# Optimal control for robust ion trap quantum logic

Lead Research Organisation:
Imperial College London

Department Name: Dept of Physics

### Abstract

Minuscule objects that follow the laws of quantum mechanics have the promise of carrying out delicate tasks fundamentally better than macroscopic objects that are bound by the laws of Newtonian classical mechanics. The superposition principle permits individual quantum mechanical objects to follow multiple trajectories in parallel, and pairs (or larger collections) of such objects can be entangled with each other, such that a measurement on one object affects the properties of the other objects even if they are far apart. The superposition principle and entanglement provide the basis for applications like precision metrology or quantum computation that are expected to revolutionise our technology, just like the steam engine or the advent of electricity has done in the past.

The explicit utilisation of these quantum mechanical effects for useful applications, however, requires extremely accurate control over quantum objects and their interaction with their surroundings. Trapped ions are one of the leading systems in this context. Selected energy levels of an ion define a qubit, which is the elementary unit of a quantum computer, just like a classical computer is comprised of many bits. Confined by electric and magnetic trapping fields, ions can be manipulated with laser beams, and the collective motion of strings of ions enables the exchange of information between several qubits. For this to work with high accuracy it is typically required to cool the ions to a temperature close to absolute zero. Once such a temperature has been reached, one makes use of the fact that any manipulation of the ions changes their motional state in order to implement logical operations that define the elementary building blocks of a quantum algorithm.

Since the ions' motion is easily heated by its room-temperature environment, the intentionally induced changes in the motional state can be accompanied by uncontrolled heating processes, and any deviation from the desired change in motional state results in reduced accuracy of the operations being implemented. The goal of the present project is the development and experimental implementation of laser control of trapped ions that achieves desired operations with high accuracy and robustness in the presence of undesired heating and other experimental imperfections.

In a strong collaboration between theory and experiment, control sequences will be developed and tested in a novel ion trap whose parameters can be varied over a wide range. The ability to tune the strength of the interaction between qubits and motion (the Lamb-Dicke parameter) and the strength of thermal effects will allow us to identify the control strategies that deal with each type of imperfection in an ideal fashion. Most current experiments are conducted with a rather weak interaction between qubits and motion, but we aim at the realisation of logical operations between qubits that interact strongly with the motion. The increased manipulation speed that comes with the strong interaction increases the number of logical operations that can be implemented within the limits imposed by finite decoherence time, and as such will help us to move from proof-of-principle experiments to a practical application.

The immediate goal of our work is the improvement in the control of trapped ions for quantum computing, but the advanced control techniques we will develop directly apply to any type of coherent manipulation of trapped ions. Since strong interactions between qubits are beneficial for fast information transfer but challenging for the implementation of accurate manipulations in essentially any quantum system, the control techniques to be developed are expected to find application in a broad range of other systems in quantum optics and quantum electronics.

The explicit utilisation of these quantum mechanical effects for useful applications, however, requires extremely accurate control over quantum objects and their interaction with their surroundings. Trapped ions are one of the leading systems in this context. Selected energy levels of an ion define a qubit, which is the elementary unit of a quantum computer, just like a classical computer is comprised of many bits. Confined by electric and magnetic trapping fields, ions can be manipulated with laser beams, and the collective motion of strings of ions enables the exchange of information between several qubits. For this to work with high accuracy it is typically required to cool the ions to a temperature close to absolute zero. Once such a temperature has been reached, one makes use of the fact that any manipulation of the ions changes their motional state in order to implement logical operations that define the elementary building blocks of a quantum algorithm.

Since the ions' motion is easily heated by its room-temperature environment, the intentionally induced changes in the motional state can be accompanied by uncontrolled heating processes, and any deviation from the desired change in motional state results in reduced accuracy of the operations being implemented. The goal of the present project is the development and experimental implementation of laser control of trapped ions that achieves desired operations with high accuracy and robustness in the presence of undesired heating and other experimental imperfections.

In a strong collaboration between theory and experiment, control sequences will be developed and tested in a novel ion trap whose parameters can be varied over a wide range. The ability to tune the strength of the interaction between qubits and motion (the Lamb-Dicke parameter) and the strength of thermal effects will allow us to identify the control strategies that deal with each type of imperfection in an ideal fashion. Most current experiments are conducted with a rather weak interaction between qubits and motion, but we aim at the realisation of logical operations between qubits that interact strongly with the motion. The increased manipulation speed that comes with the strong interaction increases the number of logical operations that can be implemented within the limits imposed by finite decoherence time, and as such will help us to move from proof-of-principle experiments to a practical application.

