Quantum

Quantum Readout Complexity for Normalized Linear Functionals

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 08/10/2026, 04:13:24 UTC.

Briefings

A 2026 arXiv preprint investigates the computational complexity of estimating an L1-linear functional from a solution encoded in an L2-normalized quantum state. The study identifies a target-dependent susceptibility chi_phi that determines the optimal number of solution state copies required. For a fixed reference state and error tolerance, the optimal copy count scales as Theta(chi_0 * epsilon^-2 * log(1/beta)), where epsilon is the error tolerance and beta is the failure probability. The authors demonstrate that two fixed single-copy measurements achieve this optimal rate. The analysis further explores how the baseline complexity changes when the interface retains classical information, uses adaptive allocation, or restricts the solution family.

Key points

• The study identifies a target-dependent susceptibility chi_phi that governs the number of solution state copies needed to estimate an L1-linear observable from an L2-normalized quantum state.
• The optimal number of copies scales as Theta(chi_0 * epsilon^-2 * log(1/beta)) for a fixed reference state and error tolerance.

Context and limitations

The analysis is limited to the specific interface conditions described in the abstract, including fixed single-copy measurements and the restricted solution family. The results are based on theoretical analysis from an arXiv preprint and do not include experimental validation or empirical data from the full study.

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