Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Memory Compression with Quantum Random-Access Gates   In the classical RAM, we have the following useful property. If we have an
algorithm that uses $M$ memory cells throughout its execution, and in addition
is sparse, in the sense that, at any point in time, only $m$ out of $M$ cells
will be non-zero, then we may "compress" it into another algorithm which uses
only $m \log M$ memory and runs in almost the same time. We may do so by
simulating the memory using either a hash table, or a self-balancing tree.
  We show an analogous result for quantum algorithms equipped with quantum
random-access gates. If we have a quantum algorithm that runs in time $T$ and
uses $M$ qubits, such that the state of the memory, at any time step, is
supported on computational-basis vectors of Hamming weight at most $m$, then it
can be simulated by another algorithm which uses only $O(m \log M)$ memory, and
runs in time $\tilde O(T)$.
  We show how this theorem can be used, in a black-box way, to simplify the
presentation in several papers. Broadly speaking, when there exists a need for
a space-efficient history-independent quantum data-structure, it is often
possible to construct a space-inefficient, yet sparse, quantum data structure,
and then appeal to our main theorem. This results in simpler and shorter
arguments.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph