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Doping an antiferromagnetic Mott insulator is central to our understanding of a variety of phenomena in strongly-correlated electrons, including high-temperature superconductors. To describe the competition between tunneling $t$ of hole dopants and antiferromagnetic (AFM) spin interactions $J$, theoretical and numerical studies often focus on the paradigmatic $t$-$J$ model, and the direct analog quantum simulation of this model in the relevant regime of high-particle density has long been sought. Here, we realize a doped quantum antiferromagnet with next-nearest neighbour (NNN) tunnelings $t'$ and hard-core bosonic holes using a Rydberg tweezer platform. We utilize coherent dynamics between three Rydberg levels, encoding spins and holes, to implement a tunable bosonic $t$-$J$-$V$ model allowing us to study previously inaccessible parameter regimes. We observe dynamical phase separation between hole and spin domains for $|t/J|\ll 1$, and demonstrate the formation of repulsively bound hole pairs in a variety of spin backgrounds. The interference between NNN tunnelings $t'$ and perturbative pair tunneling gives rise to light and heavy pairs depending on the sign of $t$. Using the single-site control allows us to study the dynamics of a single hole in 2D square lattice (anti)ferromagnets. The model we implement extends the toolbox of Rydberg tweezer experiments beyond spin-1/2 models to a larger class of $t$-$J$ and spin-$1$ models., Comment: 8 pages, 5 figures

Quantum fluctuations can disrupt long-range order in one-dimensional systems, and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasi-adiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real-space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.

Information engines produce mechanical work through measurement and adaptive control. For information engines, the principal challenge lies in how to store the generated work for subsequent utilization. Here, we report an experimental demonstration where quantized mechanical motion serves as a quantum battery and gets charged in repeated cycles by a single trapped-ion information engine. This is enabled by a key technological advancement in rapid state discrimination, allowing us to suppress measurement-induced disturbances. Consequently, we were able to obtain a charging efficiency over 50\% of the theoretical limit at the optimal temperature. The experimental results substantiate that this approach can render trapped ions a promising platform for microscopic information engines with potential applications in the future upon scaling up.

Quantum error mitigation has been extensively explored to increase the accuracy of the quantum circuits in noisy-intermediate-scale-quantum (NISQ) computation, where quantum error correction requiring additional quantum resources is not adopted. Among various error-mitigation schemes, probabilistic error cancellation (PEC) has been proposed as a general and systematic protocol that can be applied to numerous hardware platforms and quantum algorithms. However, PEC has only been tested in two-qubit systems and a superconducting multi-qubit system by learning a sparse error model. Here, we benchmark PEC using up to four trapped-ion qubits. For the benchmark, we simulate the dynamics of interacting fermions with or without spins by applying multiple Trotter steps. By tomographically reconstructing the error model and incorporating other mitigation methods such as positive probability and symmetry constraints, we are able to increase the fidelity of simulation and faithfully observe the dynamics of the Fermi-Hubbard model, including the different behavior of charge and spin of fermions. Our demonstrations can be an essential step for further extending systematic error-mitigation schemes toward practical quantum advantages., Comment: 15 pages, 11 figures

Controllable bosonic systems can provide post-classical computational power with sub-universal quantum computational capability. A network that consists of a number of bosons evolving through beam-splitters and phase-shifters between different modes, has been proposed and applied to demonstrate quantum advantages. While the network has been implemented mostly in optical systems with photons, recently alternative realizations have been explored, where major limitations in photonic systems such as photon loss, and probabilistic manipulation can be addressed. Phonons, the quantized excitations of vibrational modes, of trapped ions can be a promising candidate to realize the bosonic network. Here, we experimentally demonstrate a minimal-loss phononic network that can be programmed and in which any phononic states are deterministically prepared and detected. We realize the network with up to four collective-vibrational modes, which can be straightforwardly extended to reveal quantum advantage. We benchmark the performance of the network with an exemplary algorithm of tomography for arbitrary multi-mode states with a fixed total phonon number. We obtain reconstruction fidelities of 94.5 $\pm$ 1.95 % and 93.4 $\pm$ 3.15 % for single-phonon and two-phonon states, respectively. Our experiment demonstrates a clear and novel pathway to scale up a phononic network for various quantum information processing beyond the limitations of classical and other quantum systems.

Measurement-induced state disturbance is a major challenge in obtaining quantum statistics at multiple time points. We propose a method to extract dynamic information from a quantum system at intermediate time points, namely snapshotting quantum dynamics. To this end, we apply classical post-processing after performing the ancilla-assisted measurements to cancel out the impact of the measurements at each time point. Based on this, we reconstruct a multi-time quasi-probability distribution (QPD) that correctly recovers the probability distributions at the respective time points. Our approach can also be applied to simultaneously extract exponentially many correlation functions with various time-orderings. We provide a proof-of-principle experimental demonstration of the proposed protocol using a dual-species trapped-ion system by employing $^{171}\rm{Yb}^+$ and $^{138}\rm{Ba}^+$ ions as the system and the ancilla, respectively. Multi-time measurements are performed by repeated initialization and detection of the ancilla state without directly measuring the system state. The two- and three-time QPDs and correlation functions are reconstructed reliably from the experiment, negativity and complex values in the QPDs clearly indicate a contribution of the quantum coherence throughout dynamics., Comment: 9 pages, 6 figures

