"We demonstrate that the states of elementary quantum systems are capable of encoding mathematical axioms and show that quantum measurements are capable of revealing whether a given proposition is decidable or not within the axiomatic system."

If you have a quantum state of n qubits, does it act more like n classical bits, or does it act more like 2^n bits?

The process of self replication is not possible for quantum states, assuming either the linear structure of quantum theory, the principle of no signalling or conservation of entanglement is valid.

The first four axioms are consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory.

Bohm's interpretation of quantum mechanics tries to provide a local deterministic objective description that resolves many of the paradoxes of quantum mechanics, such as Schrödinger's cat, the measurement problem and the collapse of the wavefunction.

A result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state.

Web-based editor for setup, control and analysis of quantum computing simulation jobs.

"The vast majority of the infinite collection of programs that are written within these worlds will be buggy, ill-behaved, or even ill advised, resulting in worlds containing no self-aware-substructures at all, or perhaps even lawyers and politicians."

The experiment essentially involves looking at the Schroedinger's cat experiment from the point of view of the cat.

Explains Shor’s algorithm (a quantum algorithm for factoring) without using a single ket sign, or for that matter any math beyond arithmetic.

Introduces quantum computation from a theoretical computer science background. What are the origins of the quantum computational power, what are the limits?

How to teach mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.

If P!=NP (overwhelmingly likely) and if quantum computers can't solve NP problems in polynomal time (likely), NP-complete problems of sufficient largeness can never be solved by anything obeying the laws of physics. (Approximations are possible.)

It begins to look like randomness is a unifying principle. We not only see it in quantum mechanics and classical physics, but even in pure mathematics, in elementary number theory.

Shows that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed. Quantum computers can't solve NP-complete problems in polynomial time.

The Bekenstein bound imposes a limit on the entropy S or information that can be contained within a three-dimensional volume. (One reason why hypercomputing proposals fail.)

This course tries to connect quantum computing to the wider intellectual world: The measurement problem, computational complexity, cryptography, Gödel, Turing, Penrose, randomness, ...

Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let's try to generalize it so that the "probabilities" can be negative numbers.

Researchers explain how enzymes use quantum tunneling to speed up reactions.