⚛️ quantum physics

Observation of gravity-like signatures in holographic codes on a quantum computer

This paper reports the first experimental implementation of the HaPPY holographic code on a trapped-ion quantum computer, confirming the Faulkner-Lewkowycz-Maldacena formula and observing entropic signatures of emergent gravity and quantum wormholes.

Original authors: Debopriyo Biswas, Gong Cheng, Krishnanand Karthikeyan, Diana Muñoz-Valencia, Vincent P. Su, Hrant Gharibyan, Daiwei Zhu, Grant Salton, Evgeny Epifanovsky, Martin Roetteler, Christopher Monroe, John Pr

Published 2026-07-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Debopriyo Biswas, Gong Cheng, Krishnanand Karthikeyan, Diana Muñoz-Valencia, Vincent P. Su, Hrant Gharibyan, Daiwei Zhu, Grant Salton, Evgeny Epifanovsky, Martin Roetteler, Christopher Monroe, John Preskill, Norbert M. Linke, ChunJun Cao, Crystal Noel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic video game. For decades, physicists have been trying to figure out if the game world (spacetime) is the "real" thing, or if it's just a hologram projected from a simpler, hidden code running underneath. This paper is like a team of scientists building a tiny, working prototype of that hologram inside a real quantum computer to see if the "gravity" in the game actually works the way the theory predicts.

The Big Idea: Gravity as a Hologram
Think of our 3D universe as a movie playing on a flat 2D screen. The "AdS/CFT correspondence" is the theory that says the 3D movie (with gravity and black holes) is just a projection of a 2D quantum code on the screen. In this code, the "distance" between things in the 3D world isn't a fixed ruler; it's determined by how "entangled" (or glued together) the pieces of the 2D code are. The more entangled two pieces are, the closer they feel in the 3D world.

The Experiment: Building a Toy Universe
The researchers used a trapped-ion quantum computer (a machine that uses electrically charged atoms as tiny bits of information) to build a specific "toy model" of this hologram called the HaPPY code. You can think of this code as a complex net made of perfect geometric shapes (tensor networks) that translates 2D quantum information into a 3D-like structure.

They didn't just simulate this on a regular laptop; they ran it on real hardware with up to 36 qubits. Their goal was to test a famous formula called the Faulkner–Lewkowycz–Maldacena (FLM) formula. In plain English, this formula says: "The total 'messiness' (entropy) of a region in the 3D world is equal to the size of its boundary (the area) plus the messiness of the stuff inside it."

What They Found: The First Real Check
First, they tested the basic version of the code, which acts like a rigid, unchanging background (like a flat, empty room). They measured the "boundary messiness" and the "inside messiness" while changing how much the inside pieces were entangled.

The Result: The measurements matched the theory perfectly. When they increased the entanglement inside, the boundary messiness went up exactly as the formula predicted, while the "area" part stayed fixed. This is the first experimental confirmation of this specific holographic formula in a quantum error-correcting code.

Adding "Magic": Making Gravity Bend
Here is where it gets really cool. In the real universe, gravity isn't just a static background; massive objects (like stars) bend space. The original HaPPY code was too rigid to show this bending. To fix this, the scientists injected something called "magic" (non-stabilizer resources) into the code. Think of "magic" as adding a special, wobbly ingredient to the recipe that makes the code flexible and state-dependent.

The Result: When they added this "magic," the "area" of the hologram started to change depending on how much stuff was inside. Just like a real star bends space, the "magic" in their code made the geometry shift based on the entanglement. They observed that the "proto-area entropy" (a measure of the geometric size) increased as the bulk entanglement increased. This mimics how gravity works in a real theory: matter tells space how to curve.

The Wormhole Experiment: Gluing Two Universes
Finally, they tried to simulate a wormhole. In the famous ER=EPR idea, two separate universes can be connected by a wormhole if they are deeply entangled.

The Setup: They built two separate holographic codes (two little universes) and entangled their "logical" cores (the deep inside parts) rather than just their edges.
The Result: As they increased the entanglement between the two codes, the "proto-area" (the geometric distance between them) decreased.
What this means: It's like taking two separate rooms and, by increasing the "glue" (entanglement) between them, the distance between the walls shrinks. This suggests that entanglement really does act as the "glue" that builds spacetime connectivity.

How Sure Are We?
The paper is very careful about what it claims.

Proven: They measured the FLM formula relationship in the stabilizer code. The data matched the theory within experimental error bars.
Observed: They measured the "gravity-like" bending (state-dependent area) in the magic-enriched code. The trend was clear: more magic and more entanglement led to a stronger effect.
Simulated: They compared their real hardware results to computer simulations that included noise (errors). The simulations matched the experimental data well, confirming that the effects they saw weren't just glitches.
Not Proven (Yet): They explicitly state that this is a "toy model." They are not saying they have built a real black hole or a real wormhole. They are saying this toy model behaves as if it has gravity. The paper argues against the idea that spacetime is fundamental, suggesting instead that it emerges from these quantum codes, but they admit this is still a simplified test.

The Bottom Line
This paper shows that quantum computers can act as a laboratory for gravity. By building these holographic codes, the team successfully watched spacetime "emerge" from quantum entanglement. They saw the geometry stay rigid when it should, bend when they added "magic," and shrink when they glued two universes together. It's a small step, but it's a real, measured step toward understanding how the universe might be woven together from quantum threads.

