2026-08-18T03:26:15Z https://drops.dagstuhl.de/oai

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Power of Uninitialized Qubits in Shallow Quantum Circuits Takahashi, Yasuhiro Tani, Seiichiro quantum circuit complexity shallow quantum circuit uninitialized qubit We study the computational power of shallow quantum circuits with O(log n) initialized and n^{O(1)} uninitialized ancillary qubits, where n is the input length and the initial state of the uninitialized ancillary qubits is arbitrary. First, we show that such a circuit can compute any symmetric function on n bits that is classically computable in polynomial time. Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n qubits. Since it seems unlikely that these tasks can be done with only O(log n) initialized ancillary qubits, our results give evidences that adding uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(log n) initialized ancillary qubits. Lastly, to understand the limitations of uninitialized ancillary qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on n bits. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yasuhiro Takahashi and Seiichiro Tani 2018 Is Part Of LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2018.57 urn:nbn:de:0030-drops-84907 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.57 eng https://creativecommons.org/licenses/by/3.0/legalcode