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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240618T150000
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URL:https://uwaterloo.ca/institute-for-quantum-computing/events/circuit-ham
 iltonian-tensor-networks-and-fault-tolerance
LOCATION:QNC - Quantum Nano Centre 200 University Avenue West 1201 + ZOOM W
 aterloo ON N2L 3G1 Canada
SUMMARY:Circuit-to-Hamiltonian from tensor networks and fault tolerance
CLASS:PUBLIC
DESCRIPTION:CS MATH SEMINAR - QUYNH NGUYEN\, HARVARD UNIVERSITY\n\nQuantum-
 Nano Centre\, 200 University Ave West\, Room QNC 1201 + ZOOM\nWaterloo\, O
 N CA N2L 3G1\n\nWe define a map from an arbitrary quantum circuit to a loc
 al\nHamiltonian whose ground state encodes the quantum computation. All\np
 revious maps relied on the Feynman-Kitaev construction\, which\nintroduces
  an ancillary ‘clock register’ to track the\ncomputational steps. Our 
 construction\, on the other hand\, relies on\ninjective tensor networks wi
 th associated parent Hamiltonians\,\navoiding the introduction of a clock 
 register. This comes at the cost\nof the ground state containing only a no
 isy version of the quantum\ncomputation\, with independent stochastic nois
 e. We can remedy this -\nmaking our construction robust - by using quantum
  fault tolerance. In\naddition to the stochastic noise\, we show that any 
 state with energy\ndensity exponentially small in the circuit depth encode
 s a noisy\nversion of the quantum computation with adversarial noise. We a
 lso\nshow that any ‘combinatorial state’ with energy density\npolynomi
 ally small in depth encodes the quantum computation with\nadversarial nois
 e. This serves as evidence that any state with energy\ndensity polynomiall
 y small in depth has a similar property. As an\napplication\, we give a ne
 w proof of the QMA-completeness of the local\nHamiltonian problem (with lo
 garithmic locality) and show that\ncontracting injective tensor networks t
 o additive error is BQP- hard.\nWe also discuss the implication of our con
 struction to the quantum PCP\nconjecture\, combining with an observation t
 hat QMA verification can be\ndone in logarithmic depth.\n\nBased on joint 
 work with Anurag Anshu and Nikolas P. Breuckmann.\n(https://arxiv.org/abs/
 2309.16475)
DTSTAMP:20260425T074958Z
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