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Abstract:

We generate multipartite entangled states of two, three, and four matter qubits, where the entanglement is distributed over macroscopic distances via a photonic network link. Trapped-ion Sr + 88 qubits are entangled directly via an optical fibre link, and the entanglement is subsequently extended to Ca + 43 memory qubits cotrapped in each network node, using local mixed-species logic gates. We create remotely entangled Sr + − Ca + and Ca + − Ca + states, as well as mixed-species Greenberger-Horne-Zeilinger (GHZ) states of up to four qubits. We demonstrate storage of the remotely entangled memory qubits for ∼ 10     s , more than 100 × the state creation time.

Abstract:

Lattice gauge theories, which have both dynamical matter and gauge fields, are strongly coupled problems that lie beyond the reach of classical computation. Quantum simulations may provide a tractable approach for studying lattice gauge theories, but implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here we demonstrate a resource-efficient encoding of a Z2$${{\mathbb{Z}}}_{2}$$ lattice gauge theory using a hybrid qubit–oscillator trapped-ion quantum device, with the qubits representing the gauge fields and the vibrational modes of the ions encoding the bosonic matter fields. We use synthetic dimensions to construct higher dimensional lattice geometries, and we combine digital and analogue techniques to prepare the initial states, realize the gauge-invariant real-time evolution and measure the relevant observables. After observing dynamics obeying Gauss’s law in a Z2$${{\mathbb{Z}}}_{2}$$ link, we extend this approach to a loop geometry formed by two qubits and two oscillators. In this quasi-two-dimensional set-up, we observe Aharonov–Bohm interference with dynamical gauge fields encoding the magnetic flux, thereby demonstrating the interplay between charge and flux. Our results establish a path for scalable quantum simulations of lattice gauge theories in higher dimensions.

Abstract:

Quantum harmonic oscillators model phenomena from electromagnetic fields to molecular vibrations, with excitations represented by bosons such as photons or phonons. Linear interactions that create or annihilate single bosons generate coherent states of light or motion. Introducing higher-order nonlinear interactions produces richer quantum behaviour: second-order interactions enable squeezing, whereas higher-order interactions generate non-Gaussian states useful for continuous-variable quantum computation. However, such interactions are usually weak or require specialized hardware. Hybrid systems, where a linear interaction couples an oscillator to a spin, offer an alternative. Here we combine two spin-dependent linear bosonic interactions to implement up to fourth-order nonlinear bosonic interactions in a single trapped ion, focusing on generalized squeezing. We demonstrate and characterize squeezing, trisqueezing and quadsqueezing; reconstruct the Wigner functions of the resulting states; and achieve quadsqueezing over 100 times faster than conventional methods. The approach has no fundamental limit on the interaction order and applies to any platform supporting spin-dependent linear interactions.

Abstract:

Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.