Adaptive estimation of quantum observables

Abstract

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable, and determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications.

arXiv comment10+14 pages, 6 figures, comments welcome

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• Simulating 2D lattice gauge theories on a qudit quantum computer
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Dual frame optimization for informationally complete quantum measurements
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
• Hardware-Tailored Diagonalization Circuits
• Measurement-based infused circuits for variational quantum eigensolvers
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Ground state-based quantum feature maps
• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers
• Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation
• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information
• Active Learning for Quantum Mechanical Measurements
• Improving shadow estimation with locally-optimal dual frames
• Resource-Optimized Grouping Shadow for Efficient Energy Estimation
• Accelerating Fermionic System Simulation on Quantum Computers