sovereign-papers / QWEN_paper.tex
SNAPKITTYWEST's picture
Initial upload: sovereign-papers
aa02f91 verified
Raw History Blame Contribute Delete
21 kB
\documentclass[11pt]{article}
\usepackage{amsmath, amssymb, amsthm, graphicx, hyperref, url, booktabs, multirow, caption, subcaption, geometry, setspace, algorithm, algorithmic, enumitem, mathtools, tikz}
\usepackage{cleveref}
\geometry{margin=1in}
\setstretch{1.1}
\theoremstyle{definition}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{example}[theorem]{Example}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\FF}{\mathbb{F}}
\newcommand{\Tr}{\mathrm{Tr}}
\newcommand{\diag}{\mathrm{diag}}
\newcommand{\supp}{\mathrm{supp}}
\newcommand{\diam}{\mathrm{diam}}
\newcommand{\norm}[1]{\|#1\|}
\newcommand{\opnorm}[1]{\|#1\|_{\infty}}
\newcommand{\trnorm}[1]{\|#1\|_{1}}
\newcommand{\frob}[1]{\|#1\|_{F}}
\newcommand{\inner}[2]{\langle #1, #2 \rangle}
\newcommand{\ket}[1]{\lvert #1 \rangle}
\newcommand{\bra}[1]{\langle #1 \rvert}
\newcommand{\braket}[2]{\langle #1 | #2 \rangle}
\newcommand{\ketbra}[2]{\lvert #1 \rangle \langle #2 \rvert}
\newcommand{\id}{\mathbb{I}}
\newcommand{\sgn}{\mathrm{sgn}}
\newcommand{\floor}[1]{\lfloor #1 \rfloor}
\newcommand{\ceil}[1]{\lceil #1 \rceil}
\newcommand{\E}{\mathbb{E}}
\newcommand{\Var}{\mathrm{Var}}
\newcommand{\Cov}{\mathrm{Cov}}
\newcommand{\Prob}{\mathrm{Prob}}
\newcommand{\Cliff}{\mathcal{C}}
\newcommand{\FT}{\mathrm{FT}}
\newcommand{\code}{\mathcal{C}}
\newcommand{\synd}{\mathrm{synd}}
\newcommand{\anc}{\mathrm{anc}}
\newcommand{\data}{\mathrm{data}}
\newcommand{\ancilla}{\mathrm{anc}}
\newcommand{\codeblock}{\mathcal{B}}
\newcommand{\gateset}{\mathcal{G}}
\newcommand{\err}{\mathcal{E}}
\newcommand{\errset}{\mathcal{E}}
\newcommand{\errmodel}{\mathcal{M}}
\newcommand{\codeparam}{[\![n,k,d]\!]}
\newcommand{\codeparamZ}{[\![n,k,d]\!]}
\newcommand{\codeparamX}{[\![n,k,d]\!]}
\newcommand{\codeparamY}{[\![n,k,d]\!]}
\newcommand{\codeparamT}{[\![n,k,d]\!]}
\newcommand{\codeparamS}{[\![n,k,d]\!]}
\newcommand{\codeparamC}{[\![n,k,d]\!]}
\newcommand{\codeparamF}{[\![n,k,d]\!]}
\newcommand{\codeparamG}{[\![n,k,d]\!]}
\newcommand{\codeparamH}{[\![n,k,d]\!]}
\newcommand{\codeparamI}{[\![n,k,d]\!]}
\newcommand{\codeparamJ}{[\![n,k,d]\!]}
\newcommand{\codeparamK}{[\![n,k,d]\!]}
\newcommand{\codeparamL}{[\![n,k,d]\!]}
\newcommand{\codeparamM}{[\![n,k,d]\!]}
\newcommand{\codeparamN}{[\![n,k,d]\!]}
\newcommand{\codeparamO}{[\![n,k,d]\!]}
\newcommand{\codeparamP}{[\![n,k,d]\!]}
\newcommand{\codeparamQ}{[\![n,k,d]\!]}
\newcommand{\codeparamR}{[\![n,k,d]\!]}
\newcommand{\codeparamSs}{[\![n,k,d]\!]}
\newcommand{\codeparamTt}{[\![n,k,d]\!]}
\newcommand{\codeparamU}{[\![n,k,d]\!]}
\newcommand{\codeparamV}{[\![n,k,d]\!]}
\newcommand{\codeparamW}{[\![n,k,d]\!]}
\newcommand{\codeparamXx}{[\![n,k,d]\!]}
\newcommand{\codeparamYy}{[\![n,k,d]\!]}
\newcommand{\codeparamZz}{[\![n,k,d]\!]}
\newcommand{\codeparamAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHH}{[\![n,k,d]\!]}
\newcommand{\codeparamII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMMMMMM}{[\![n,k,d]\!]}
\newcommand{\codeparamNNNNNNNNNNNNNNN}{[\![n,k,d]\!]}
\newcommand{\codeparamOOOOOOOOOOOOOOO}{[\![n,k,d]\!]}
\newcommand{\codeparamPPPPPPPPPPPPPPP}{[\![n,k,d]\!]}
\newcommand{\codeparamQQQQQQQQQQQQQQQ}{[\![n,k,d]\!]}
\newcommand{\codeparamRRRRRRRRRRRRRRR}{[\![n,k,d]\!]}
\newcommand{\codeparamSSSSSSSSSSSSSSS}{[\![n,k,d]\!]}
\newcommand{\codeparamTTTTTTTTTTTTTTT}{[\![n,k,d]\!]}
\newcommand{\codeparamUUUUUUUUUUUUUUU}{[\![n,k,d]\!]}
\newcommand{\codeparamVVVVVVVVVVVVVVV}{[\![n,k,d]\!]}
\newcommand{\codeparamWWWWWWWWWWWWWWW}{[\![n,k,d]\!]}
\newcommand{\codeparamXXXXXXXXXXXXXXX}{[\![n,k,d]\!]}
\newcommand{\codeparamYYYYYYYYYYYYYYY}{[\![n,k,d]\!]}
\newcommand{\codeparamZZZZZZZZZZZZZZZ}{[\![n,k,d]\!]}
\newcommand{\codeparamAAAAAAAAAAAAAAAA}{[\![n,k,d]\!]}
\newcommand{\codeparamBBBBBBBBBBBBBBBB}{[\![n,k,d]\!]}
\newcommand{\codeparamCCCCCCCCCCCCCCCCC}{[\![n,k,d]\!]}
\newcommand{\codeparamDDDDDDDDDDDDDDDDD}{[\![n,k,d]\!]}
\newcommand{\codeparamEEEEEEEEEEEEEEEEE}{[\![n,k,d]\!]}
\newcommand{\codeparamFFFFFFFFFFF}{[\![n,k,d]\!]}
\newcommand{\codeparamGGGGGGGGGGGGGGGG}{[\![n,k,d]\!]}
\newcommand{\codeparamHHHHHHHHHHHHHHHH}{[\![n,k,d]\!]}
\newcommand{\codeparamIIIIIIIIIIIIIIII}{[\![n,k,d]\!]}
\newcommand{\codeparamJJJJJJJJJJJJJJJJ}{[\![n,k,d]\!]}
\newcommand{\codeparamKKKKKKKKKKKKKKKK}{[\![n,k,d]\!]}
\newcommand{\codeparamLLLLLLLLLLLLLLLL}{[\![n,k,d]\!]}
\newcommand{\codeparamMMMMMMMMMMMM