Først lest om i [[End-to-end quantum algorithms survey]], hvor de skriver: > The Sachdev-Ye-Kitaev (SYK) model is a simplified model of a quantum black hole that is strongly coupled and «maximally chaotic,» but still solvable. This remarkable and, to date, unique combination of properties has led to great activity surrounding SYK. It has applications in high-energy physics through its connections to black holes and quantum gravity (…) While many interesting properties of the SYK model can be computed analytically in certain limits, not all properties qualify, and questions remain about the behaviour of the model outside these limits—these questions can potentially be adressed numerically by a quantum computer. Altså, [[Kvantedatamaskiner]] kan sannsynligvis simulere [[Kvantegravitasjon]] direkte gjennom denne modellen! Som deretter kan brukes til å undersøke CFT-er som [[Kvantekromodynamikk]] via [[AdS-CFT-korrespondansen]]. #### Matematisk formulering > The SYK model has many variants; a common version to consider is the four-body ($q = 4$) Majorana fermion Hamiltonian with Gaussian coefficients > $H_{\text{SYK}} = \frac{1}{4 \cdot 4!} \sum_{i,j,k,l=1}^N g_{ijkl} \chi_i \chi_j \chi_k \chi_l$, > where $\chi_i$ denote Majorana fermion mode operators obeying the anticommutation relation $\chi_i \chi_j + \chi_j \chi_i = 2 \delta_{ij}$ and $g_{ijkl}$ are coefficients draw independently at random from a Gaussian distribution with zero mean and variance $\sigma^2 = 3! g^2 / N^3$ (with $g$ the tunable coupling strength). #### Time evolution Se [[End-to-end quantum algorithms survey]], side 21: Første metode hadde en $O(N^{10})$ scaling, teknisk sett polynom men ikke særlig nyttig. En senere metode har scaling roughly $O(N^{3.5})$, som er langt bedre, og virker som den har krevd litt cleverness som ville vært vel verdt å prøve å forstå. Surveyen skriver: > This gate complexity grows more slowly than the number of terms in $H_{SYK}$ ($O(N^4)$), a feat that is only possible because the simulation method (…) … og så en lengre teknisk, men nesten-intuitivt beskrivelse av metoden de bruker. #### Kilder - Paper: Sachdev, S. and Ye, J. «Gapless spin-fluid ground state in a random quantum Heisenberg magnet.» (1993), arXiv:cond-mat/9212030 - Talk: Kitaev, A. «A simple model of quantum holography.» ([Part 1](https://www.youtube.com/watch?v=wFH1huu9Jcs)) - *todo: se!* - Survey paper: Rosenhaus, V. «An introduction to the SYK model.» (2019), arXiv:1807.03334 - *todo: sjekk ut!* - paper - paper - Fra [[End-to-end quantum algorithms survey]]: «In another example, (these two papers) give a detailed proposal to **‘simulate quantum gravity in the lab’** via computing expectation values of observables and states formed via simulation of the SYK model.» (Emphasis added.) - Brown, A. R., Gharibyan, H., Leichenauer, S., Lin, H. W., Nezami, S., Salton, G., **Susskind, L.**, Swingle, B., and Walter, M. «Quantum Gravity in the Laba. I. Teleportation by Size and Traversable Wormholes.» (2023), arXiv:1911.06314, and «Quantum Gravity in the Lab. II. Teleportation by Size and Traversable Wormholes.» (2023). arXiv:2102.01064 - *Todo: definitivt sjekk ut!* - Luo, Z., You, Y.-Z., Li, J., Jian, C.-M., Lud, D., Xu, C., Zeng, B., and La, R. «Quantum simulation of the non-Fermi-liquid state of Sachdev-Ye-Kitaev model.» (2019), arXiv:1712.06458 - NISQ-simulering proposal - *todo: sjekk ut!*