Holographic quantum algorithms for simulating correlated spin systems

• DOI: 10.1103/physrevresearch.3.033002
• Publication Date: 2021-07-01T14:20:49Z
• Authors: Michael Foss-Feig; David Hayes; Joan M. Dreiling; Caroline Figgatt; John P. Gaebler; Steven A. Moses; Juan M. Pino; Andrew C. Potter
• Keywords: Matrix product state; Heisenberg model; Superdense coding

We present a suite of ``holographic'' quantum algorithms for efficient ground-state preparation and dynamical evolution correlated spin systems, which require far fewer qubits than the number spins being simulated. The exploit equivalence between matrix-product states (MPS) channels, along with partial measurement qubit reuse, in order to simulate $D$-dimensional system using only $(D\ensuremath{-}1)$-dimensional subset an ancillary register whose size scales logarithmically amount entanglement simulated state. Ground can either be directly prepared from known MPS representation or obtained via holographic variational eigensolver (holoVQE). Dynamics under local Hamiltonians time $t$ also additional (multiplicative) $\mathrm{poly}(t)$ overhead resources. These techniques open door simulation exponentially large bond dimension, including ground two- three-dimensional thermalizing dynamics rapid growth. As demonstration potential resource savings, we implement holoVQE antiferromagnetic Heisenberg chain on trapped-ion computer, achieving within $10(3)%$ exact energy infinite pair qubits.