macros+pkgs--random-features.tex

\usepackage{braket}

\newcommand{\Z}{{\mathbb{Z}}} 
\newcommand{\C}{{\mathbb{C}}} 
\newcommand{\R}{{\mathbb{R}}}
\newcommand{\id}{{\mathbbm{1}}} % identity matrix 

\newcommand{\CNOT}{\mathop\mathrm{CNOT}}     % CNOT gate inside math environments
\newcommand{\SU}{\mathrm{SU}} % Lie group SU
\newcommand{\su}{\mathfrak{su}} % Lie algebra SU
\newcommand{\qft}{\mathrm{qft}}
\newcommand{\qftf}{\mathrm{\mathbf{f}}} % qft f

\newcommand{\ii}{\mathrm{i}}
\newcommand{\ee}{\mathrm{e}}
% an alias because otimes occurs too often
\newcommand{\ox}{\otimes}

\newcommand{\bolma}{\mathbf{\upsigma}} % tensor product of paulis

\newcommand{\floor}[1]{\left \lfloor #1 \right \rfloor}
\renewcommand{\O}{\mathcal{O}}
\newcommand{\norm}[1]{\|{#1}\|}
\newcommand{\Norm}[1]{\left\|{#1}\right\|}
\newcommand{\Abs}[1]{\left|{#1}\right|}
\newcommand{\Tr}[1]{\mathop{}\text{Tr}\left({#1}\right)}
% \newcommand{\ketbra}[2]{\ket{#1}\!\!\bra{#2}}
\newcommand{\proj}[1]{\ketbra{{#1}}{{#1}}}

\DeclareMathOperator{\spn}{span}
\DeclareMathOperator{\spec}{Spec}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\argmax}{argmax}
\DeclareMathOperator{\tr}{Tr}

\newcommand{\curly}[1]{\mathcal{{#1}}} % `script' or gothic/curly letters
\newcommand{\cc}[1]{\mathsf{{#1}}}	% complexity class

\newcommand{\parahead}[1]{\noindent\textbf{{#1}}} % left-indented bold paragraph headers

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\x}{{\mathbf{x}}} % vectors in bold
\newcommand{\w}{{\mathbf{w}}}
\renewcommand{\v}{{\mathbf{v}}}
\newcommand{\polylog}{\text{poly}\log}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator{\BigO}{\mathcal{O}}
\DeclareMathOperator{\smallO}{\mathrm{o}}
\newcommand\field\mathds

\newcommand{\dd}{\mathrm d}
\renewcommand{\H}{\mathcal{H}}
\newcommand\op\mathbf
\DeclareMathOperator{\diag}{diag}

\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\Expect}{\mathbbm E}
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\Cov}{Cov}
\DeclareMathOperator{\smallOmega}{\omega}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% random features- essential macros
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% bold operator type symbols
% 1. probability density operators
\newcommand{\q}{\mathbf{q}} 
\newcommand{\Q}{\mathbf{Q}} 
\newcommand{\uQ}{\underline{\Q}}  		% for the normalised Q/Q_max
\newcommand{\SgOp}{\mathbf{\Sigma}} 
\newcommand{\F}{\mathbf{F}} 
% 2. generic quantum operators
\newcommand{\A}{\mathbf{A}}
\newcommand{\U}{\mathbf{U}}
\newcommand{\Rot}{\mathbf{R}}
% 3. kernel operator
\newcommand{\krn}{\mathbf{k}} 
\newcommand{\Lam}{\mathbf{\Lambda}}


\newcommand{\trInv}{{\mathrm{TI}}} 

% tilde-d letters
\newcommand{\tx}{\tilde{x}}
\newcommand{\tk}{\tilde{k}}
\newcommand{\tv}{\tilde{v}}

% hatted letters
\newcommand{\hbq}{\hat{\q}}
\newcommand{\hq}{\hat{q}}
\newcommand{\hg}{\hat{g}}
\newcommand{\hSgOp}{\hat{\SgOp}}

% sets in domains and ranges of functions etc
\newcommand{\sX}{\mathcal{X}} 
\newcommand{\sH}{\mathcal{H}} 
\newcommand{\sV}{\mathcal{V}} 
\newcommand{\sW}{\mathcal{W}} 
\newcommand{\tsX}{\tilde{\sX}}
\newcommand{\tsV}{\tilde{\sV}}  

