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Simulating 2d Spin Lattices with Ion Crystals

Periodic Reporting for period 1 - SPICY (Simulating 2d Spin Lattices with Ion Crystals)

Reporting period: 2017-09-01 to 2019-02-28

The field of quantum-many body physics investigates systems of particles that interact with each other according to the laws of quantum physics. Examples for such systems are magnetic particles interacting with each other in a solid or electrons interacting with each other in an atom or molecule. While it is often easy to write down equations describing the most important interactions, it can be extremely challenging to analyze the important physical phenomena that arise from these interactions. Exact numerical simulations can be carried out for systems composed of a small number of particles but fail even for systems containing a few tens of particles, due to the computation costs of numerical solving the equations. Quantum simulation is a subfield of quantum information science aiming providing an alternative approach to numerical simulations by using a well-controlled laboratory quantum system as an additional computational resource. In recent years, a number of different experimental platforms, ranging from laser-cooled and trapped atoms and ions to solid-state systems have been investigated as laboratory quantum simulators. Within this project, we aim to develop trapped-ion based quantum simulations to larger numbers of particles by developing an experimental apparatus capable of manipulating two-dimensional ion crystals containing 50-100 particles with quantum control over each individual ion. In the first period of the project, a new apparatus has been designed that is currently being assembled. In parallel, first experiments with small two-dimensional crystals have been carried out in an existing apparatus that have provided input for the development of the new setup. Additionally, experiments have been carried out that demonstrate new methods for the characterization of complex entangled quantum states and their use in variational quantum simulations in which the quantum systems serves as a kind of quantum co-processor for a computer in an optimization problem.

At the level of the individual constituents of matter, the behaviour of our world is governed by quantum mechanics. However, the effects predicted by quantum theory are often masked by the strong interactions of the particles with their environment. Thus, the experimental investigation of quantum effects requires the creation of well-controlled quantum systems, which are well isolated from the rest of the world, and whose quantum states can be efficiently prepared and measured. This endeavour, the creation of highly-controlled quantum systems in the laboratory, has made great progress over the last thirty years. While this research field started with studies of the physics of an individual quantum system like an ion or an atom, the focus has shifted more and more to the investigation of highly controlled quantum many-body systems.
Quantum many-body systems are being studied for at least two reasons: on the one-hand side, simple interactions between identical quantum particles can give rise to a bewildering complexity of emergent physical phenomena, like for example quantum phases at low temperature, which are theoretically hard to understand or to predict. On the other hand, the processing of information based on the laws of quantum physics has led to a new model of computation whose computational power is superior to the classical one.
In a quantum processor, information is encoded in a collection of two-level quantum systems (qubits) and processed by a series of unitary operations coupling the qubits. This scheme requires an interacting quantum many-body system with near-perfect control over the interaction between its individual constituents. Following the seminal work of I. Cirac and P. Zoller, many research groups set out to demonstrate basic quantum operations in trapped ions and other quantum systems. Currently, systems with up to twenty qubits have been demonstrated and quantum gates entangling two qubits have been achieved with fidelities of up to 9
Overview:
The following subsection describe the work performed from the beginning of the project to the end of the period covered by the report and the main result. Broadly, they fall into two categories: First and foremost, the main focus of our work has been on the design of a new experimental apparatus, which often necessitated extended numerical simulation, and the purchase of the required equipment, which often involved technical discussions with companies about how to meet the criteria of our design. Secondly, experiments have been carried out in parallel in an existing apparatus, that was used to (a) develop methods for characterizing and using multi-qubit entangled states and testing them with linear ion strings and (b) to carry out first experiments with small two-dimensional ion crystals to obtain input needed for the new setup.


