Improving shadow estimation with locally-optimal dual frames

Abstract

Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a variation of the classical shadows protocol in which the measurements are kept local while allowing the resulting classical shadows themselves to be correlated. By constructing locally optimal shadows, we obtain unbiased estimators that are competitive with state-of-the-art methods in terms of measurement overhead, while requiring only single-qubit measurements and allowing for the estimation of any observable in pure post-processing, reducing estimation errors by orders of magnitude over standard classical shadows. We validate our approach through numerical experiments on molecular Hamiltonians with up to 40 qubits consistently observing significant reductions in estimation errors, including for estimations of multiple chemically relevant observables simultaneously.

21 pages, 11 figures

References in corpus (30)

• From Louvain to Leiden: guaranteeing well-connected communities
• The density-matrix renormalization group in the age of matrix product states
• Quantum Simulation
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Predicting Many Properties of a Quantum System from Very Few Measurements
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Reconstructing quantum states with generative models
• Tight informationally complete quantum measurements
• Efficient estimation of Pauli observables by derandomization
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Informationally complete measurements and groups representation
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Semidefinite Programming in Quantum Information Science
• Quantum state estimation with informationally overcomplete measurements
• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Optimal data processing for quantum measurements
• Adaptive estimation of quantum observables
• Uncertainty Relations for Positive Operator Valued Measures
• Estimating expectation values using approximate quantum states
• Shadow tomography on general measurement frames
• Dual frame optimization for informationally complete quantum measurements
• Enhanced observable estimation through classical optimization of informationally over-complete measurement data -- beyond classical shadows
• Classical shadows based on locally-entangled measurements
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
• Self-consistent quantum measurement tomography based on semidefinite programming
• Optimising quantum tomography via shadow inversion
• Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation
• Low variance estimations of many observables with tensor networks and informationally-complete measurements