Optimal Control for Robust Ion Trap Quantum Logic

使用捕获离子作为实现量子信息协议的实验介质是在19951年建立的{3。Mmer S rensen方案4;5实现了66个量子比特的纠缠，然后是147个量子比特的纠缠，并且两个量子比特门延迟远高于容错计算的阈值8 {10}。捕获的离子目前用于量子模拟11;12，然而，为了增加可扩展性，从而这些系统的效用，陷阱的规模必须减少，操作的速度增加。然而，离子与它们的阱电极的接近度的增加了系统中的加热速率，而更快的门操作需要更高强度的激光器，从而增加了o -共振激发并因此降低了门延迟。本项目的目的是设计和建造一个线性的“刀片”射频陷阱，并使用它来研究量子门协议，在这些条件下，通过使用最优控制技术的鲁棒性。通常通过在Lamb-Dicke范围内操作来实现o -共振跃迁的减少，其中仅载波和第一阶边带跃迁被认为是显著的。所有的多量子比特门操作都涉及离子的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退相干。在Mlmer S Renesen方案中，通过增加拉曼光束的失谐来减少对运动态的占据，起到使这种不灵敏度源最小化的作用。然而，增加失谐需要增加拉比频率，这降低了到边带跃迁的耦合强度。因此，需要更高强度的辐射或更长的相互作用时间来实现门-这两者都是不期望的。对于给定的激光强度，在Lamb-Dicke机制之外的操作使得能够更强地耦合到边带，这因此可以减少选通时间，但是增加了对不想要的跃迁的耦合强度。通过考虑这些转变，最优控制设计的脉冲序列，其抑制或否定o -谐振驱动的效应，将被设计和实验实现。我们计划实现传统的纠缠门，并随后研究增加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，并且它们对噪声和加热的弹性将被优化。

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.