Technical Summary: Observation of gravity-like signatures in holographic codes on a quantum computer

Problem Statement
The unification of quantum mechanics and general relativity remains a central open problem in theoretical physics. A leading hypothesis suggests that spacetime is not fundamental but emerges from more elementary quantum degrees of freedom, a concept concretized by the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. In this framework, bulk spacetime geometry is encoded in the entanglement structure of a boundary quantum field theory. While theoretical tools like the Ryu–Takayanagi (RT) and Faulkner–Lewkowycz–Maldacena (FLM) formulae quantify this relationship, existing holographic codes (such as the HaPPY code) largely describe fixed background geometries. They fail to capture how quantum matter modifies the emergent geometry—a feature known as gravitational backreaction. Furthermore, experimental verification of these concepts has been limited, with previous demonstrations (e.g., NMR tests) not directly investigating the influence of quantum matter on emergent geometry.

Methodology
The authors implement a toy model of holographic duality, the HaPPY code, on a programmable trapped-ion quantum computer (IonQ Forte). The trapped-ion platform was selected for its native all-to-all qubit connectivity, which is well-suited for the all-to-all entanglement patterns required by holographic encoding circuits.

The experimental approach involves three main stages:

Code Reduction and Encoding: The authors utilize the isometric structure of the tensor network to reduce the full $[[25, 11, 3]]$ HaPPY code to smaller, entropically equivalent reduced codes (specifically $[[8, 2, 3]]$ and $[[5, 1, 3]]$ ) tailored to specific boundary subregions. This reduction preserves the necessary bulk entropy dependencies while minimizing the number of physical qubits required (up to 36 qubits).
FLM Formula Test: They first test the standard stabilizer HaPPY code. Using quantum state tomography (QST), they measure the boundary entropy ( $S_B$ ) and the recovered bulk entropy ( $S_b$ ) for a connected boundary subregion. They verify the FLM relation, $S_A = S_{area} + S_a$ , by demonstrating that the "proto-area" entropy ( $S_{PA} = S_B - S_b$ ) remains constant (equal to the minimal cut size) even as the bulk entanglement is varied.
Magic-Enriched and Double-Sided Experiments: To probe emergent gravity, the authors introduce "magic" (non-stabilizerness) into the encoding circuit by applying controlled coherent over-rotations ( $\lambda_i$ $λ_{i}$ ) to the Clifford gates. This transforms the code from a fixed-stabilizer model to one where the geometry can depend on the state.
- Single-Copy: They measure $S_{PA}$ as a function of bulk entanglement in a single magic-enriched code.
- Double-Sided (Wormhole Analog): They couple two disjoint copies of the magic-enriched code by entangling their logical (bulk) qubits. This setup serves as an analog for entangling two AdS spacetimes (ER=EPR proposal). They measure the $S_{PA}$ of the combined boundary region to observe how inter-code entanglement affects the effective geometric connectivity.

Key Contributions

Experimental Verification of FLM: The paper presents the first experimental confirmation of the Faulkner–Lewkowycz–Maldacena formula in a holographic quantum error-correcting code, validating the relationship between boundary entropy, bulk entropy, and the geometric "area" term in a quantum processor.
Observation of State-Dependent Geometry: By introducing non-Clifford resources ("magic"), the authors demonstrate that the proto-area entropy becomes dependent on the bulk state. Specifically, $S_{PA}$ increases with bulk entanglement in a single-copy code, mimicking the gravitational backreaction expected in theories where matter modifies spacetime geometry.
Wormhole Signature: In the double-sided experiment, the authors observe a decrease in $S_{PA}$ as the entanglement between the two code copies increases. This behavior is interpreted as a signature of increased geometric connectivity, analogous to the shortening of a wormhole throat in holographic models.

Results

FLM Test: Experimental data from the IonQ hardware showed that for the stabilizer code, the proto-area entropy remained constant at $S_{PA} \approx 2$ (the reduced minimal cut) regardless of the bulk entanglement angle $\theta$ , matching theoretical predictions within experimental uncertainty.
Magic-Enriched Single-Code: When magic was injected ( $M > 0$ ), the proto-area entropy $S_{PA}$ was observed to increase linearly with the bulk entanglement angle $\theta$ . The slope of this increase correlated with the amount of injected magic, confirming a state-dependent geometric response.
Double-Sided Experiment: For the entangled two-code systems, the measured $S_{PA}$ decreased as the bulk entanglement angle $\theta$ increased. This trend was consistent with numerical simulations that included stochastic gate noise and coherent errors. The magnitude of the negative slope increased with higher injected magic, supporting the hypothesis that entanglement acts as a "glue" for emergent geometry.

Significance
The authors claim that these experiments illustrate how quantum computers can serve as testbeds for modeling the emergence of spacetime. By realizing holographic codes on programmable hardware, they provide a method to experimentally probe the interplay between bulk matter and emergent geometry in regimes inaccessible to classical simulation. The observation of gravity-like signatures, such as state-dependent area terms and entanglement-induced connectivity, offers a pathway to building intuition for quantum gravity models that may lack a complete theoretical description. The work suggests that future scalable experiments could further explore the conditions under which semi-classical geometry emerges from quantum entanglement.

Technical Summary: Observation of gravity-like signatures in holographic codes on a quantum computer

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