Spectral Benchmarking of Holographic Quantum Simulations

In the paper's words

The simulation of quantum gravity on near-term quantum processors is hindered by a critical tension between hardware feasibility and physical fidelity, creating an “Artifact Zone” where simplified models produce misleading, non-physical results. This paper addresses this challenge by proposing a robust benchmarking framework to certify the structural integrity of holographic quantum simulations. We argue that dynamical metrics like Out-of-Time-Ordered Correlators (OTOCs) can be ambiguous in noisy systems, and advocate for the adoption of a structural metric based on Random Matrix Theory (RMT): the adjacent gap ratio, or r-statistic.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. We hypothesize that the clear separation observed in H1 will remain reliable and statistically significant even for the small system sizes (e.g., N=8 to N=16 qubits) that are characteristic of the NISQ era.

   from 1.4 Hypothesis and

2. We generate and present simulation data that explicitly connects a measured r-statistic value to a validated non-artifactual outcome, even at the small scales of 8 to 14 qubits.

   from 1.7 Contribution

3. Our primary and most fundamental test was to confirm that the r-statistic can quantitatively and unambiguously separate the spectral statistics of the ‘Artifact Zone’ from those of the ‘Holographic Regime.’ To establish this crucial baseline, we generated an ensemble of 20 matrices for each of our two primary model classes—the integrable Poisson ensemble and the chaotic Gaussian Unitary Ensemble (GUE)—at a representative system size of N=12 qubits.

   from 3.1 Spectral Statistics of Integrable vs. Chaotic Ensembles

4. To address this, we performed a comprehensive finite-size scaling analysis, computing the mean r-statistic for systems of N=8, 10, 12, and 14 qubits.

   from 3.2 Finite-Size Effects and Statistical Power on NISQ Devices

5. The goal of this analysis was to determine the number of independent measurements of the r-statistic that would be required to distinguish a genuinely chaotic system ($r \approx 0.60$) from a system on the edge of the artifact zone (e.g., a hypothetical system with $r = 0.50$) with a standard statistical power of 80% at a significance level of $\alpha =0.05$.

   from 3.2 Finite-Size Effects and Statistical Power on NISQ Devices

6. The metric’s core ability to distinguish chaos from integrability remains remarkably robust even down to N=8 qubits, confirming our second operational hypothesis.

   from 3.2 Finite-Size Effects and Statistical Power on NISQ Devices

How it is done

1. Our methodology involves a computational experiment using synthetic Hamiltonians to model both integrable (artifact) and chaotic (holographic) systems.

   from Abstract

2. Classical supercomputers, bound by the binary logic of bits, are fundamentally incapable of representing the exponentially large Hilbert spaces required to describe even modest quantum gravitational systems.

   from 1.1 The

3. Grounded in the powerful mathematical framework of Random Matrix Theory (RMT), this approach posits that the energy level spacings of a chaotic quantum system should obey universal statistical laws that are distinctly different from those of an integrable, non-chaotic system.

   from 1.2

4. This provides an unambiguous, quantitative method to distinguish a system capable of holographic dynamics from one residing in the Artifact Zone.

   from 1.3

What would falsify it

1. This provides a clear, falsifiable method to escape the Artifact Zone, raising the standard of evidence for quantum advantage claims and guiding the development of more physically faithful quantum simulators.

   from Abstract

2. This framework aims to establish a clear, falsifiable line between physically meaningful simulations and their deceptive, artifactual counterparts.

   from 1.1 The

3. Specifically, we predict that the distribution of r-statistic values for an ensemble of integrable Hamiltonians will be tightly clustered around the theoretical Poisson value of approximately 0.39, representing the Artifact Zone.

   from 1.4 Hypothesis and

Where the claim stops

1. No single computational study can be entirely comprehensive, and the boundaries of our investigation must be clearly delineated to guide future work and prevent over-interpretation of our findings.

   from 4.5 Limitations of the

2. While these simulations are based on well-understood physical principles and provide a strong proof-of-principle, they cannot capture the full complexity and richness of a real quantum device.

   from 4.5 Limitations of the

3. The ultimate validation of our proposed benchmark will require its application to an actual quantum processor, a crucial next step that is outlined in our discussion of future work.

   from 4.5 Limitations of the

Where to read

1. A Proposed22 words · 1 min
2. Abstract260 words · 1 min
3. Keywords14 words · 1 min
4. Chapter4,864 words · 21 min
5. Chapter 3: Empirical Results of the Computational Experiment5,036 words · 22 min
6. Chapter4,953 words · 22 min
7. Chapter 6: Limitations and Future Directions2,628 words · 11 min
8. Chapter3,412 words · 15 min
9. Appendices |474 words · 2 min