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Journal of Modern Optics

Towards (scalable) quantum simulations in ion traps

Tobias Schaetz, Axel Friedenauer, H. Schmitz, L. Petersen, S. Kahra

Published Nov 10, 2007• 53 citations
Publisher

Abstract

Experiments directed towards the development of an analogue quantum simulator based on trapped atomic magnesium ions are described. We report on the required initialization including ground state cooling of 25Mg+ ions for the first time—parallel to the group at NIST/Boulder. We discuss basic operations to implement quantum spin Hamiltonians like a one-dimensional quantum Ising model and some challenges to be addressed in reaching for larger scale and higher dimensional devices.

DOI
10.1080/09500340701639631

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Experiments directed towards the development of an analogue quantum simulator based on trapped atomic magnesium ions are described. We report on the required initialization including ground state cooling of 25Mg+ ions for the first time—parallel to the group at NIST/Boulder. We discuss basic operations to implement quantum spin Hamiltonians like a one-dimensional quantum Ising model and some challenges to be addressed in reaching for larger scale and higher dimensional devices.
The basic requirements for quantum computing and quantum simulation (single‐ and multi‐qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large‐scale information processor will require synthesis of these elements and implementation of high‐fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi‐zone arrays of traps that would allow highly‐parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schrödinger’s cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.
In a proof-of-principle experiment, we simulate the dynamics of a quantum spin system in an ion trap. Following a theoretical proposal by D. Porras and I. Cirac, we use a system of ground state cooled trapped ions to simulate and study the dynamics of a quantum-mechanical system, or more precisely, the dynamics of a quantum spin Hamiltonian. We implement the smallest non-trivial quantum spin Hamiltonian, the quantum Ising model for two spins. Each spin is represented by two hyperfine ground levels of trapped 25Mg+ ions. The interaction with an external magnetic field is simulated by coherently coupling these hyperfine levels via laser and radiofrequency radiation. The spin-spin interaction is simulated via optical dipole forces, where the effective interaction is mediated by the phonons of the linear ion chain. We demonstrate the adiabatic evolution from a paramagnetically ordered system to ferromagnetic order. The final state of this adiabatic transition is a superposition state of the two degenerate spin configurations of ferromagnetic order Psi_final = 1/sqrt(2) (|up up> + |down down>) with a quantum magnetisation of 98%. We also show the transition from paramagnetic to antiferromagnetic order with the final state Psi_final = 1/sqrt(2) (|up down> + |down up>). Moreover, we prove that this transition which is to become a quantum phase transition in the thermodynamic limit of infinitely many spins, is driven by quantum fluctuations which dominate the dynamics of such systems at the absolute zero-point of temperature rather than thermal fluctuations which are absent at 0 K. This is verified by the fact that the final state of our adiabatic evolution is entangled, close to a Bell state at a fidelity exceeding 88%. The set of tools presented in this thesis might serve as a basis for larger scale quantum simulations which might help in gaining insight into many-particle effects that are intractable on classical computers such as spin frustration in triangular lattices or high-Tc superconductivity.
This thesis provides an overview of an approach to quantum simulations using magnesium-25 ions stored in a linear Paul trap as the carriers of quantum information. Their quantum state is manipulated and read out using ultraviolet laser beams. Several important steps towards realising the first experiments have been undertaken, the most striking of which is cooling the ions to their motional ground state. We describe a first experiment simulating cosmological particle creation in the Early Universe and discuss the expected results.
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.
The purpose of this paper is to evaluate the possibility of constructing a large-scale storage-ring-type ion-trap system capable of storing, cooling, and controlling a large number of ions as a platform for scalable quantum computing (QC) and quantum simulations. In such a trap, the ions form a crystalline beam moving along a circular path with a constant velocity determined by the frequency and intensity of the cooling lasers. In this paper, we consider a large leap forward in terms of the number of ions that serve as qubits in QC, from fewer than 100 available in state of the art linear ion-trap devices today to an order of 1051{0}^{5}105 crystallized ions in the storage-ring setup. This new trap design unifies two different concepts: the storage rings of charged particles and the linear ion traps used for QC and mass spectrometry. In this paper, we use the language of particle accelerators to discuss the ion state and dynamics. We outline the differences between the above concepts, analyze challenges of the large ring with a revolving chain of ions, and propose goals for the research and development required to enable future quantum computers with 1000 times more qubits than available today. The challenge of creating such a large-scale quantum system while maintaining the necessary coherence of the qubits and the high fidelity of quantum logic operations is significant. Performing analog quantum simulations may be an achievable initial goal for such a device. Quantum calculations and simulations of complex quantum systems will move forward both the fundamental science and the applied research. Nuclear and particle physics, many-body quantum systems, lattice gauge theories, and nuclear structure calculations are just a few examples in which a large-scale quantum simulation system will become a very powerful tool to move forward our understanding of nature.