Optimal Control for Robust Ion Trap Quantum Logic

利用俘获离子作为实现量子信息协议的实验介质是在1995年建立的{3}。M - mer - S - rensen方案4；5使66和147个量子位纠缠，两个量子位门交付远远超过容错计算的阈值[10]。捕获离子目前用于量子模拟；然而，为了提高这些系统的可扩展性和效用，必须减小陷阱的规模并提高操作速度。然而，离子与捕获电极的接近度增加增加了系统中的加热速率，而更快的栅极操作需要更高强度的激光场，从而增加了o -谐振激发，从而降低了栅极的质量。该项目的目的是设计和构建一个线性“刀片”射频陷阱，并使用它来研究量子门协议，通过使用最优控制技术，在这些条件下具有鲁棒性。o谐振跃迁的减少通常是通过在Lamb-Dicke范围内操作来实现的，其中只有载波和一阶边带跃迁被认为是重要的。所有的多量子位门操作都涉及到离子内部状态和集体运动模式之间的纠缠。因此，任何运动加热都会使量子比特的最终状态脱相干。通过增加拉曼光束在M - S - renesen方案中的失谐，减少了对运动状态的占用，从而最大限度地减少了这种不稳定的来源。然而，失谐的增加需要增加拉比频率，这降低了边带跃迁的耦合强度。因此，要么需要更高强度的辐射，要么需要更长的相互作用时间来实现栅极，这两者都是不希望的。在给定的激光强度下，在Lamb-Dicke范围之外的操作可以使侧带的耦合更强，从而可以减少栅极时间，但会增加不需要的跃迁的耦合强度。通过考虑这些过渡，将设计并实验实现抑制或消除无谐振驱动影响的最优控制脉冲序列。我们计划实现传统的纠缠门，随后研究增加Lamb-Dicke参数的影响。实验结果将被反馈，以改进脉冲序列的设计，并优化其对噪声和加热影响的弹性。

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.