Optimal Control for Robust Ion Trap Quantum Logic

The use of trapped ions as an experimental medium for the realisation of quantum information protocol was established in 19951{3. The M lmer S rensen scheme 4;5 enabled the entanglement of 66 and then 147 qubits, and two qubit gate delities well above the threshold for fault tolerant computation8{10. Trapped ions are currently used in quantum simulations11;12, however in order to increase the scalability, and thus utility of these systems, both the scale of traps must be reduced and the speed of operations increased. The increased proximity of ions to their trap electrodes however increases heating rates in the system, whilst faster gate operation requires higher intensity laser elds, increasing o -resonant excitation and thus reducing gate delity. The aim of this project is to design and build a linear `blade' radio-frequency trap, and use it to investigate quantum gate protocol, robust under these conditions, through the use of optimal control techniques. The reduction of o -resonant transitions is usually achieved by operating within the Lamb-Dicke regime, where only carrier and rst order sideband transitions are considered to be signi cant. All multi-qubit gate operations involve entanglement between the internal state of an ion and a collective motional mode. Any motional heating therefore acts to decohere the nal state of the qubit. Reduced occupation of the motional state, by the increased detuning of Raman beams in the M lmer S renesen scheme, acts to minimise this source of in delity. Increased detuning however requires increased Rabi frequencies, which reduce the coupling strength to sideband transitions. Consequently, either higher intensity radiation, or longer interaction time, is required to implement the gate - both of which are undesirable. Operation outside the Lamb-Dicke regime enables stronger coupling to sidebands for a given laser intensity, which can thus reduce gate time, but increases coupling strength to unwanted transitions. By considering these transitions, optimal control designed pulse sequences, which suppress or negate the e ects of o -resonant driving, will be designed and realised experimentally. We plan to implement conventional entangling gates, and subsequently investigate the e ects of increasing Lamb-Dicke parameter. Experimental ndings will be fed back to improve the design of pulse sequences, and their resilience to the e ects of noise and heating will be optimised.

The main impact of the proposed Hub will be in training quantum engineers with a skillset to understand cutting-edge quantum research and a mindset toward developing this innovation, and the entrepreneurial skills to lead the market. This will grow the UK capacity in quantum technology. Through our programme, we nurture the best possible work force who can start new business in quantum technology. Our programme will provide multi-level skills training in quantum engineering in order to enhance the UK quantum technologies landscape at several stages. Through the training we will produce quantum engineers with training in innovation and entrepreneurship who will go into industry or quantum technology research positions with an understanding of innovation in quantum technology, and will bridge the gap between the quantum physicist and the classical engineer to accelerate quantum technology research and development. Our graduates will have to be entrepreneurial to start new business in quantum technology. By providing late-stage training for current researchers and engineers in industry, we will enhance the current landscape of the quantum technology industry. After the initial training composed of advanced course works, placements and short projects, our students will act as a catalyzer for collaboration among quantum technology researchers, which will accelerate the development of quantum technology in the UK. Our model actively encourages collaboration and partnerships between Imperial and national quantum tehcnology centres and we will continue to maintain the strong ties we have developed through the Centre for Doctoral Training in order to enhance our on-going training provisions. The Hub will also have an emphasis on industrial involvement. Through our new partnerships students will be exposed to a broad spectrum of non-academic research opportunities. An important impact of the Hub is in the research performed by the young researchers, PhD students and junior fellows. They will greatly enhance the research capacity in quantum technology. Imperial College has many leading engineers and quantum scientists. One of the important outcomes we expect through this Hub programme is for these academics to work together to translate the revolutionary ideas in quantum science to engineering and the market place. We also aim to influence industry and policy makers through our outreach programme in order to improve their awareness of this disruptive technology.