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Fast amplification of QMA
Given a verifier circuit for a problem in QMA, we show how to exponentially amplifythe gap between its acceptance probabilities in the 'yes' and 'no' cases, with a methodthat is quadratically fasterExpand
Hamiltonian quantum cellular automata in one dimension
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of ten-dimensional qudits that makes it possible to realize universal quantum computing without any externalExpand
Quantum 3-SAT Is QMA1-Complete
  • D. Gosset, Daniel Nagaj
  • Mathematics, Computer Science
  • IEEE 54th Annual Symposium on Foundations of…
  • 1 February 2013
TLDR
It is proved that quantum 3-SAT is QMA1-hard, and therefore complete for this complexity class. Expand
Fast universal quantum computation with railroad-switch local Hamiltonians
We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors and the second one requires onlyExpand
Criticality without frustration for quantum spin-1 chains.
TLDR
This work proposes the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. Expand
Achieving perfect completeness in classical-witness quantum merlin-arthur proof systems
This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard andExpand
Unfrustrated qudit chains and their ground states
We investigate chains of d-dimensional quantum spins (qudits) on a line with generic nearest-neighbor interactions without translational invariance. We find the conditions under which these systemsExpand
Quantum speedup by quantum annealing.
TLDR
The glued-trees problem is studied in the adiabatic model of quantum computing and an annealing schedule is provided to solve an oracular problem exponentially faster than classically possible even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. Expand
HOW TO MAKE THE QUANTUM ADIABATIC ALGORITHM FAIL
TLDR
It is shown that poor choices for the Hamiltonian can guarantee that the quantum adiabatic algorithm will not find the minimum if the run time grows more slowly than . Expand
Quantum algorithm for approximating partition functions
We achieve a quantum speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain methodExpand
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