Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum advantage for computations with limited space   Quantum computations promise the ability to solve problems intractable in the
classical setting. Restricting the types of computations considered often
allows to establish a provable theoretical advantage by quantum computations,
and later demonstrate it experimentally. In this paper, we consider
space-restricted computations, where input is a read-only memory and only one
(qu)bit can be computed on. We show that $n$-bit symmetric Boolean functions
can be implemented exactly through the use of quantum signal processing as
restricted space quantum computations using $O(n^2)$ gates, but some of them
may only be evaluated with probability $1/2 + O(n/\sqrt{2}^n)$ by analogously
defined classical computations. We experimentally demonstrate computations of
$3$-, $4$-, $5$-, and $6$-bit symmetric Boolean functions by quantum circuits,
leveraging custom two-qubit gates, with algorithmic success probability
exceeding the best possible classically. This establishes and experimentally
verifies a different kind of quantum advantage -- one where quantum scrap space
is more valuable than analogous classical space -- and calls for an in-depth
exploration of space-time tradeoffs in quantum circuits.

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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con