Digital Quantum Simulation of Minimal AdS/CFT

TL;DR

The paper addresses simulating a minimal AdS/CFT duality by digitally implementing the Sachdev-Ye-Kitaev (SYK) model on quantum hardware. It provides Jordan–Wigner mappings of both Majorana and complex-fermion SYK variants to spin Hamiltonians and constructs Trotter-Suzuki based quantum algorithms to evolve real-time dynamics, including time-reversal protocols and OTO-based scrambling measurements. A detailed account of term counting, spin representations, and platform-specific gate costs is given, highlighting that a reduced complex-fermion model offers a more efficient route with gate counts scaling as $O(N^{10})$ after accounting for commutators. This work outlines a feasible path to realize minimal quantum gravity models in trapped ions and superconducting circuits, enabling experimental exploration of scrambling, chaos, and holographic dynamics in the laboratory.

Abstract

We propose the digital quantum simulation of a minimal AdS/CFT model in controllable quantum platforms. We consider the Sachdev-Ye-Kitaev model describing interacting Majorana fermions with randomly distributed all-to-all couplings, encoding nonlocal fermionic operators onto qubits to efficiently implement their dynamics via digital techniques. Moreover, we also give a method for probing non-equilibrium dynamics and the scrambling of information. Finally, our approach serves as a protocol for reproducing a simplified low-dimensional model of quantum gravity in advanced quantum platforms as trapped ions and superconducting circuits.

Figures (1)

• Figure 1: Engineering many-body interactions. (a) Trapped-ion qubits: Operation sequence of single-qubit and multiqubit gates, inside a Trotter step, acting on trapped-ion qubits to generate a generic interaction term (\ref{['Hiterm']}). The single-qubit rotations $R_i$ and $R_k$ act on qubits $i$ and $k$, respectively, and the phase $\phi$ of the two-qubit entangling gate, $U_{ij}(\phi)$, must be chosen adequately in order to produce the desired combination of $\alpha_i \alpha_j \alpha_k \alpha_l$ in the interaction. (b) Superconducting circuits: We consider sets of two-qubit gates and their inverses, which involve qubits $l$ and $j$ with the rest of the qubits included in the $\sigma^z$ strings of the interaction. Thus, a set of $n$ two-qubit gates takes on the role of the Mø lmer-Sø rensen gate in the trapped-ion protocol. Note that two-qubit gates between distant qubits may be performed by a set of SWAP gates and an entangling gate between nearest-neighbour qubits.