Papers › Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries
Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries
Priyanka Mukhopadhyay
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In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary multi-qubit unitaries. We analyse the channel representation of the generating set elements, with the help of which we infer |𝒥ₙᵀᵒᶠ|<|𝒥ₙᵀ|, where 𝒥ₙᵀᵒᶠ and 𝒥ₙᵀ are the set of unitaries exactly implementable by the Clifford+Toffoli and Clifford+T gate set, respectively. We develop Toffoli-count optimal synthesis algorithms for both approximately and exactly implementable multi-qubit unitaries. With the help of these we prove |𝒥ₙᵀᵒᶠ|=|𝒥ₙ^(CS)|, where 𝒥ₙ^(CS) is the set of unitaries exactly implementable by the Clifford+CS gate set.
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