Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Role of Multiplicative Complexity in Compiling Low T-count Oracle
  Circuits   We present a constructive method to create quantum circuits that implement
oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus
f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low
$T$-count. In our method $f$ is given as a 2-regular Boolean logic network over
the gate basis $\{\land, \oplus, 1\}$. Our construction leads to circuits with
a $T$-count that is at most four times the number of AND nodes in the network.
In addition, we propose a SAT-based method that allows us to trade qubits for
$T$ gates, and explore the space/complexity trade-off of quantum circuits.
  Our constructive method suggests a new upper bound for the number of $T$
gates and ancilla qubits based on the multiplicative complexity $c_\land(f)$ of
the oracle function $f$, which is the minimum number of AND gates that is
required to realize $f$ over the gate basis $\{\land, \oplus, 1\}$. There
exists a quantum circuit computing $f$ with at most $4 c_\land(f)$ $T$ gates
using $k = c_\land(f)$ ancillae. Results known for the multiplicative
complexity of Boolean functions can be transferred.
  We verify our method by comparing it to different state-of-the-art compilers.
Finally, we present our synthesis results for Boolean functions used in quantum
cryptoanalysis.

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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci