Bosonic model of quantum holography

We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

Section: Future Directionsmentioning

confidence: 99%

Toward QCD on quantum computer: orbifold lattice approach

Bergner,

Hanada,

Rinaldi

et al. 2024

A model of randomly-coupled Pauli spins

Hanada,

Jevicki,

Liu

et al. 2024

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.

Bosonic near-CFT1 models from Fock-space fluxes

Jia

2024

We construct a family of near-CFT1 models with a conserved U(1) charge, whose basic degrees of freedom are canonical bosons. The Sachdev-Ye-Kitaev (SYK) model — the first microscopic model that realizes the near-CFT1 dynamics — is based on random p-local interactions among fermions. However, a bosonic near-CFT1 model has remained elusive in the p-local approach because such constructions generally suffer from unwanted orderings at low temperatures. Our construction is based on a recent insight that near-CFT1 dynamics can quite generally arise if we place a large amount of random fluxes in a many-body Fock space and p-locality is not essential. All such models are essentially solved by chord diagrams regardless of the nature of the underlying degrees of freedom. We further argue that such bosonic models do not suffer from energetic instablities or unwanted low-temperature orderings. For comparison we also consider a second class of charge-conserving models which are based on qubits. The thermodynamic scalings of these models are very similar to those of the double-scaled complex SYK model but are free of certain singularities the latter suffers from. We also show the level statistics of both models are described by random matrix theory universality down to very low energies.