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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 duality 1 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 AdS 2 , 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 protocol 9 . This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits 9 . 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 shockwave 14 , a Shapiro time delay 15 , 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 duals 18 and other SYK-like models 19 ., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Efficient and reversible optical to microwave transducers are required for entanglement transfer between superconducting qubits and light in quantum networks. Rare-earth-doped crystals with narrow optical and spin transitions are a promising system for enabling these devices. Current resonant transduction approaches use ground-state electron spin transitions that have coherence lifetimes often limited by spin flip-flop processes and spectral diffusion, even at very low temperatures. We investigate spin coherence in an optically excited state of an Er^{3+}:  Y_{2}SiO_{5} crystal at temperatures from 1.6 to 3.5 K for a low 8.7 mT magnetic field compatible with superconducting resonators. Spin coherence and population lifetimes of up to 1.6  μs and 1.2 ms, respectively, are measured by optically detected spin echo experiments. Analysis of decoherence processes suggest that ms coherence can be reached at lower temperatures for the excited-state spins, whereas ground-state spin coherence would be limited to a few μs due to resonant interactions with other Er^{3+} spins in the lattice and greater instantaneous spectral diffusion from the radio-frequency control pulses. We propose a quantum transducer scheme with potential for close to unity efficiency that exploits the advantages offered by spin states of the optically excited electronic energy levels.

We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation is then mapped into a spin state using a series of π pulses and subsequently transferred to a superconducting qubit via a microwave cavity. To overcome the intrinsic and engineered inhomogeneous broadening of the optical and spin transitions in rare-earth doped crystals, we make use of a special transfer protocol using staggered π pulses. We predict total transfer efficiencies on the order of 90%.