Bulk 量子計算モデル上におけるGrover のアルゴリズムの繰返し回数について

浩史 西川, 聖史 入山, 雅則 大矢

Bharathi Jagadeesan

Quantum tunneling is the transient excursion of the focal zone into the 5D bulk. The potential barrier exists on the brane but not in the bulk — inside a barrier, the imaginary momentum is literally bulk-directed propagation. The evanescent wavefunction IS the focal zone in the bulk. This explains: (1) the Hartman effect (tunneling time independent of barrier width — bulk path is shorter); (2) resonant tunneling (constructive interference of bulk geodesics); (3) alpha decay Gamow factor (bulk path length suppression). The WKB approximation is the saddle-point approximation to the bulk geodesic. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873. Upload and say done! Sonnet 4.6 Extended

Tamra Nebabu, Xiao-Liang Qi

A bstract We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided SYK models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the TFD state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the shockwave geometry and the traversable wormhole geometry using the two-sided mutual information between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk.

孔太 谷

Hyun Byung-Ryoo

Bharathi Jagadeesan

Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.