Sachdev-Ye-Kitaev model on a noisy quantum computer

Abstract

We study the SYK model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the gate complexity of the time evolution using the first-order product formula for $N$ Majorana fermions is $\mathcal{O}(N^5{J}^2{t}^2/\epsilon )$ where $J$ is the dimensionful coupling parameter, $t$ is the evolution time, and $\epsilon$ is the desired precision. With this improved resource requirement, we perform the time evolution for $N=6,8$ with maximum two-qubit circuit depth of 343. We perform different error mitigation schemes on the noisy hardware results and find good agreement with the exact diagonalization results on classical computers and noiseless simulators. In particular, we compute return probability after time $t$ and out-of-time order correlators (OTOC) which is a standard observable of quantifying the chaotic nature of quantum systems.

v4: Title change due to editor's request. New result for finiteT OTOC. Version matches to the one accepted for publication in PRD. v2: Fixed typos, added references, and new hardware results. v1: 9 + 6 pages with hardware results with depth & count of 300+ two-qubit gates!

References in corpus (4)

• Synthesis of Quantum Logic Circuits
• Dynamical decoupling for superconducting qubits: a performance survey
• Binary-coupling sparse SYK: an improved model of quantum chaos and holography
• Sparse random matrices and Gaussian ensembles with varying randomness

Cited by in corpus (16)

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• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• A model of randomly-coupled Pauli spins
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Hamiltonian simulation of minimal holographic sparsified SYK model
• Probing Entanglement Dynamics in the SYK Model using Quantum Computers
• Sparsity dependence of Krylov state complexity in the SYK model
• Two-local modifications of SYK model with quantum chaos
• Complexity of Quadratic Quantum Chaos
• Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
• Trotter error and gate complexity of the SYK and sparse SYK models
• Sachdev-Ye-Kitaev physics from the Hubbard model: A Floquet engineering approach
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
• Quantum Circuit Optimization by Graph Coloring