Noise in Quantum and Classical Computation & Non-locality

Quantum computers seem to have capabilities which go beyond those of classical computers. A particular example which is important for cryptography is that quantum computers are able to factor numbers much faster than what seems possible on classical machines. In order to actually build quantum computers it is necessary to build sufficiently accurate hardware, which is a big challenge. In part 1 of this thesis we prove lower bounds on the accuracy of the hardware needed to do quantum computation. We also present a similar result for classical computers. One resource that quantum computers have but classical computers do not have is entanglement. In Part 2 of this thesis we study certain general aspects of entanglement in terms of quantum XOR games and non-locality

On small hard leaf languages

Abstract. This paper deals with balanced leaf language complexity classes, introduced independently in [1] and [14]. We propose the seed concept for leaf languages, which allows us to give “short ” representations for leaf words. We then use seeds to show that leaf languages A with NP ⊆ BLeaf P (A) cannot be polylog-sparse (i.e. censusA ∈ O(log O(1))), unless P H collapses. We also generalize balanced ≤ P,bit m-reductions, which were introduced in [6], to other bit-reductions, for example (balanced) truth-table- and Turing-bit-reductions. Then, similarly to above, we prove that NP and Σ P 2 cannot have polylog-sparse hard sets under those balanced truthtable-and Turing-bit-reductions, if the polynomial-time hierarchy is infinite