Quantum Resources Required to Block-Encode a Matrix of Classical Data
Quantum Resources Required to Block-Encode a Matrix of Classical Data
We provide a modular circuit-level implementation and resource estimates for several methods of block-encoding a dense <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N\times N$</tex-math></inline-formula> matrix of classical data to precision <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> ; the minimal-depth method achieves a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> -depth of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal{O}(\log (N/\epsilon)),$</tex-math></inline-formula> while the …