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SUMMARY:Quantum circuit lower bounds with entangled inputs - Natalie Parha
 m (Columbia University)
DTSTART:20241210T140000Z
DTEND:20241210T150000Z
UID:TALK225175@talks.cam.ac.uk
CONTACT:Tom Gur
DESCRIPTION:Abstract:\n\nProving circuit lower bounds for preparing explic
 it quantum states has long relied on the lightcone argument\, which restri
 cts correlations between qubits based on the circuit depth. However\, this
  approach assumes that the input state is a product state\, such as $\\ket
 {0}^{\\otimes n}$. In this talk\, I will introduce new techniques to prove
  circuit lower bounds for state preparation even when the initial state is
  entangled. \n\nThese techniques allow us to prove logarithmic depth circu
 it lower bounds even when starting with any stabilizer state. This include
 s all stabilizer quantum error correcting code states\, many of which have
  topological order. Circuit lower bounds of this type have interesting mot
 ivations from both Hamiltonian complexity and condensed matter physics.\n\
 nWe will discuss two different new lower bound techniques: one based on qu
 antum mutual information properties of the state\, and the other for state
 s that are locally unique and highly pairwise entangled. Time permitting\,
  I will also introduce a few more examples of state transformation problem
 s where these techniques can be used.\n\nThis talk is based on work soon t
 o be on arxiv.
LOCATION:Computer Laboratory\, William Gates Building\, Room FW26
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