Approximating Unitary Preparations of Orthogonal Black Box States

Joshua Alan Cook

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arXiv · 1906.10495

Approximating Unitary Preparations of Orthogonal Black Box States

Joshua Alan Cook

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Abstract

In this paper, I take a step toward answering the following question: for m different small circuits that compute m orthogonal n qubit states, is there a small circuit that will map m computational basis states to these m states without any input leaving any auxiliary bits changed. While this may seem simple, the constraint that auxiliary bits always be returned to 0 on any input (even ones besides the m we care about) led me to use sophisticated techniques. I give an approximation of such a unitary in the m = 2 case that has size polynomial in the approximation error, and the number of qubits n.

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Joshua Alan Cook. 2019-06-23. Approximating Unitary Preparations of Orthogonal Black Box States. https://arxiv.org/abs/1906.10495

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