The immediate goal of our work is the improvement in the control of trapped ions for quantum computing, but the advanced control techniques we will develop directly apply to any type of coherent manipulation of trapped ions. Since strong interactions between qubits are beneficial for fast information transfer but challenging for the implementation of accurate manipulations in essentially any quantum system, the control techniques to be developed are expected to find application in a broad range of other systems in quantum optics and quantum electronics.

### Planned Impact

We expect the primary impact of our work to be within the quantum information processing and ion trap academic communities, but we will also ensure that our work reaches a wider audience. We will achieve this partly by improving and extending our web page at www.imperial.ac.uk/ion-trapping to include material aimed not only at active scientists in the field but also students and other people interested in the science that we do.

We are intending to organise a small workshop roughly half way through the project, and as part of the workshop we will invite one of our external participants to deliver an evening lecture aimed at non-specialists, which we will advertise on our web page, through the Imperial physics undergraduate and postgraduate mailing lists, and on the College web site through the Imperial College communications team.

Imperial College has a strong tradition of organising events for the general public and in particular the Imperial Festival, held each year over a weekend in May, will be an excellent opportunity to present our work in an interactive manner with a stall at the Festival. In addition our Centre for Doctoral Training in Controlled Quantum Dynamics, from which we hope to recruit two PhD students, runs a Quantum Show each year for the general public, and we intend to contribute to that event. Quantum computing is a topic which has attracted great interest among the general public and so it will be appropriate to address that interest with these outreach activities. Material from our research will also naturally be included in any other presentations that we give, e.g. in schools and open day talks.

Industrial interest in quantum technologies is growing as the research yields devices which are getting closer to the market place, so we expect interest in our work from the relevant industries (e.g. Toshiba and Microsoft, both in Cambridge). We will work with contacts in these industries to develop links and investigate possible industrial and commercial applications for our work.

Finally, our project will help to train the next generation of highly-skilled scientists, who will have expertise in a wide range of skills and techniques that are relevant for employment throughout science and engineering. These skills include for example the ability to develop and work with laser systems, electronics, RF technology, vacuum systems and computer control on the experimental side, and high level mathematical, simulation and programming skills on the theory side. Furthermore, these scientists will have developed strong transferable skills through literature research, group meetings, conference presentations and writing papers that will equip them for employment in many different areas.

We are intending to organise a small workshop roughly half way through the project, and as part of the workshop we will invite one of our external participants to deliver an evening lecture aimed at non-specialists, which we will advertise on our web page, through the Imperial physics undergraduate and postgraduate mailing lists, and on the College web site through the Imperial College communications team.

Imperial College has a strong tradition of organising events for the general public and in particular the Imperial Festival, held each year over a weekend in May, will be an excellent opportunity to present our work in an interactive manner with a stall at the Festival. In addition our Centre for Doctoral Training in Controlled Quantum Dynamics, from which we hope to recruit two PhD students, runs a Quantum Show each year for the general public, and we intend to contribute to that event. Quantum computing is a topic which has attracted great interest among the general public and so it will be appropriate to address that interest with these outreach activities. Material from our research will also naturally be included in any other presentations that we give, e.g. in schools and open day talks.

Industrial interest in quantum technologies is growing as the research yields devices which are getting closer to the market place, so we expect interest in our work from the relevant industries (e.g. Toshiba and Microsoft, both in Cambridge). We will work with contacts in these industries to develop links and investigate possible industrial and commercial applications for our work.

Finally, our project will help to train the next generation of highly-skilled scientists, who will have expertise in a wide range of skills and techniques that are relevant for employment throughout science and engineering. These skills include for example the ability to develop and work with laser systems, electronics, RF technology, vacuum systems and computer control on the experimental side, and high level mathematical, simulation and programming skills on the theory side. Furthermore, these scientists will have developed strong transferable skills through literature research, group meetings, conference presentations and writing papers that will equip them for employment in many different areas.

### Publications

Holmes Z
(2019)

*Coherent fluctuation relations: from the abstract to the concrete*in Quantum
Joshi M
(2019)

*Population dynamics in sideband cooling of trapped ions outside the Lamb-Dicke regime*in Physical Review A