The separation is obtained through a one-bit filtered-parity construction and a space-sensitive quantum lower bound based on compressed-oracle capacity and a new parity-to-capacity inequality, which may be of independent interest.
Abstract
Hao, Huang, and Liu (STOC'26) recently showed that optimal quantum query complexity may require large workspace even for short-output problems, and asked whether a quantum query advantage over classical computation can itself require space. We resolve this question by exhibiting an explicit total Boolean function with quantum query complexity $Q=\widetilde{\Theta}(M)$, and randomized query complexity $R=\Theta(M^{21/20})$, whereas, for every fixed $0<\eta<1/100$ and $S\le O(M^{1/100-\eta})$, its $S$-space quantum query complexity satisfies $Q_S=\omega(M^{21/20})$. Consequently, $$ Q<R<Q_S, $$ so the unrestricted quantum query advantage disappears under sufficiently small workspace. The separation is obtained through a one-bit filtered-parity construction and a space-sensitive quantum lower bound based on compressed-oracle capacity and a new parity-to-capacity inequality, which may be of independent interest.
This work settles this conjecture for parallel quantum algorithms, showing that every $t-query $d-round quantum algorithm can be simulated on most inputs with $t^{O(d^2)}$ classical queries, suggesting that for unstructured problems, superpolynomial speedups would require quantum circuits of superconstant depth, and ex...
Guy Blanc, Jordan Docter, Carmen Strassle et al.· 2 citations· ⚡1
We prove the first non-trivial upper bound for the quantum query complexity of Boolean Matrix Product Verification ($\mathsf{BMPV}$), answering a longstanding open question in quantum query complexity. For $n\times n$ matrices, our upper bound is $\widetilde O(n^{17/12})$, improving on the standard $O(n^{3/2})$ bound o...
Amin Shiraz Gilani, François Le Gall, Xing-Yu Zhou· 0 citations
We study the quantum query complexity of computing a semigroup product $x_1\cdots x_n$, when one query reveals one input element and the multiplication table is given. For a finite aperiodic semigroup of size $N-1$, the argument of Aaronson, Grier, and Schaeffer gives an upper bound of $\sqrt n\,(N\log(nN+2))^{O(N)}$ q...
Given oracle access to an unknown unitary $U=e^{iH}$ , the fractional query problem asks how many queries are required to implement a noninteger power $U^t=e^{itH}$, $0<t<1$, when the spectrum is separated from the branch cut by a gap $\delta$. Quantum singular value transformation gives an upper bound of $O\!\left(\fr...
A. Liu, Adam Wesolowski, Jayne Thompson et al.· 0 citations
We study hybrid quantum-classical algorithms in the query model. The computation consists of quantum subroutines that make at most $q$ oracle queries; between subroutines, all qubits are measured and discarded. We prove matching upper and lower bounds for several problems in this model: (i) (Unbiased) Phase estimation...
A. Ambainis, A. Gilyén, M. Kokainis· 1 citation· ⚡1
Quantum query complexity enjoys a variety of pleasing joint computation properties: for example, a composition theorem asserting $Q(f\circ g)=\Theta(Q(f)Q(g))$ for all Boolean functions $f$ and $g$; a direct sum theorem asserting that computing $k$ copies of a function (or search problem) costs $\Omega(k)$ times as muc...
S. Ben-David, M. H. Ebtehaj· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