Setting up of the new experiments

Ion trap: development and setup design

A novel micro fabricated ion trap constitutes the centerpiece of the new ion-trap quantum simulator that is being built in the course of the SPICY project. In ion trap based quantum information experiments one of the most widely and reliably used trap designs is a 3D linear Paul trap. Here, static voltages as well as voltages oscillating at several tens of MHz are applied to the ion trap electrodes to confine ions, usually a 1 dimensional crystal of ions, in three spatial directions. SPICY aims at trapping and investigating 2 dimensional ion crystals, which demands for the conventional 3D Paul trap design to be modified and requires microfabrication techniques to be applied in the trap manufacturing process.
Here provided is a short summary of the work performed, related to ion trap development and setup design, more details can be found below: Over the course of the past year, we created two novel 3D linear Paul trap designs for SPICY, which we optimized via computer simulations. Test electrode structures were fabricated and metallized in collaboration with the company Translume to quantify the feasibility of our novel ion trap designs and our approach of electrode separation. Eventually, three ion traps were commissioned, one of which has yet to be installed in the laboratory. Moreover, we designed a helical resonator which will be employed to amplify the radio-frequency (RF) voltages that will be applied to the ion trap electrodes, as required for achieving sufficiently strong confinement of the ions in the trap. Finally, we designed a custom vacuum vessel which will be housing our ion trap and allows for sufficient access for laser beams, electrical feedthroughs and connection to vacuum pumping equipment.

Ion trap design

General aspects of the novel Paul trap design for SPICY:

Figure 2:
uploaded separately

A simple 3D linear Paul trap consists of three pairs of electrodes – two pairs of long blades and one pair of endcap electrodes (see figure 2a): Typically, an RF voltage is applied to one pair of blades, to create a pseudopotential in which the ions are trapped in the radial directions. Applying a static voltage to the second pair of blades lifts the degeneracy of the trap frequencies, which quantify the trapping confinement, in the two radial directions. Additionally, a positive static voltage is applied to the endcap electrodes to confine the ions in the axial direction. Typically, the axial confinement in such a 3D linear Paul trap is much weaker than the confinement in the two radial directions, in order to trap 1D strings of ions. However, it is also possible to create planar ion crystals, when the confinement in two directions is much weaker than in the third direction. In practice this can e.g. be achieved by applying high positive static voltages along one direction, the strongly confining one, to squeeze the crystal into a pancake like structure. SPICY aims at trapping 2d ion crystals in the plane that is spanned between the two RF blades and the axial direction, which can be achieved by applyi
While it is difficult to quantify progress beyond state of the art in the early stage of delevoping a new apparatus that has not been tested yet, the project has already defined a new state of the art in the experiments analyzing and using complex multi-ion entangled states:

The implementation of random measurements for analyzing the purity of an entangled state is an important tool for assessing how close to unitary the entangling interactions used for creating the state are. While the method is not efficient in the sense of requiring measurement resources that scale polynomially with the number of qubits, it has a more favorable scaling than full quantum state tomography and enables an analysis of states that is assumption-free with respect to the state to be analyzed. We believe that the method can be experimentally applied to systems with up to 20 qubits. Carrying out a state analysis on 20-qubit systems and finding them to be close to a pure state would be an important step in building up confidence in the quality of entangling interactions to be used for entangling larger systems that can no longer be analyzed with this measurement protocol.

Another experiment demonstrating results beyond state of the art is the implementation of 20-qubit variational quantum simulation. The demonstration that a state with high overlap with the ground state of a Hamiltonian can be found variationally in a 15-dimensional parameter space shows the potential of analogue quantum simulations for the investigation of Hamiltonians that go beyond the ones that can be directly realized in the experimental setup.

A few more achievements are worth mentioning that are more on the technical side: we are optimistic that the development of a monolithic three-dimensional segmented trap will provide an interesting tool for trapping and handling rather large ion crystals (as opposed to microtraps that were developed for transporting and splitting linear strings of crystals). The demonstration of polarization gradient cooling of large ion crystals adds another cooling technique to the set of available laser cooling methods that is easy to implement, offers fast cooling rates and enables sub-Doppler cooling of vibrational modes over a fairly large frequency range. Finally, the cooling of two-dimensional zig-zag crystals to low temperatures and the observation that the cooled crystals stay cold over tens of milliseconds constitute a first step demonstrating the preparation of 2d-crystals at low temperatures.

Regarding the question of expected results until the end of the project, we expect to have an experimental apparatus with single-qubit control at our disposition that is capable of creating complex entangled states of 50-100 qubits whose properties can no longer be exactly simulated using numerical methods as outlined in the proposal describing this project.
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