Quantum random sampling is the leading proposal for demonstrating a computational
advantage of quantum computers over classical computers. Recently the first large-scale …

Key static and dynamic properties of matter—from creation in the Big Bang to evolution into
subatomic and astrophysical environments—arise from the underlying fundamental …

Quantum algorithms offer significant speed-ups over their classical counterparts for a variety
of problems. The strongest arguments for this advantage are borne by algorithms for …

This chapter describes the possibility of simulating physics in the classical approximation, a
thing which is usually described by local differential equations. But the physical world is …

A digital computer is generally believed to be an efficient universal computing device; that is,
it is believed to be able to simulate any physical computing device with an increase in …

For many decades, the proponents of artificial intelligence'have maintained that computers
will soon be able to do everything that a human can do. In his bestselling work of popular …

We show that a set of gates that consists of all one-bit quantum gates [U (2)] and the two-bit
exclusive-O R gate [that maps Boolean values (x, y) to (x, x⊕ y)] is universal in the sense …

Neural networks are a computing paradigm that is finding increasing attention among
computer scientists. In this book, theoretical laws and models previously scattered in the …

Just as the theory of computability had its foundations in the Church-Turing thesis,
computational complexity theory rests upon a modern strengthening of this thesis, which …

Computers may be thought of as engines for transforming free energy into waste heat and
mathematical work. Existing electronic computers dissipate energy vastly in excess of the …