The Gottesman-Knill theorem, which says that a stabilizer circuit, a quantum circuit consisting solely of controlled-NOT, Hadamard, and phase gates can be simulated efficiently on a classical computer, is improved in several directions.Expand

A model of computation in which identical photons are generated, sent through a linear-optical network, then nonadaptively measured to count the number of photons in each mode is defined, giving new evidence that quantum computers cannot be efficiently simulated by classical computers.Expand

It is shown that several simple changes to the axioms of quantum mechanics would let us solve PP-complete problems efficiently, or probabilistic polynomial-time, and implies, as an easy corollary, a celebrated theorem of Beigel, Reingold and Spielman that PP is closed under intersection.Expand

These lower bounds provide evidence for the existence of cryptographic primitives that are immune to quantum cryptanalysis, and implies a quantum lower bound of Ω(<i>n</i><sup>2/3</sup>) queries for the element distinctness problem, which is to determine whether <i*n> integers are all distinct.Expand

This article systematically goes through basic results and open problems in complexity theory to delineate the power of the new algebrization barrier, and shows 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

An 0(/spl radic/n)-qubit communication protocol for the disjointness problem is given, which improves an upper bound of Hoyer and de Wolf and matches a lower bound of Razborov.Expand

This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense and has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.Expand

This work shows a lower bound on the number of queries needed by a quantum computer to solve the problem of finding a local minimum of a black-box function and gives the first nontrivial lower bounds for finding local minima on grids of constant dimension d.Expand

This fascinating book takes readers on a tour through some of the deepest ideas of maths, computer science and physics, beginning in antiquity with Democritus and progressing through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics.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