Quantum-inspired estimators for F_alpha(P) and F_alpha(rho) achieve optimal sample complexity n ~ alpha and minimax MSE rate alpha/n, improving prior O(alpha^2) bounds.
Huggins, Sam McArdle, Thomas E
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CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
Proves finite-shot mean-squared-error laws for virtual distillation and symmetry verification that define certified operating windows and a selection trichotomy for their comparison.
Gaussian randomized rounding on two-qubit marginals of depth-D circuits with local depolarizing noise p yields samples whose expected Max-Cut cost matches the noisy quantum device up to an approximation ratio of 1-O[(1-p)^D].
SNT merges SV and PEC for subspace-tailored error mitigation in Trotterized FHM simulations, mapping out optimal combinations by hardware quality and shot budget while quantifying when noisy devices could surpass classical methods.
citing papers explorer
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Towards Minimax Estimation of High-Order Functionals by Quantum Arguments
Quantum-inspired estimators for F_alpha(P) and F_alpha(rho) achieve optimal sample complexity n ~ alpha and minimax MSE rate alpha/n, improving prior O(alpha^2) bounds.
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Quantum Nonlinear Properties from a Single Measurement Setting
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
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Exponential speedups in fault-tolerant processing of quantum experiments
Embedding experimental quantum states into high-distance codes enables exponential speedups in fault-tolerant shadow tomography and cubic observable estimation over unencoded adaptive strategies.
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Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification
Proves finite-shot mean-squared-error laws for virtual distillation and symmetry verification that define certified operating windows and a selection trichotomy for their comparison.
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Sampling (noisy) quantum circuits through randomized rounding
Gaussian randomized rounding on two-qubit marginals of depth-D circuits with local depolarizing noise p yields samples whose expected Max-Cut cost matches the noisy quantum device up to an approximation ratio of 1-O[(1-p)^D].
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Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
SNT merges SV and PEC for subspace-tailored error mitigation in Trotterized FHM simulations, mapping out optimal combinations by hardware quality and shot budget while quantifying when noisy devices could surpass classical methods.