This work introduces holographic quantum computing, a novel paradigm that leverages the holographic principle and the AdS/CFT correspondence to address key challenges in quantum information processing, such as scalability and error correction. By encoding quantum information holographically on the boundary of a higher-dimensional space, we propose a framework that offers significant improvements in scalability and error resilience compared to traditional qubit-based approaches. Our comprehensive theoretical model for holographic quantum computing includes the construction of holographic quantum error-correcting codes that exhibit intrinsic error-correcting properties and lower overhead for fault tolerance. We present novel algorithms that exploit the geometric encoding of information, such as quantum walks on curved spaces and path-finding in hyperbolic graphs, demonstrating potential speedups and resource efficiency. Furthermore, we explore the implementation of standard quantum algorithms, like the Quantum Fourier Transform (QFT), within the holographic framework. The paper also details physical implementation strategies using analog quantum simulators, superconducting qubit arrays, and hybrid classical-quantum systems, highlighting practical pathways to realizing holographic quantum computers. Our results suggest that holographic quantum computing not only enhances the capabilities of quantum computation but also provides deep insights into the fundamental connections between quantum information, spacetime, and gravity. This interdisciplinary approach opens new frontiers in quantum computing and fundamental physics, offering potential breakthroughs in post-quantum cryptography, quantum simulations, and accelerated scientific discovery.
Quantum error-correcting codes underpin models of holographic spacetime, yet the relationship between code geometry and complexity dynamics remains unexplored. We present a unified machine learning framework that (i)~encodes stabilizer code structure via a hypergraph GNN achieving distance prediction MAE of~
0.10, (ii)~predicts Krylov complexity trajectories with a DeepONet conditioned on GNN-derived code embeddings (
R2=0.67 vs.\
R2=−10 without), and (iii)~reveals that code geometry constrains complexity dynamics through partial correlation analysis (distance
→max complexity:
rpartial=−0.60,
p=5.1×10−65). Our key insight is that code-space projections
P=∏i(I+gi)/2 act as a dynamical filter: they mathematically annihilate operator branches that anti-commute with any stabilizer, effectively pruning the Krylov tree and making complexity growth sensitive to the code's geometric distance. We validate robustness across XXZ and random Hamiltonians while identifying that Ising symmetry decouples geometry from dynamics---a physically interpretable null result. Across 661 stabilizer codes (
n≤12), within-size correlations confirm that the geometry--complexity link persists after controlling for system size and \emph{strengthens} at larger
n (reaching
r=−0.91 at
n=12). Multi-seed averaging over 10 Haar-random projections per code confirms that
99.8% of trajectory variance is between-code (structural), with seed-averaged correlations strengthening to
rpartial=−0.70, providing computational evidence for holographic intuitions connecting code distance to constrained Krylov evolution.
As new deep-learned error-correcting codes continue to be introduced, it is important to develop tools to interpret the designed codes and understand the training process. Prior work focusing on the deep-learned TurboAE has both interpreted the learned encoders post-hoc by mapping these onto nearby "interpretable" encoders, and experimentally evaluated the performance of these interpretable encoders with various decoders. Here we look at developing tools for interpreting the training process for deep-learned error-correcting codes, focusing on: 1) using the Goldreich-Levin algorithm to quickly interpret the learned encoder; 2) using Fourier coefficients as a tool for understanding the training dynamics and the loss landscape; 3) reformulating the training loss, the binary cross entropy, by relating it to encoder and decoder parameters, and the bit error rate (BER); 4) using these insights to formulate and study a new training procedure. All tools are demonstrated on TurboAE, but are applicable to other deep-learned forward error correcting codes (without feedback).