Traversable wormhole dynamics on a quantum processor

Abstract

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality¹ is the principal example of holography. The Sachdev-Ye-Kitaev (SYK) model of N ≫ 1 Majorana fermions^2,3 has features suggesting the existence of a gravitational dual in AdS₂, and is a new realization of holography^4-6. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry^7,8 through the traversable wormhole mechanism as implemented in the SYK model^9,10. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol⁹. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits⁹. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding^11-13, coupling on either side of the wormhole that is consistent with a negative energy shockwave¹⁴, a Shapiro time delay¹⁵, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics^16,17. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals¹⁸ and other SYK-like models¹⁹.