Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information
arXiv:2502.01730 · doi:10.1021/acs.jctc.5c00370
Abstract
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy estimates with error bounds, as captured by guarantees on the problem's sampling complexity. In particular, when limited to Pauli basis measurements, the smallest sampling complexity guarantee comes from a simple single-shot estimator via a straightforward argument based on Hoeffding's inequality. In this work, we construct an adaptive estimator using the state's actual variance. Technically, our estimation method is based on the Empirical Bernstein stopping (EBS) algorithm and grouping schemes, and we provide a rigorous tail bound, which leverages the state's empirical variance. In a numerical benchmark of estimating ground-state energies of several Hamiltonians, we demonstrate that EBS consistently improves upon elementary readout guarantees up to one order of magnitude.
7 + 2 pages, 2 + 1 figures and 3 pseudocodes
References in corpus (25)
- A variational eigenvalue solver on a quantum processor
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- The theory of variational hybrid quantum-classical algorithms
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Scalable Quantum Simulation of Molecular Energies
- Elucidating Reaction Mechanisms on Quantum Computers
- Hartree-Fock on a superconducting qubit quantum computer
- Towards Practical Quantum Variational Algorithms
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Quantum chemistry calculations on a trapped-ion quantum simulator
- The randomized measurement toolbox
- Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
- Quantum computing enhanced computational catalysis
- Efficient estimation of Pauli observables by derandomization
- Emerging quantum computing algorithms for quantum chemistry
- Efficient quantum measurement of Pauli operators in the presence of finite sampling error
- Qibo: a framework for quantum simulation with hardware acceleration
- Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
- Measurement reduction in variational quantum algorithms
- Prospects of Quantum Computing for Molecular Sciences
- Overlapped grouping measurement: A unified framework for measuring quantum states
- Adaptive estimation of quantum observables
- Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
- Modeling singlet fission on a quantum computer