Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping

• URL: http://arxiv.org/abs/2301.03385v2
• Date: Mon, 11 Sep 2023 15:04:19 GMT
• Title: Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
• Authors: Alexander Gresch, Martin Kliesch
• Abstract summary: 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.
• Score: 55.47824411563162
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish new tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name suggests, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping outperforms state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians.

Related papers

• Resource-Optimized Grouping Shadow for Efficient Energy Estimation [2.5636932629466735]
  We introduce a Resource-d Grouping Shadow (ROGS) algorithm, which optimally allocates measurement resources by minimizing the estimation error bound through a novel overlapped grouping strategy and convex optimization. Our numerical experiments demonstrate that ROGS requires significantly fewer quantum circuits for accurate estimation accuracy compared to existing methods given a fixed measurement budget, addressing a major cost factor for compiling and executing circuits on quantum computers.
  arXiv  Detail & Related papers  (2024-06-25T03:37:35Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient [4.490097334898205]
  We propose an efficient strategy combining maximum likelihood estimation, gradient descent, and quantum many-body algorithms. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges.
  arXiv  Detail & Related papers  (2022-12-28T06:54:15Z)
• Critical quantum metrology assisted by real-time feedback control [0.0]
  We first derive a no-go result stating that any non-adaptive measurement strategy will fail to exploit quantum critical enhancement. We then consider different adaptive strategies that can overcome this no-go result. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot noise scaling.
  arXiv  Detail & Related papers  (2022-11-14T19:06:14Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation [50.591267188664666]
  Quantum chemistry and materials is one of the most promising applications of quantum computing. Much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them.
  arXiv  Detail & Related papers  (2022-03-14T16:51:36Z)
• 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)
• Hardware-efficient entangled measurements for variational quantum algorithms [0.0]
  Variational algorithms can be used to solve practical problems using noisy intermediate-scale quantum (NISQ) devices. We propose hardware-efficient entangled measurements (HEEM), that is, measurements that permit only between physically connected qubits. We show that this strategy enhances the evaluation of molecular Hamiltonians in NISQ devices by reducing the number of circuits required.
  arXiv  Detail & Related papers  (2022-02-14T19:00:16Z)
• Overlapped grouping measurement: A unified framework for measuring quantum states [2.1166716158060104]
  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.
  arXiv  Detail & Related papers  (2021-05-27T12:38:18Z)
• 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.