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SUMMARY:Constant-depth circuits for Uniformly Controlled Gates and Boolean
  functions with application to quantum memory circuits - Alessandro Luongo
 \, CQT\, National University of Singapore
DTSTART:20231116T141500Z
DTEND:20231116T153000Z
UID:TALK208534@talks.cam.ac.uk
CONTACT:Subhayan Roy Moulik
DESCRIPTION:We explore the power of the unbounded Fan-Out gate and the Glo
 bal Tunable gates generated by Ising-type Hamiltonians in constructing con
 stant-depth quantum circuits\, with particular attention to quantum memory
  devices. We propose two types of constant-depth constructions for impleme
 nting Uniformly Controlled Gates. These gates include the Fan-In gates (a 
 generalization of the oracles for Boolean functions). The first of our con
 structions is based on computing the one-hot encoding of the input registe
 r\, while the second is based on Boolean analysis and exploits different r
 epresentations of f such as its Fourier expansion. Via these constructions
 \, we obtain constant-depth circuits for the quantum counterparts of read-
 only and read-write memory devices - Quantum Random Access Memory (QRAM) a
 nd Quantum Random Access Gate (QRAG) - of memory size n. The implementatio
 n based on one-hot encoding requires either O(nlogn(loglogn)) ancillae and
  O(nlogn) Fan-Out gates or O(nlogn) ancillae and 6 Global Tunable gates. O
 n the other hand\, the implementation based on Boolean analysis requires o
 nly 2 Global Tunable gates at the expense of O(n^2) ancillae.
LOCATION:MR2
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