On the Power of Quantum Computation: Oracles
Sammanfattning: Quantum computation solve some computational problems faster than the best-known alternative in classical computation. The evidence for this consists of examples where a quantum algorithm outperforms the best-known classical algorithm. A large body of these examples relies on oracle query complexity, where the performance (complexity) of the algorithms is measured by the number of times they need to access an oracle. Here, an oracle is usually considered to be a black box that computes a specific function at unit cost.However, the quantum algorithm is given access to an oracle with more structure than the classical algorithm. This thesis argues that the two oracles are so vastly different that comparing quantum and classical query complexity should not be considered evidence, but merely hints for a quantum advantage.The approach used is based on a model that can be seen as an approximation of quantum theory, but can be efficiently simulated on a classical computer. This model solves several oracular problems with the same performance as their quantum counterparts, showing that there is no genuine quantum advantage for these problems. This approach also clarifies the assumptions made in quantum computation, and which properties that can be seen as resources in these algorithms.
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