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Computing with highly mixed states

Andris Ambainis·Leonard J. Schulman·Umesh Vazirani
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Abstract

We consider quantum computing in the k-qubit model where the starting state of a quantum computer consists of k qubits in a pure state and n-k qubits in a maximally mixed state. We ask the following question: is there a general method for simulating an arbitrary m-qubit pure state quantum computation by a quantum computation in the k-qubit model? We show that, under certain constraints, this is impossible, unless m=O(k+ log n).

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Andris Ambainis, Leonard J. Schulman, Umesh Vazirani. 2000-03-29. Computing with highly mixed states. https://arxiv.org/abs/quant-ph/0003136

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