C. Zhang

Molecules containing short-lived isotopes, namely radioactive molecules, are among the most promising candidates for probing new physics beyond the Standard Model, although their production and spectroscopic measurements remain technically challenging. Here, we demonstrate an integrated methodology that combines formation of molecular ion beams in a radiofrequency quadrupole cooler-buncher with collinear laser spectroscopy. As a proof-of-principle experiment, we successfully produce molecular ions such as $\rm BaF^+$ and $\rm YbF^+$ via in-trap ion-molecule reactions and perform high-resolution laser spectroscopy of the target molecule $\rm ^{138}BaF$. Vibrational and rotational structures of $\rm ^{138}BaF$ across different electronic states are obtained using resonance-enhanced multiphoton ionization schemes, confirming the feasibility of the proposed methodology. This work establishes a practical route for future formation and spectroscopic studies of short-lived radioactive molecules, such as those containing $\rm ^{225}Ra$, at radioactive ion beam facilities.

The maintenance of quantum entanglement lays the elementary building block of quantum information processing, requiring an integration of long coherence time, sufficient storage capacity, and high-fidelity entangling gates. Here we encode two-qubit entangled states into the decoherence-free subspaces (DFS) of four ions in a cryogenic trap. By crosstalk-free sympathetic cooling under dual-type encoding and multi-state detection which discards the collision-induced leakage error, we achieve a storage lifetime of about one hour for the entangled logical states. We further study the second-order DFS and show its advantage in suppressing the spatially nonuniform noise over the first-order DFS. Our work paves the way for applications of DFS quantum memories in quantum computing, quantum network and precision measurement.

The dual-type qubit scheme is an emerging method to suppress crosstalk errors in scalable trapped-ion quantum computation and quantum network. Here we report a hardware-economic way to control dual-type $^{171}\mathrm{Yb}^+$ qubits using a single $355\,$nm mode-locked pulsed laser. Utilizing its broad frequency comb structure, we drive the Raman transitions of both qubit types encoded in the $S_{1/2}$ and the $F_{7/2}$ hyperfine levels, and probe their carrier transitions and the motional sidebands. We further demonstrate a direct entangling gate between the two qubit types. Our work can simplify the manipulation of the $^{171}\mathrm{Yb}^+$ qubits both at the hardware and the software level.

A quantum memory is an essential element for quantum computation, quantum network and quantum metrology. Previously, a single-qubit quantum memory with a coherence time of about an hour has been realized in a dual-species setup where a coolant ion provides sympathetic cooling for a memory ion of different species. However, the frequent random position hopping between the ions in the room-temperature trap limits the technique there only applicable to single-qubit storage. Here we report a multi-ion quantum memory in a cryogenic trap based on the dual-type scheme, and demonstrate a coherence time above two hours for a logical qubit encoded in the decoherence-free subspace, i.e. two-ion entangled states, after correcting the dominant leakage error. Our scheme alleviates the necessity of an ultra-stable frequency reference for the stored qubit, and has a preferable scalability owing to the same mass of the metastable-state memory ions and the ground-state coolant ion.

Trapped ions constitute a promising platform for implementation of a quantum network. Recently, a dual-type qubit scheme has been realized in a quantum network node where the communication qubits and the memory qubits are encoded in different energy levels of the same ion species, such that the generation of ion-photon entanglement on the communication qubits has negligible crosstalk error on the preloaded quantum information in the memory qubits. However, to achieve the versatile applications of a quantum network, a crucial component of the dual-type node, namely the entangling gate between the communication and the memory qubits, is still missing. Here we report a dual-type quantum network node equipped with ion-photon entanglement generation, crosstalk-free quantum memory and entangling gates between the dual-type qubits simultaneously. We demonstrate its practical applications including the quantum state teleportation and the preparation of multipartite entangled state. Our work achieves the necessary components of a dual-type quantum network node and paves the way toward its applications in a large-scale quantum internet.

The requirement for Hermiticity in quantum mechanics ensures the reality of energies, while the parity-time symmetry offers an alternative route to achieve this goal. Interestingly, in a three-level system, the parity-time symmetry-breaking can lead to a third-order exceptional point with distinctive topological properties and enhanced sensitivity. To experimentally implement this in open quantum systems, it is essential to introduce two well-controlled loss channels. However, the requirement for these two loss channels presents a challenge in experimental implementation due to the lack of methods to realize the dynamics governed by an effective non-Hermitian Hamiltonian. Here we address the challenge by employing two approaches to eliminate the effects of quantum jump terms so that the dynamics is governed by an effective non-Hermitian Hamiltonian in a dissipative trapped ion with two loss channels. Based on this, we experimentally observe the parity-time symmetry-breaking-induced third-order exceptional point through non-Hermitian absorption spectroscopy. In particular, we perform quantum state tomography to directly demonstrate the coalescence of three eigenstates into a single eigenstate at the exceptional point. Finally, we identify an intrinsic third order Liouvillian exceptional point associated with a parity-time symmetry breaking via quench dynamics. Our experiments can be extended to observe other non-Hermitian phenomena involving more than two levels and potentially find applications in quantum information technology.

Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity universal gate operations in the noisy intermediate-scale quantum era. Here we demonstrate the Hamiltonian learning of a two-dimensional ion trap quantum simulator with 300 qubits. We employ global manipulations and single-qubit-resolved state detection to efficiently learn the all-to-all-coupled Ising model Hamiltonian, with the required quantum resources scaling at most linearly with the qubit number. Our work paves the way for wide applications of large-scale ion trap quantum simulators.

Two-dimensional (2D) ion crystals have become a promising way to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal.

The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions where a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates the ion trap as a powerful platform for simulating open quantum dynamics with complicated reservoir structures.

A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation. As one of the leading physical platforms for quantum information processing, the ion trap has achieved quantum simulation of tens of ions with site-resolved readout in 1D Paul trap, and that of hundreds of ions with global observables in 2D Penning trap. However, integrating these two features into a single system is still very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner crystal and the sideband cooling of their transverse motion. We demonstrate the quantum simulation of long-range quantum Ising models with tunable coupling strengths and patterns, with or without frustration, using 300 ions. Enabled by the site resolution in the single-shot measurement, we observe rich spatial correlation patterns in the quasi-adiabatically prepared ground states, which allows us to verify quantum simulation results by comparing with the calculated collective phonon modes and with classical simulated annealing. We further probe the quench dynamics of the Ising model in a transverse field to demonstrate quantum sampling tasks. Our work paves the way for simulating classically intractable quantum dynamics and for running NISQ algorithms using 2D ion trap quantum simulators.

Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the portion and the location of different ion species, and can be subject to inefficient sympathetic cooling. Here we demonstrate a trapped-ion quantum network node in the dual-type qubit scheme where two types of qubits are encoded in the $S$ and $F$ hyperfine structure levels of ${}^{171}\mathrm{Yb}^+$ ions. We generate ion photon entanglement for the $S$-qubit in a typical timescale of hundreds of milliseconds, and verify its small crosstalk on a nearby $F$-qubit with coherence time above seconds. Our work demonstrates an enabling function of the dual-type qubit scheme for scalable quantum networks.

We propose and implement a novel scheme for dissipatively pumping two qubits into a singlet Bell state. The method relies on a process of collective optical pumping to an excited level, to which all states apart from the singlet are coupled. We apply the method to deterministically entangle two trapped ${}^{40}\text{Ca}^+$ ions with a fidelity of $93(1)\%$. We theoretically analyze the performance and error susceptibility of the scheme and find it to be insensitive to a large class of experimentally relevant noise sources.

We employ a trapped ion to study quantum contextual correlations in a single qutrit using the 5-observable KCBS inequality, which is arguably the most fundamental non-contextuality inequality for testing Quantum Mechanics (QM). We quantify the effect of systematics in our experiment by purposely scanning the degree of signaling between measurements, which allows us to place realistic bounds on the non-classicality of the observed correlations. Our results violate the classical bound for this experiment by up to 25 standard deviations, while being in agreement with the QM limit. In order to test the prediction of QM that the contextual fraction increases with the number of observables, we gradually increase the complexity of our measurements from 5 up to 121 observables. We find stronger-than-classical correlations in all prepared scenarios up to 101 observables, beyond which experimental imperfections blur the quantum-classical divide.

We use a single trapped-ion qutrit to demonstrate the violation of an input-state-independent non-contextuality inequality using a sequence of randomly chosen quantum non-demolition projective measurements. We concatenate 54 million sequential measurements of 13 observables, and violate an optimal non-contextual bound by 214 standard deviations. We use the same dataset to characterize imperfections including signaling and repeatability of the measurements. The experimental sequence was generated in real time with a quantum random number generator integrated into our control system to select the subsequent observable with a latency below 50 μs, which can be used to constrain hidden-variable models that might describe our results. The state-recycling experimental procedure is resilient to noise, self-correcting and independent of the qutrit state, substantiating the fact that quantumness is connected to measurements as opposed to designated states.