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. In… Expand

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

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

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

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

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

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

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