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A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.
The first separation between quantum polynomial time and classical bounded-error polynomial time was due to Bernstein and Vazirani in 1993. They first showed a O(1) vs. Omega(n) quantum-classical oracle separation based on the quantum Hadamard transf
We consider the hypothesis that quantum mechanics is not fundamental, but instead emerges from a theory with less computational power, such as classical mechanics. This hypothesis makes the prediction that quantum computers will not be capable of suf
We study the explicit relation between violation of Bell inequalities and bipartite distillability of multi-qubit states. It has been shown that even though for $Nge 8$ there exist $N$-qubit bound entangled states which violates a Bell inequality [Ph
We introduce the multipartite collision model, defined in terms of elementary interactions between subsystems and ancillae, and show that it can simulate the Markovian dynamics of any multipartite open quantum system. We develop a method to estimate
The goal of quantum circuit transformation is to map a logical circuit to a physical device by inserting additional gates as few as possible in an acceptable amount of time. We present an effective approach called TSA to construct the mapping. It con