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The computational complexity of linear optics
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. InExpand
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Improved Simulation of Stabilizer Circuits
TLDR
The Gottesman-Knill theorem says that a stabilizer circuit consisting solely of controlled-NOT (CNOT), Hadamard, and phase gates\char22{}can be simulated efficiently on a classical computer. Expand
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Quantum computing, postselection, and probabilistic polynomial-time
  • S. Aaronson
  • Mathematics, Computer Science
  • Proceedings of the Royal Society A: Mathematical…
  • 23 December 2004
TLDR
I study the class of problems efficiently solvable by a quantum computer, given the ability to ‘postselect’ on the outcomes of measurements. Expand
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Quantum lower bounds for the collision and the element distinctness problems
TLDR
We prove that any quantum algorithm for finding a collision in an <i>r</i>-to-one function must evaluate the function Ω((<i>n</i><sup>1/3</sup>) times, which matches an upper bound of Brassard, Høyer, and Tapp. Expand
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Algebrization: A New Barrier in Complexity Theory
TLDR
We show that almost all of the major open problems---including P versus NP, P versus RP, and NEXP versus P/poly---will require non-algebrizing techniques. Expand
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Quantum search of spatial regions
  • S. Aaronson, A. Ambainis
  • Mathematics, Computer Science
  • 44th Annual IEEE Symposium on Foundations of…
  • 9 March 2003
TLDR
A model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Expand
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Lower bounds for local search by quantum arguments
  • S. Aaronson
  • Mathematics, Computer Science
  • STOC '04
  • 21 July 2003
TLDR
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. Expand
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The learnability of quantum states
  • S. Aaronson
  • Computer Science, Physics
  • Proceedings of the Royal Society A: Mathematical…
  • 18 August 2006
TLDR
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits. Expand
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Quantum money from hidden subspaces
TLDR
We give the first private-key quantum money scheme that allows unlimited verifications and that remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank. Expand
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NP-complete Problems and Physical Reality
  • S. Aaronson
  • Physics, Computer Science
  • Electron. Colloquium Comput. Complex.
  • 1 February 2005
Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms,Expand
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