Testing the computational power of discord

目前，量子世界的任何一个特征都没有被确定为量子技术的计算增强、效率和加速的来源。虽然纠缠被广泛认为是量子技术中的一个关键资源，但在非经典相关的情况下，如果没有它，可以实现相对于经典技术的指数优势。此外，对于特定的任务，不和谐的可分离态已经被证明比纠缠更有效。纠缠和不和谐的动力学有很大的不同，纠缠在退相干时非常脆弱（甚至经历纠缠的“突然死亡”），而不和谐则更加强大。由于退相干是量子技术发展的一个主要障碍，因此对不和谐的研究是推动该领域发展的一条有前途的路线。虽然不和谐已被证明是加速特定计算任务和对退相干具有鲁棒性的宝贵资源，更普遍的证据表明，不和谐可以为任何计算任务提供计算增强，但还没有提供。这使得不和谐成为一个非常有争议的问题。量子信息处理的资产，虽然它被广泛认为，如果有一天它可以用于量子计算，其影响将是真正的突破性的。这个项目的目标是实验研究物理和量子不和谐的计算能力在多atomensemble的一个特定的算法，执行归一化的跟踪估计。我们将使用DQC 1模型来计算非常大的数字串的总和，这使得计算经典地难以处理。作为一个说明性的例子，考虑一百个原子被困在光学偶极阱中。对这些原子的幺正操作可以用一个2^100 × 2^100的矩阵来描述。找到这个矩阵的归一化迹相当于把10^30个数字加起来，这是一个经典上难以处理的任务：现代超级计算机每秒可以执行10^12次运算，因此需要大约宇宙的年龄才能完成同样的任务。这是潜在的变革，因为量子不和谐尚未在具有大希尔伯特空间的系统中进行研究，并且计算能力的指数加速的成功演示将是该领域的一大飞跃。这一研究理念的最终影响将是获得各种实验见解，从而更深入地了解所有量子系统中存在的量子相关性。

At present, no single feature of the quantum world has been identified as the source of the computational enhancement, efficiency and speed-up of quantum technology. Whilst entanglement is widely recognised as a key resource in quantum technology, an exponential advantage over classical technology can be achieved without it in the presence of non-classical correlations. Furthermore for specific tasks separable states with discord have been proved to be even more efficient than entanglement.The dynamics of entanglement and discord differ considerably, with entanglement being extremely fragile towards decoherence (even undergoing entanglement "sudden death" ) and discord being much more robust. Since decoherence is a major hurdle to the development of quantum technologies, the investigation of discord is a promising route for progressing the field.Whilst discord has been proved to be a valuable resource for speed up of specific computationaltasks and for being robust towards decoherence, the more general demonstration that discord can providecomputational enhancement for any computational task has not been provided.This makes discord a verycontroversial asset for quantum information processing, although it is widely recognised that if one day itcould be made of use for quantum computation, the impact would be truly ground-breaking.The goal of this project is to experimentally investigate the physics and the computational power of quantum discord in many-atomensembles for a specific algorithm that performs the normalized trace estimation. We will be using the DQC1 model to computesums over extremely large strings of numbers, which make the computation classically intractable. As an illustrative example, consider one hundred atoms trapped in an optical dipole trap. A unitary operation on these atoms would be described by a 2^100-by-2^100 matrix. Finding the normalised trace of this matrix is equivalent to adding up 10^30 numbers, which is a task that is classically intractable: modern supercomputers can perform 10^12 operations per second and therefore it would take about the age of the universe to have the same task. This is potentially transformative because quantum discord has not yet been studied in systems with large Hilbert spaces, and the successful demonstration of the exponential speed-up of the computational capability would be amajor leap forward in the field. The ultimate impact of this research idea would be to gain a variety of experimental insights into, and thus a deeper understanding of, the quantum correlations that would be present in all quantum systems