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

Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation.

Experimental progress in controlling and manipulating trapped atomic ions has opened the door for a series of proof-of-principle quantum simulations. This article reviews these experiments, together with the methods and tools that have enabled them, and provides an outlook on future directions in the field.

Preparing finite-temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu et al., PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite-temperature phase transition in the long-range transverse-field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions.

Designing unconventional interactions between single phonons and spins is fascinating for its applications in quantum phononics. Here we propose a reliable scheme for coupling spins and phonons in phononic dimer and trimer lattices, with the combination of solid-state defects and diamond phononic (optomechanical) crystals. The dimer and trimer lattices used are an array of coupled phononic cavities with spatially modulated hopping rates. We predict a series of unconventional sound-matter interaction phenomena in this hybrid quantum system. In the dimer lattice we show the formation of chiral spin-phonon bound states and topology-dependent phononic collective radiation. While in the trimer lattice, chiral bound states still exist and the spin relaxation is sublattice dependent. The chiral bound states existing in both types of lattices are robust to a large amount of disorder, which can mediate chiral and robust spin-spin interactions. This work provides a promising platform for phonon-based quantum information processing and quantum simulation.

Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.

Next generation ion traps will likely need to support tens if not hundreds of ions in order to achieve several logical qubits. As we scale to those sizes, the same problems we face now – rf dissipation, control I/O, and optical access – will only grow and become more complicated. While many of these challenges can potentially be solved with technology integration, independently researching the feasibility of that integration and other solutions may help reduce the time and risk in scaling up to larger traps, by testing on smaller less complex devices. We should also consider other fabrication techniques that may help scale to larger devices, such as: through-substrate-vias (TSVs), different metal coatings, exotic rf routing, on chip laser sources, or even a secondary macroscopic trap to reload ions from. To have these technologies ready for full scale integration when we need them, ion traps with some of these capabilities need to be produced now. Developing the rigorous fabrication methods for producing reliable traps takes time and experimentation. We propose developing larger ion traps and reliable integrated technology in conjunction to make both available faster.

The optimization of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimized for the highest ratio of ion–ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a ‘Biot–Savart like law’ method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimization. A method for maximizing the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the polygon radii and separations scale to optimize the ratio between the interaction and decoherence rate. The optimal polygon radius and separation for a 2D lattice is found to be a function of the ratio between radio-frequency (rf) voltage and drive frequency applied to the array. We then provide a case study for 171Yb+ ions to show how a 2D quantum simulator array could be designed.

Fault-tolerant quantum computers promise the simulation of complex quantum systems beyond the reach of classical computation. In contrast, current noisy intermediate-scale quantum devices are constrained by hardware noise. Consequently, quantum simulation methods remain limited in their near-term applicability. Two prominent techniques addressing these challenges are zero-noise extrapolation (ZNE) and incremental structural learning (ISL). In this work, ZNE and ISL are benchmarked for simulating the Trotterized time evolution of two models: the Tavis-Cummings model (TCM) and the Heisenberg spin chain (HSC), using a classically simulated noisy hardware backend. The methods are evaluated on the basis of the accuracy of expectation values relative to noiseless simulations and their resource demands such as circuit depths and shot counts. The impact of noise on optimization routines in ISL, previously underexplored, is also investigated. Results indicate that ISL performs more favorably in HSC systems, consistently surpassing ZNE in expectation value accuracy. Conversely, for the TCM, ISL generally yields lower accuracies despite reduced Trotter circuit depths, with weak interactions often leading to pronounced phase lags or flat expectation curves. Notably, when performing ISL optimization under noiseless conditions, the protocol is generally able to reduce dephasing errors, but average accuracies still vary on the simulated Hamiltonian. Our findings highlight the sensitivity of quantum simulation protocols to the structure of the Hamiltonian encoding system dynamics. Trends across systems suggest that ISL optimization benefits from Trotter circuits with stronger interactions, and that ansatz construction favors isotropic couplings. Moreover, although ISL introduces approximation errors, it demonstrates greater robustness than ZNE in systems with deeper Trotter circuits.

Geometric frustration in two-dimensional Ising models allows for a wealth of exotic universal behavior, both Ising and non-Ising, in the presence of quantum fluctuations. In particular, the triangular antiferromagnet and Villain model in a transverse field can be understood through distinct XY pseudospins, but have qualitatively similar phase diagrams including a quantum phase transition in the (2+1)-dimensional XY universality class. While the quantum dynamics of modestly-sized systems can be simulated classically using tensor-based methods, these methods become infeasible for larger lattices. Here we perform both classical and quantum simulations of these dynamics, where our quantum simulator is a superconducting quantum annealer. Our observations on the triangular lattice suggest that the dominant quench dynamics are not described by the quantum Kibble-Zurek scaling of the quantum phase transition, but rather a faster coarsening dynamics in an effective two-dimensional XY model in the ordered phase. Similarly, on the Villain model, the scaling exponent does not match the Kibble-Zurek expectation. These results demonstrate the ability of quantum annealers to perform coherent quantum dynamics simulations that are hard to classically scale beyond small systems, and open the avenue to predictive simulations of the dynamics of Ising magnetic materials on quantum simulators.

