamiltonian on a quantum computer.
  arXiv  Detail & Related papers  (2024-02-02T18:45:12Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• 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)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Iterative Quantum Assisted Eigensolver [0.0]
  We provide a hybrid quantum-classical algorithm for approximating the ground state of a Hamiltonian. Our algorithm builds on the powerful Krylov subspace method in a way that is suitable for current quantum computers.
  arXiv  Detail & Related papers  (2020-10-12T12:25:16Z)
• K-spin Hamiltonian for quantum-resolvable Markov decision processes [0.0]
  We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using quantum algorithms.
  arXiv  Detail & Related papers  (2020-04-13T16:15:25Z)
• Roadmap for quantum simulation of the fractional quantum Hall effect [0.0]
  A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron gas---cooled to absolute zero and pierced by a strong magnetic field---on a quantum computer.
  arXiv  Detail & Related papers  (2020-03-05T10:17:21Z)

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.