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• W4330335310 abstract "We introduce magic measures to quantify the nonstabilizerness of multiqubit quantum gates and establish lower bounds on the $T$ count for fault-tolerant quantum computation. First, we introduce the stabilizer nullity of multi-qubit unitary, which is based on the subgroup of the quotient Pauli group associated with the unitary. This unitary stabilizer nullity extends the state-stabilizer nullity by Beverland et al. to a dynamic version. In particular, we show this nonstabilizerness measure has desirable properties such as subadditivity under composition and additivity under tensor product. Second, we prove that a given unitary's stabilizer nullity is a lower bound for the $T$ count, utilizing the above properties in gate synthesis. Third, we compare the state- and the unitary-stabilizer nullity, proving that the lower bounds for the $T$ count obtained by the unitary-stabilizer nullity are never less than the state-stabilizer nullity. Moreover, we show an explicit $n$-qubit unitary family of unitary-stabilizer nullity $2n$, which implies that its $T$ count is at least $2n$. This gives an example where the bounds derived by the unitary-stabilizer nullity strictly outperform the state-stabilizer nullity by a factor of $2$. We finally showcase the advantages of unitary-stabilizer nullity in estimating the $T$ count of quantum gates with interests." @default.
• W4330335310 created "2023-03-22" @default.
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• W4330335310 date "2023-03-15" @default.
• W4330335310 modified "2023-09-30" @default.
• W4330335310 title "Lower Bound for the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll><mml:mi>T</mml:mi></mml:math> Count Via Unitary Stabilizer Nullity" @default.
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• W4330335310 doi "https://doi.org/10.1103/physrevapplied.19.034052" @default.
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