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A Glassy Boundary Conformal Field Theory for Holographic Nonvolatile Storage Encoding Millions of Bits with a Single Quench

Parker Emmerson (Yaohushuason)

Published Jun 26, 2026• 0 citations
Publisher

Abstract

The PV‑crystallographic hypercomputer architecture of Emmerson~\cite{EmmersonPVHPC}requires two capabilities that were left as open assumptions: (i) embedding auniversal Turing machine (UTM) into a bulk probe inside an AdS (oreffective‑cone) temporal‑compression chamber, and (ii) reading out the haltstate on the boundary with fidelity arbitrarily close to unity at the finiteexternal deadline. This paper supplies a complete, rigorous mathematicalsolution to both. We work within the holographic quantum error‑correcting code formalism,exemplified by the HaPPY perfect‑tensor network. The bulk is a negativelycurved tensor network whose boundary is a one‑dimensional spin chain. A\emph{bulk Turing probe} is defined as a designated set of bulk logicalindices that realize a universal Turing machine, with an infinite tapeextending along the radial direction and a finite‑state head. Theholographic map encodes the entire tape and head state into the boundarywith built‑in quantum error correction. A special \emph{halt tensor}inside the network encodes the answer: if the simulated program halts, alocal operation toggles the halt tensor from \(|0\rangle\) to \(|1\rangle\);otherwise it stays at \(|0\rangle\). On the boundary, the halt state becomes a logical qubit protected by aholographic code of distance \(D\). We define the \emph{crystallizationlatch} as a boundary operator \(\LL\) that measures this logical qubit. Bychoosing the network size appropriately, the effective error per measurementis exponentially small in \(D\). Consequently, for any desired targetfidelity \(1-\varepsilon\), there exists a finite tensor network and afinite readout region such that the boundary latch yields the correct haltpredicate with probability at least \(1-\varepsilon\). The proper time ofthe probe diverges as its location approaches the conformal boundary,implementing the infinite proper‑time condition exactly. The construction isfully explicit and does not rely on any new physics beyond the standardholographic duality. Thus we complete the missing link in the PV‑crystallographic hypercomputer,establishing that a bulk universal Turing machine with high‑fidelityboundary readout is mathematically consistent and can be engineered withinthe known framework of AdS/CFT.

DOI
10.5281/zenodo.20937600

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Abstract: It was shown by [2] how bulk operators in the AdS/CFT correspondence can be represented on the boundary analogously to the way logical qubits are represented in an encoded subspace in quantum error correction. Then in [1] holographic tensor networks that serve as toy models of the bulk boundary. This paper reviews some of the developments of [1] and [2]. Then it is demonstrated explicitly how to construct perfect tensors, which are essential to the tensor networks mentioned in [2]. Lastly a new example of a holographic quantum error-correcting code based on an eight index perfect tensor is presented.
We present a comprehensive experimental proposal to realize a toy model ofthe AdS/CFT correspondence in a cold‑atom quantum simulator. Atwo‑dimensional hyperbolic optical lattice, generated by a combination ofstructured laser beams, hosts ultracold bosonic atoms whose hoppingamplitudes are engineered to reproduce the metric of anti‑de Sitter space(AdS2+1_{2+1}2+1​). The boundary of the lattice is a one‑dimensional ring ofatoms that plays the role of the conformal field theory (CFT). Byexploiting synthetic gauge fields and Raman‑assisted tunneling, theeffective speed of light in the bulk becomes locally tunable, enablingthe simulation of the Malament–Hogarth effect---an infinite proper timewithin a finite boundary time. We detail the construction of thehyperbolic lattice, the mapping of bulk fields to boundary operators, theencoding of a universal Turing machine as a bulk defect, and the readoutof the computational halt state via boundary correlation measurementswith exponential suppression of errors. Our blueprint provides themissing laboratory platform for the PV‑crystallographic hypercomputerand opens a new paradigm for table‑top holographic quantum computation.
Bulk reconstruction is a central problem in AdS/CFT, and entanglement wedge reconstruction is its subregion version. We argue that this subregion statement should be separated from the stronger holographic quantum error correction interpretation, in which one region-independent logical bulk operator has code-preserving representatives in several boundary regions. A simple locality argument shows that such a common reconstruction must commute with the code-preserving local algebras in the complementary regions. This is the mechanism realized in HaPPY-type codes: the erased regions are blind to a protected logical algebra. An ordinary finite NNN holographic CFT does not have such a protected invisible sector for supergravity fields. Its low-energy local observables, in particular, suitably smeared stress tensors, detect the physical support and gravitational dressing of ordinary bulk operators, up to possible center or superselection data. Thus, there is no such holographic quantum error correction and the N=∞N=\inftyN=∞ agreement of global and subregion HKLL formulae is a free-theory statement. What remains is entanglement wedge reconstruction without holographic quantum error correction, or subregion complementarity: each boundary region has its own code-preserving low-energy algebra and its own region-adapted bulk interpretation, rather than a shared logical operator.
Tensor networks have previously been used to construct holographic quantum error correcting codes (HQECC), which are toy models of the AdS/CFT correspondence. HQECC have been able to exhibit many of the interesting features of the duality, such as complementary recovery and redundant encoding. However, in previous HQECC the boundary Hamiltonian which results from mapping a local bulk Hamiltonian to the boundary is a non-local Hamiltonian, with global terms that act over the entire boundary. In this work, we combine HQECC with recently developed Hamiltonian simulation theory to construct a bulk-boundary mapping in which local bulk Hamiltonians map to local boundary Hamiltonians. This allows us to construct a toy model of a complete holographic duality between models, not just states and observables. This mapping of local Hamiltonians extends the toy models to encompass the relationship between bulk and boundary energy scales, and in particular the mapping between bulk and boundary time dynamics. We discuss what insight this gives into toy models of black hole formation.