Optimal Control for Robust Ion Trap Quantum Logic

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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.