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The Complexity of Simulating Local Measurements on Quantum Systems Gharibian, Sevag Yirka, Justin Complexity theory Quantum Merlin Arthur (QMA) local Hamiltonian local measurement spectral gap An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians. Recently, Ambainis defined the complexity class P^QMA[log], and motivated its study by showing that the physical task of estimating the expectation value of a local observable against the ground state of a local Hamiltonian is P^QMA[log]-complete. In this paper, we continue the study of P^QMA[log], obtaining the following results. The P^QMA[log]-completeness result of Ambainis requires O(log n)-local observ- ables and Hamiltonians. We show that simulating even a single qubit measurement on ground states of 5-local Hamiltonians is P^QMA[log]-complete, resolving an open question of Ambainis. We formalize the complexity theoretic study of estimating two-point correlation functions against ground states, and show that this task is similarly P^QMA[log]-complete. P^QMA[log] is thought of as "slightly harder" than QMA. We justify this formally by exploiting the hierarchical voting technique of Beigel, Hemachandra, and Wechsung to show P^QMA[log] \subseteq PP. This improves the containment QMA \subseteq PP from Kitaev and Watrous. A central theme of this work is the subtlety involved in the study of oracle classes in which the oracle solves a promise problem. In this vein, we identify a flaw in Ambainis' prior work regarding a P^UQMA[log]-hardness proof for estimating spectral gaps of local Hamiltonians. By introducing a "query validation" technique, we build on his prior work to obtain P^UQMA[log]-hardness for estimating spectral gaps under polynomial-time Turing reductions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sevag Gharibian and Justin Yirka 2018 Is Part Of LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2017.2 urn:nbn:de:0030-drops-85776 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.2 eng https://creativecommons.org/licenses/by/3.0/legalcode