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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/hamiltonian
 s-whose-low-energy-states-require-t-gates
LOCATION:QNC - Quantum Nano Centre 200 University Avenue West QNC 1201 Wate
 rloo ON N2L 3G1 Canada
SUMMARY:Hamiltonians whose low-energy states require Ω(n) T gates
CLASS:PUBLIC
DESCRIPTION:CS/MATH SEMINAR - NOLAN COBLE - UNIVERSITY OF MARYLAND\, COLLEG
 E PARK\n\n200 University Ave. Waterloo ON. QNC 1201 + ZOOM\n\nThe recent r
 esolution of the NLTS Conjecture [ABN22] establishes a\nprerequisite to th
 e Quantum PCP (QPCP) Conjecture through a novel use\nof newly-constructed 
 QLDPC codes [LZ22]. Even with NLTS now solved\,\nthere remain many indepen
 dent and unresolved prerequisites to the QPCP\nConjecture\, such as the NL
 SS Conjecture of [GL22]. In this talk we\nfocus on a specific and natural 
 prerequisite to both NLSS and the QPCP\nConjecture\, namely\, the existenc
 e of local Hamiltonians whose\nlow-energy states all require ω(log n) T g
 ates to prepare. In fact\,\nwe will show a stronger result which is not ne
 cessarily implied by\neither conjecture: we construct local Hamiltonians w
 hose low-energy\nstates require Ω(n) T gates. We further show that our pr
 ocedure can\nbe applied to the NLTS Hamiltonians of [ABN22] to yield local
 \nHamiltonians whose low-energy states require both Ω(log n)-depth and\n
 Ω(n) T gates to prepare. This result represents a significant\nimprovemen
 t over [CCNN23] where we used a different technique to give\nan energy bou
 nd which only distinguishes between stabilizer states and\nstates which re
 quire a non-zero number of T gates.
DTSTAMP:20260425T095901Z
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