We propose the use of two-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions. This approach involves placing arrays of microstructured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction. We solve for the normal modes of ion motion in such arrays and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections. We use these techniques to investigate the feasibility of quantum simulation and quantum computation in fixed ion lattices. In homogeneous arrays, we show that sufficiently dense arrays are achievable, with axial, magnetron, and cyclotron motions exhibiting interion dipolar coupling with rates significantly higher than expected decoherence. With the addition of laser fields, these can realize tunable-range interacting spin Hamiltonians. We also show how local control of potentials allows isolation of small numbers of ions in a fixed array and can be used to implement high-fidelity gates. The use of static trapping fields means that our approach is not limited by power requirements as the system size increases, removing a major challenge for scaling which is present in standard radio-frequency traps. Thus, the architecture and methods provided here appear to open a path for trapped-ion quantum computing to reach fault-tolerant scale devices.
We propose the use of two-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions. This approach involves placing arrays of microstructured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction. We solve for the normal modes of ion motion in such arrays and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections. We use these techniques to investigate the feasibility of quantum simulation and quantum computation in fixed ion lattices. In homogeneous arrays, we show that sufficiently dense arrays are achievable, with axial, magnetron, and cyclotron motions exhibiting interion dipolar coupling with rates significantly higher than expected decoherence. With the addition of laser fields, these can realize tunable-range interacting spin Hamiltonians. We also show how local control of potentials allows isolation of small numbers of ions in a fixed array and can be used to implement high-fidelity gates. The use of static trapping fields means that our approach is not limited by power requirements as the system size increases, removing a major challenge for scaling which is present in standard radio-frequency traps. Thus, the architecture and methods provided here appear to open a path for trapped-ion quantum computing to reach fault-tolerant scale devices.
We propose the use of two-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions.This approach involves placing arrays of microstructured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction.We solve for the normal modes of ion motion in such arrays and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections.We use these techniques to investigate the feasibility of quantum simulation and quantum computation in fixed ion lattices.In homogeneous arrays, we show that sufficiently dense arrays are achievable, with axial, magnetron, and cyclotron motions exhibiting interion dipolar coupling with rates significantly higher than expected decoherence.With the addition of laser fields, these can realize tunable-range interacting spin Hamiltonians.We also show how local control of potentials allows isolation of small numbers of ions in a fixed array and can be used to implement highfidelity gates.The use of static trapping fields means that our approach is not limited by power requirements as the system size increases, removing a major challenge for scaling which is present in standard radio-frequency traps.Thus, the architecture and methods provided here appear to open a path for trapped-ion quantum computing to reach fault-tolerant scale devices.
Trapped-ion quantum information processors are among the leading candidates to realise large-scale quantum computing. In trying to scale the number of confined ions in radio-frequency (rf) traps, several challenges arise due to the use of the rf fields. Ion placement is restricted to the vicinity of the rf null in order to minimise excess micromotion. Miniaturisation of trap geometries is desirable for increased ion density, but is at odds with the need to deliver high-voltage rf and tolerate the resulting power dissipation. We demonstrate a platform based on Penning traps, where ions are radially confined using a strong magnetic field. Static electric fields are then sufficient to provide confinement along the axis. We confine a single9Be + ion in a 3 T magnetic field using a micro-fabricated trap and realise transport to arbitrary positions above the trap chip. Furthermore, we show full quantum control of the spin and motion of the trapped ion. Ground state cooling of all motional modes is achieved and we measure the rate of motional heating due to electric field noise in the absence of an rf drive, obtaining noise levels below those observed in similar rf traps. Since only static fields are required for ion confinement, we can temporarily electrically isolate the trap electrodes from technical noise using switches, further reducing the observed electric field noise.
Abstract Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, because of high-fidelity quantum gates and long coherence times1–3. However, the use of radio-frequencies presents several challenges to scaling, including requiring compatibility of chips with high voltages4, managing power dissipation5 and restricting transport and placement of ions6. Here we realize a micro-fabricated Penning ion trap that removes these restrictions by replacing the radio-frequency field with a 3 T magnetic field. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the quantum charge-coupled device architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.
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.
Realising large-scale quantum computation in the near future will require increasing the number of low-error two-qubit gates that can be implemented on a quantum computer before decoherence. One of the biggest challenges facing current trapped ion quantum computers is implementing high-speed two-qubit operations, whilst increasing the number of qubits. One of the most promising proposals for overcoming current limitations is the use of ultra-fast pulses to implement fast two-qubit gates between nearest-neighbour pairs of ions. In this thesis, I investigate these ‘fast gates’ in two-dimensional arrays of microtraps, each containing a single ion. I argue that two-dimensional architectures allow for a significant reduction in the number of two-qubit gates required for a particular computation, as compared to one-dimensional ion chains. I demonstrate this reduction for a quantum simulation of a 40-mode Fermi-Hubbard Hamiltonian. I develop an efficient scheme that allows fast gates to be numerically optimised for two-dimensional geometries. I find that this optimisation scheme is capable of designing gates that are faster, higher fidelity, and require lower laser repetition rates. Using this scheme, I find that high-speed two-qubit gates can be optimised for two-dimensional architectures, with fidelities well above thresholds required for fault tolerant error correction, around 99.99%. Furthermore, I find that fast gates in these architectures are robust to the presence of large numbers of surrounding ions. Following previous studies [1, 2] which have identified pulse imperfections as a dominant source of error in fast gates, I perform a worst-case error analysis. I find the fast gates presented in this thesis to require very small errors in single-qubit rotations, and I present recommendations for achieving those requirements. I also investigate other experimental considerations, and make recommendations for overcoming other technical challenges in realising fast gates.
Quantum computers have the potential to solve problems far beyond the reach of classical computers by using the principles of superposition and entanglement. However, existing platforms face challenges such as short coherence times, interference from the environment, and difficulties in scaling up.Trapped electrons in a planar Penning trap offer a promising alternative. Unlike other qubits, electrons do not interact with nuclear spins, which helps maintain quantum states for much longer. Additionally, their strong confinement allows for fast and precise quantum operations. In our approach, electron spins serve as logical qubits, while their motional states are used for entanglement. Our setup consists of 2-dimensional array of micro-sized Penning traps fabricated on a ceramic chip, placed inside a 1T superconducting magnet and cooled in a dilution refrigerator to reach millikelvin temperatures. This extreme cooling reduces unwanted motion and makes it possible to entangle electron spins and perform quantum gates with high accuracy. At Inter-University Accelerator Centre (IUAC), New Delhi, India, we are developing a prototype planar Penning trap. This new system offers a stable, scalable, and high-coherence platform for quantum computing.