High-Fidelity Two-Qubit Gates Using a Microelectromechanical-System-Based Beam Steering System for Individual Qubit Addressing

A site-resolved two-dimensional quantum simulator with hundreds of trapped ions

A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation1. As one of the leading physical platforms for quantum information processing, the ion trap has achieved a quantum simulation of tens of ions with site-resolved readout in a one-dimensional Paul trap2-4 and of hundreds of ions with global observables in a two-dimensional (2D) Penning trap5,6. 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 the measured two-spin correlations 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 noisy intermediate-scale quantum algorithms7,8 using 2D ion trap quantum simulators.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Realization of a crosstalk-avoided quantum network node using dual-type qubits of the same ion species

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 can be subject to inefficient sympathetic cooling due to the mass mismatch of the ions. 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 171Yb+ 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.

Quantum simulation of conical intersections using trapped ions

Conical intersections often control the reaction products of photochemical processes and occur when two electronic potential energy surfaces intersect. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface, and although conical intersections have been observed experimentally, the geometric phase has not been directly observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The ion's internal state serves as the electronic state, and the motion of the atomic nuclei is encoded into the motion of the ions. The simulated electronic potential is constructed by applying state-dependent optical forces to the ion. We experimentally observe a clear manifestation of the geometric phase using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees for quantum simulation of chemical reactions.

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

Simulating the real-time dynamics of gauge theories represents a paradigmatic use case to test the hardware capabilities of a quantum computer, since it can involve non-trivial input states' preparation, discretized time evolution, long-distance entanglement, and measurement in a noisy environment. We implemented an algorithm to simulate the real-time dynamics of a few-qubit system that approximates the Schwinger model in the framework of lattice gauge theories, with specific attention to the occurrence of a dynamical quantum phase transition. Limitations in the simulation capabilities on IBM Quantum were imposed by noise affecting the application of single-qubit and two-qubit gates, which combine in the decomposition of Trotter evolution. The experimental results collected in quantum algorithm runs on IBM Quantum were compared with noise models to characterize the performance in the absence of error mitigation.

Robust Two-Qubit Gates for Trapped Ions Using Spin-Dependent Squeezing

Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.

Cold-atom shaping with MEMS scanning mirrors

We demonstrate the integration of micro-electro-mechanical-systems (MEMS) scanning mirrors as active elements for the local optical pumping of ultra-cold atoms in a magneto-optical trap. A pair of MEMS mirrors steer a focused resonant beam through a cloud of trapped atoms shelved in the F = 1 ground-state of ⁸⁷Rb for spatially selective fluorescence of the atom cloud. Two-dimensional control is demonstrated by forming geometrical patterns along the imaging axis of the cold atom ensemble. Such control of the atomic ensemble with a microfabricated mirror pair could find applications in single atom selection, local optical pumping, and arbitrary cloud shaping. This approach has significant potential for miniaturization and in creating portable control systems for quantum optic experiments.

Crosstalk Suppression in Individually Addressed Two-Qubit Gates in a Trapped-Ion Quantum Computer

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual Xσ[over ^]_{ϕ} interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians.

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.