Quantum and Circuits

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1 \providecommand{\F}{\mathbb F}
2 \providecommand{\C}{\mathbb C}
3 \providecommand{\R}{\mathbb R}
4 \providecommand{\Z}{\mathbb Z}
5 \providecommand{\N}{\mathbb N}
6 \providecommand{\GL}{\operatorname{GL}}
7 \providecommand{\SL}{\operatorname{SL}}
8 \providecommand{\Sp}{\operatorname{Sp}}
9 \providecommand{\Egrp}{\operatorname{E}}
10 \providecommand{\U}{\operatorname{U}}
11 \providecommand{\Mat}{\operatorname{Mat}}
12 \providecommand{\Span}{\operatorname{span}}
13 \providecommand{\rank}{\operatorname{rank}}
14 \providecommand{\ord}{\operatorname{ord}}
15 \providecommand{\supp}{\operatorname{supp}}
16 \providecommand{\codim}{\operatorname{codim}}
17 \providecommand{\Prob}{\mathbb P}
18 \providecommand{\Exp}{\mathbb E}
19 \providecommand{\id}{I}
20 \providecommand{\ellDown}{\ell_{\downarrow}}
21 \providecommand{\ellAll}{\ell_{*}}
22 \providecommand{\ellBudget}[1]{\ell_{\le #1}}
23 \providecommand{\ellWeight}[1]{\ell_{#1}}
24 \providecommand{\tauGate}[3]{\tau_{#1,#2}(#3)}
25 \providecommand{\ellExc}[2]{\ell^{(#1,#2)}}
26 \providecommand{\ellRes}{\ell_{\mathrm{res}}}
27 \providecommand{\ellAmb}{\ell_{\mathrm{amb}}}
28 \providecommand{\DeltaDef}{\Delta}
29 \providecommand{\Gate}{\mathsf G}
30 \providecommand{\Res}{\mathsf R}
31 \providecommand{\Amb}{\mathsf A}
32 \providecommand{\cost}{\operatorname{cost}}
33 \providecommand{\Syn}{\operatorname{Syn}}
34 \providecommand{\Cliff}{\operatorname{Cliff}}
35 \providecommand{\Pauli}{\mathcal P}
36 \providecommand{\CX}{\operatorname{CX}}
37 \providecommand{\CZ}{\operatorname{CZ}}
38 \providecommand{\SWAP}{\operatorname{SWAP}}
39 \providecommand{\SUM}{\operatorname{SUM}}
40 \providecommand{\TOF}{\operatorname{TOF}}
41 \providecommand{\diag}{\operatorname{diag}}
42 \providecommand{\Aff}{\mathbb A}
43 \providecommand{\ket}[1]{\lvert #1\rangle}
44 \providecommand{\bra}[1]{\langle #1\rvert}
45 \providecommand{\braket}[2]{\langle #1\mid #2\rangle}

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