Two-dimensional (2D) quantum magnetism is a paradigm in strongly correlated many-body physics. The understanding of 2D quantum magnetism can be expedited by employing a controllable quantum simulator that faithfully maps 2D-spin Hamiltonians. The 2D quantum simulators can exhibit exotic phenomena such as frustrated quantum magnetism and topological order and can be used to show quantum computational advantages. Many experimental platforms are being developed, including Rydberg atoms and superconducting annealers. However, with trapped-ion systems, which showed the most advanced controllability and quantum coherence, quantum magnetism was explored in one-dimensional chains. Here, we report simulations of frustrated quantum magnetism with 2D ion crystals. We create a variety of spin-spin interactions for quantum magnets, including those that exhibit frustration by driving different vibrational modes and adiabatically prepare the corresponding ground states. The experimentally measured ground states are consistent with the theoretical predictions and are highly degenerate for geometrically frustrated spin models in two dimensions. Quantum coherence of the ground states is probed by reversing the time evolution of the B-field to the initial value and then measuring the extent to which the remaining state coincides with the initial state. Our results open the door for quantum simulations with 2D ion crystals., Comment: 11 pages, 9 figures

Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the first observation of quantum contextuality simultaneously free of the detection, sharpness and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of $100\%$ and a measurement repeatability $>98\%$. The compatibility loophole is closed by targeting correlations between observables for two different ions in a Paul trap, a $^{171}\mathrm{Yb}^{+}$ ion and a $^{138}\mathrm{Ba}^{+}$ ion, chosen so measurements on each ion use different operation laser wavelengths, fluorescence wavelengths, and detectors. The experimental results show a violation of the bound for the most adversarial noncontextual models and open a new way to certify quantum systems., Comment: 8 pages, 6 figures, 1 table, 65 references

Realizing a long coherence time quantum memory is a major challenge of current quantum technology. Here, we report a single \Yb ion-qubit memory with over one hour coherence time, an order of improvement compared to the state-of-the-art record. The long coherence time memory is realized by addressing various technical challenges such as ambient magnetic-field noise, phase noise and leakage of the microwave oscillator. Moreover, systematically study the decoherence process of our quantum memory by quantum process tomography, which enables to apply the strict criteria of quantum coherence, relative entropy of coherence. We also benchmark our quantum memory by its ability in preserving quantum information, i.e., the robustness of quantum memory, which clearly shows that over 6000 s, our quantum memory preserves non-classical quantum information. Our results verify the stability of the quantum memory in hours level and indicate its versatile applicability in various scenarios., Comment: 7 pages, 7 figures

We theoretically and experimentally investigate double electromagnetically induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for \Yb ions with clock state, for which EIT cooling has not been realized like many other ions with a simple $\Lambda$-scheme. A cooling rate of $\dot{\bar n}=34~(\pm1.8)~\rm{ms}^{-1}$ and a cooling limit of $\bar n=0.06~(\pm 0.059)$ are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12 ions crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences., Comment: 17 pages, 11 figures

We present a simple Paul trap that stably accommodates up to a couple of dozens of \ensuremath{^{171}\mathrm{Yb}^+~} ions in a stationary two-dimensional lattice. The trap is constructed on a single plate of gold-plated laser-machined alumina and can produce a pancake-like pseudo-potential that makes ions form a self-assembly two-dimensional crystal which locates on the plane composed of axial and one of the transverse axes with around 5 $\mu$m spacing. We use Raman laser beams to coherently manipulate these ion-qubits where the net propagation direction is perpendicular to the plane of the crystal and micromotion. We perform the coherent operations and study the spectrum of vibrational modes through globally addressed Raman laser-beams on a dozen of ions in the two-dimensional crystal. We measure the amplitude of micro-motion by comparing the strengths of carrier and micro-motion sideband transitions with three ions, where the micro-motion amplitude is similar to that of a single ion. The spacings of ions are small enough for large coupling strengths, which is a favorable condition for two-dimensional quantum simulation., Comment: 10 pages, 9 figures

The output randomness from a random number generator can be certified by observing the violation of quantum contextuality inequalities based on the Kochen-Specker theorem. Contextuality can be tested in a single quantum system, which significantly simplifies the experimental requirements to observe the violation comparing to the ones based on nonlocality tests. However, it is not yet resolved how to ensure compatibilities for sequential measurements that is required in contextuality tests. Here, we employ a modified Klyachko-Can-Binicio\u{g}lu-Shumovsky contextuality inequality, which can ease the strict compatibility requirement on measurements. On a trapped single \Ba ion system, we experimentally demonstrate violation of the contextuality inequality and realize self-testing quantum random number expansion by closing detection loopholes. We perform $1.29 \times 10^8$ trials of experiments and extract the randomness of $8.06 \times 10^5$ bits with a speed of 270 bits s$^{-1}$. Our demonstration paves the way for the practical high-speed spot-checking quantum random number expansion and other secure information processing applications., Comment: Main text: 12 pages, 5 figures, Supplementary Materials: 5 pages