Fano resonances in photonics arise from the coupling and interference between two resonant modes in structures with broken symmetry. They feature an uneven and narrow and tunable lineshape and are ideally suited for optical spectroscopy. Many Fano resonance structures have been suggested in nanophotonics over the last ten years, but reconfigurability and tailored design remain challenging. Herein, an all-optical "pick-and-place" approach aimed at assembling Fano metamolecules of various geometries and compositions in a reconfigurable manner is proposed. Their coupling behavior by in situ dark-field scattering spectroscopy is studied. Driven by a light-directed opto-thermoelectric field, silicon nanoparticles with high-quality-factor Mie resonances (discrete states) and low-loss BaTiO3 nanoparticles (continuum states) are assembled into all-dielectric heterodimers, where distinct Fano resonances are observed. The Fano parameter can be adjusted by changing the resonant frequency of the discrete states or the light polarization. Tunable coupling strength and multiple Fano resonances by altering the number of continuum states and discrete states in dielectric heterooligomers are also shown. This work offers a general design rule for Fano resonance and an all-optical platform for controlling Fano coupling on demand.

A modifled Y -parameters approach is proposed to model the behavior of coupled oscillator arrays (COA's). A coupling network with tunable coupling strength is proposed, which has a near- constant input conductance, to ensure the oscillation condition under difierent attenuation levels. The parameters of oscillators and the coupling network are derived on the TSMC 0.18m technology, and their Y parameters are extracted around 10GHz for illustration. After being verifled with full- circuit simulations and other behavior models, including the Adler's equation and the conventional Y - parameters approach, this method is applied to estimate the maximum allowable number of oscillators that can be coupled together. The inter-element phase shift of a COA is controlled by tuning the free-running frequencies of oscillators at both ends. Injection signals with proper phases are proposed to synchronize multiple COA's into a bigger COA.

Tunable Coupling Strength between Two Tamm Plasmons in the Ultraviolet Region

Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods. Published by the American Physical Society 2024

The understanding of quantum mechanical systems is essential to modern physics and its applications. However, already for entangled systems of a few tens of constituents, exact numerical simulations on classical computers can become impossible. Quantum simulators based on well-controlled quantum system might provide the only effective approach to these systems. Trapped atomic ions offer a uniquely precise and controllable platform. They are used as platforms for, e.g., future quantum computers, quantum simulators, and extremely precise clocks. Quantum-simulation problems of interest and out-of-reach for modern theoretical methods include the dynamics of one-dimensional systems on long time scales and more-than-one dimensional systems with long-range interaction. For the latter, two-dimensional arrays of ions, individually trapped and controlled above microfabricated surface-electrode traps, present a promising approach. In the first realizations so far, the inter-site distance between the ions was too large to allow for sufficient inter-site coupling. We aim for a scalable approach to an analog quantum simulator based on a two-dimensional array of individually trapped ions. As a first demonstration, we operate an array of three magnesium ions in triangular arrangement with a side-length of 40µm. Therein, we previously demonstrated the individual control of internal (electronic) and external (motional) degrees of freedom of the ions. Here, we present the first realization of inter-site coupling in the two-dimensional array. We demonstrate the coupling by a transfer of large coherent states of motion between the sites. We investigate the influence of the amplitude of these motional states in the anharmonic trapping potential and extrapolate to future experiments on the single-phonon level. We apply the real-time control of the coupling and concatenate the two-site coupling to transfer motional excitation between all three sites of the array. To demonstrate the scalability of our techniques, we couple all three sites simultaneously and investigate the evolution of an initial excitation at one and two sites of the array. The latter shows interference effects of the different pathways in the triangle. Current motional heating rates on the order of the inter-site coupling, preclude working with single phonons near the motional ground-state. We present a new experimental apparatus and vacuum chamber which will allow in-situ cleaning of surface-electrode traps. This has shown to reduce motional heating rates by two orders of magnitude. In this apparatus, we additionally realize a magnetic-field insensitive qubit in 25Mg+ with a coherence time exceeding six seconds. We generate the magnetic field around 10.9mT by a hybrid magnet assembly based on solid-state magnets and fine-tuned by electric coils. Once we have reduced the heating rate in the triangle trap array using the new setup, first quantum simulation experiments, investigating spin-frustration or artificial gauge fields, will come in reach. Here our triangle represents a basic, scalable, building block of future latices designed at will.

We consider the $d$-dimensional transverse-field Ising model with power-law\ninteractions $J/r^{d+\\sigma}$ in the presence of a noisy longitudinal field\nwith zero average. We study the longitudinal-magnetization dynamics of an\ninitial paramagnetic state after a sudden switch-on of both the interactions\nand the noisy field. While the system eventually relaxes to an\ninfinite-temperature state with vanishing magnetization correlations, we find\nthat two-time correlation functions show aging at intermediate times. Moreover,\nfor times shorter than the inverse noise strength $\\kappa$ and distances longer\nthan $a(J/\\kappa)^{2/\\sigma}$ with $a$ being the lattice spacing, we find a\ncritical scaling regime of correlation and response functions consistent with\nthe model A dynamical universality class with an initial-slip exponent\n$\\theta=1$ and dynamical critical exponent $z=\\sigma/2$. We obtain our results\nanalytically by deriving an effective action for the magnetization field\nincluding the noise in a non-perturbative way. The above scaling regime is\ngoverned by a non-equilibrium fixed point dominated by the noise fluctuations.\n