Quantum singular value transformation: Difference between revisions

Revision as of 13:58, 23 April 2025

Latest revision as of 19:06, 28 May 2025

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# Prepare a unitary <math>U</math> that encodes <math>A</math> on the top left side of <math>U</math>, that is <math>U = \begin{bmatrix}A & . \\. & . \end{bmatrix}</math>

# Initialize an <math>n</math> qubit state <math>|0\rangle^{\otimes n}</math>

# If the polynomial is odd, first apply <math>\tilde{\Pi}_{\phi_{1}} U </math> and then <math> \prod_{k=1}^{\frac{d-1}{2}} \Pi_{\phi_{2k}}U^{\dagger}\tilde{\Pi}_{\phi_{2k+1}} U </math> to <math>|0\rangle^{\otimes n}</math>

# If the polynomial is even apply <math> \prod_{k=1}^{\frac{d}{2}} \Pi_{\phi_{2k}-1}U^{\dagger}\tilde{\Pi}_{\phi_{2k}} U </math> to <math>|0\rangle^{\otimes n}</math>

<ref name=grand_unification2021 />