% oracles
\newcommand{\Or}{{\mathrm{Orc}}} 

\DeclareMathOperator{\erf}{erf}
\DeclareMathOperator{\poly}{poly}
\DeclareMathOperator{\diam}{diam}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% referencing
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
% clever references
\usepackage[nameinlink]{cleveref}
\crefname{lemma}{lemma}{lemmas}
\crefname{proposition}{Proposition}{Propositions}
\crefname{definition}{Definition}{Definitions}
\crefname{theorem}{Theorem}{Theorems}
\crefname{conjecture}{conjecture}{conjectures}
\crefname{corollary}{Corollary}{Corollaries}
\crefname{example}{example}{examples}
\crefname{section}{Section}{Sections}
\crefname{chapter}{Chapter}{Chapters}
\crefname{appendix}{Appendix}{Appendices}
\crefname{subappendix}{Appendix}{Appendices}
\crefname{figure}{fig.}{figs.}
\crefname{equation}{eq.}{eqs.}
\crefname{table}{Table}{Tables}
\crefname{item}{property}{properties}
\crefname{remark}{Remark}{Remarks}
\crefname{algorithm}{Algorithm}{Algorithms}
\crefname{problem}{}{}

%https://tex.stackexchange.com/questions/54728/hyperref-jumps-to-the-wrong-equation-if-the-equation-has-a-tag-and-cleveref-is
\makeatletter

  \def\make@df@tag@@#1{%
    \gdef\df@tag{%
      \maketag@@@{\Hy@make@anchor#1}%
      \def\@currentlabel{#1}%
      \def\cref@currentlabel{[equation][2147483647][]#1}%
    }%
  }
  \def\make@df@tag@@@#1{%
    \gdef\df@tag{%
      \tagform@{\Hy@make@anchor#1}%
      \toks@\@xp{\p@equation{#1}}%
      \edef\@currentlabel{\the\toks@}%
      \edef\cref@currentlabel{[equation][2147483647][]\the\toks@}
    }%
  }
\makeatother

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% theorem, lemma etc. environments
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% newtheorem
\newtheorem{theorem}{Theorem}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{example}[theorem]{Example}
\newtheorem{remark}[theorem]{Remark}
\newtheorem*{remark*}{Remark}
\newtheorem*{theorem*}{Theorem}
\newtheorem*{proposition*}{Proposition}
\newtheorem*{lemma*}{Lemma}


\newenvironment{abstract}
 {% \small
  \list{\textbf{Synopsis:}}{%
    \setlength{\leftmargin}{6mm}
    \setlength{\rightmargin}{6mm}%
  }%
  \item\relax}
 {\endlist}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% code listings
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{listings}
\lstset{basicstyle=\ttfamily, keywordstyle=\bfseries}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% bibliography with biblatex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[backend=biber,
            style=trad-alpha,
            % style=alphabetic,
            % citestyle=authoryear-comp,
            sorting=nty,
            doi=true,
            isbn=false,
            url=false,
            maxbibnames=20,
            maxcitenames=2, 
            % refsection=chapter,
            backref,
            backrefstyle=three]{biblatex}  
            
\DefineBibliographyStrings{english}{%
  backrefpage = {page},% originally "cited on page"
  backrefpages = {pages},% originally "cited on pages"
}

\renewcommand\multicitedelim{\addcomma\space} % comma between multiple citations, instead of semicolon

\addbibresource{bibs/featureSamp.bib}


% Use DOI links in titles
% \newbibmacro{string+doi}[1]{\iffieldundef{doi}{#1}{\href{https://dx.doi.org/\thefield{doi}}{#1}}}
% mod to check if URL is available when DOI isn't
\newbibmacro{string+doi}[1]{\iffieldundef{doi}%
                                  {\iffieldundef{url}{#1}{\href{\thefield{url}}{#1}}}%
                                  {\href{https://dx.doi.org/\thefield{doi}}{#1}}}
\DeclareFieldFormat{title}{\usebibmacro{string+doi}{\mkbibemph{#1}}}
\DeclareFieldFormat[article]{title}{\usebibmacro{string+doi}{\mkbibquote{#1}}}
\DeclareFieldFormat[incollection]{title}{\usebibmacro{string+doi}{\mkbibquote{#1}}}

% changing bibliography heading style
\defbibheading{customhead}[]{%
    \chapter*{#1}}
% can give an optional name argument