Qsnipps ❲Proven❳

[ \textRel(S,Q) = \langle \psi_S | \hatM_Q | \psi_S \rangle ]

The off-diagonal terms ( \beta_kl ) encode —e.g., if “quantum” and “computer” co-occur often in the query corpus, ( \beta_kl ) is high. 3.3 Collapse and Relevance Score Measuring ( |\psi_S\rangle ) with ( \hatM_Q ) yields an expected relevance: QSnipps

where ( \alpha_i ) is a complex amplitude proportional to (normalized term frequency) (\times e^i\theta_i), with phase ( \theta_i ) encoding positional relationships (e.g., word order proximity). Two terms that appear together often (e.g., “quantum” and “computer”) have correlated phases. A query ( Q = q_1, \dots, q_m ) defines a Hermitian observable: [ \textRel(S,Q) = \langle \psi_S | \hatM_Q |

[ |\psi_S\rangle = \sum_i=1^N \alpha_i |w_i\rangle, \quad \sum |\alpha_i|^2 = 1 ] \quad \sum |\alpha_i|^2 = 1 ]