Measurement-based entanglement of single-dopant As spin qubits

量子信息的基本单位是量子比特或量子比特。与经典比特一样，量子比特是一个两级系统，但具有以叠加态存在的有趣能力。这意味着它可以同时处于开和关状态，如果我们考虑多个量子比特的量子系统，这将产生深远的影响。不是每个量子比特都携带任何定义明确的信息，而是将信息编码在它们的联合属性中。在量子力学中，量子比特被描述为纠缠的。挑战在于找到利用量子现象（如叠加和纠缠）来构建量子计算机的方法，该量子计算机能够执行在经典环境中无法实现的计算任务。一个非常自然的量子比特是电子自旋。电子自旋状态之间的能量差可以通过磁场精确控制，并且使用电子的电荷，也可以通过电子隔离和操纵单个自旋。实现自旋量子比特之间纠缠的一种途径是通过将它们放置在非常接近的位置来利用它们的电子波函数重叠的相互作用。虽然这种方法对于少量量子比特是可行的，但依赖于直接最近邻耦合的大规模量子处理器很快变得不切实际。因此，我们提出了另一种策略，即利用一种有趣的量子力学效应，如果测量无法区分两个空间分离的量子比特，那么它们就会纠缠在一起。正如理论上所示，基于测量的纠缠可以用来耦合大量物理上分离的量子比特，建立所谓的图形状态。然后通过对消耗纠缠的单个量子比特进行一系列测量来实现计算-称为单向量子计算-这与标准的基于电路的方法完全不同。在实践中，这还需要存在量子存储器，其中存储量子信息以允许图形状态增长，而没有丢失现有纠缠的风险。在这里，我们建议使用一个非常适合这个任务的固态实现：在同位素纯Si-28中的单一As掺杂剂。为了制造器件，我们将使用最精确的硅掺杂剂掺入技术：扫描隧道显微镜（STM）氢抗蚀剂光刻。原子级精确的掺入单个As掺杂剂对于满足基于测量的纠缠协议的关键要求是必不可少的：量子比特不可分割性。制造出这些设备后，我们将能够操纵As掺杂剂的电子自旋，并使用投影测量在远程量子比特之间产生纠缠。为此，我们将使用射频反射技术，使我们能够在比电子自旋寿命快得多的时间尺度上执行这些任务。一旦实现纠缠产生，超精细耦合将用于将量子信息从电子转移到As核自旋态。这种方法利用了Si中掺杂剂在10-100秒范围内的记录核自旋相干性，并允许我们生长纠缠图态。此外，由于As原子核具有非零电四极矩和四维希尔伯特空间，我们将能够以电学方式控制核自旋，并在每个掺杂剂中存储和控制相当于两个量子比特的量子比特。对于原理验证演示器，我们将纠缠四个空间分离的设备，每个设备由两个具有全对全量子比特连接的As掺杂剂原子量子比特组成，相当于一个16量子比特处理器。实验工作将得到理论研究的支持，以进一步开发最有效的策略，以增加弹性远程网络，同时考虑到现实的实验参数，如自旋退相和信号丢失。

The elementary unit of quantum information is the quantum bit or qubit. Like the classical bit, the qubit is a two-level system but with the intriguing ability to exist in a superposition of states. This means it can be in the on and off state at the same time which has profound implications if we consider quantum systems of more than one qubit. Instead of each qubit carrying any well-defined information of its own, the information is encoded in their joint properties. In quantum mechanics, the qubits are described as being entangled. The challenge is to find ways to harness quantum phenomena such as superposition and entanglement to construct a quantum computer that is able to perform computational tasks that are unattainable in a classical context.A very natural qubit is the electron spin. The energy difference between spin states of an electron can be precisely controlled by magnetic fields and, using the electron's charge, it is also possible to isolate and manipulate individual spins electrically. One route to achieve entanglement between spin qubits is to use the interaction of their electron wavefunction overlap by placing them in close proximity. While such an approach is feasible for a small number of qubits, a large-scale quantum processor which relies on direct nearest neighbour coupling becomes rapidly impractical. Here we therefore propose an alternative strategy which makes use of an intriguing quantum mechanical effect by which two spatially separated quantum bits become entangled if a measurement cannot tell them apart.As has been shown theoretically, measurement-based entanglement can be used to couple large numbers of physically separated qubits, building up so-called graph states. Computation is then achieved by a sequence of measurements on individual qubits that consumes the entanglement - known as one-way quantum computation - which is entirely different from the standard circuit-based approach. In practise this also requires the presence of a quantum memory where quantum information is stored to allow graph-state growth without the risk of losing existing entanglement. Here we propose to use a solid-state implementation which is ideally suited to this task: single As-dopants in isotopically pure Si-28.To fabricate the devices, we will use the most precise silicon dopant incorporation technique available: scanning tunnelling microscopy (STM) hydrogen resist lithography. The atomically precise incorporation of individual As-dopants is essential in satisfying a key requirement of the measurement-based entanglement protocol: qubit indistinguishability.Having fabricated the devices, we will be able to manipulate the electron spins of the As-dopants and create entanglement between remote qubits using projective measurements. For this we will be using radio-frequency reflectometry techniques which allows us to perform these tasks on a timescale significantly faster than electron spin lifetimes. Once entanglement generation has been achieved, hyperfine coupling will be used to transfer the quantum information from the electron to the As nuclear spin states. This approach takes advantage of record nuclear spin coherence, in the 10-100 second range, of dopants in Si and allows us to grow the entangled graph state. Moreover, since the As nucleus has a non-zero electric quadrupole moment and a four dimensional Hilbert space we will be able to control the nuclear spins electrically and store and control the equivalent of two qubits in each dopant.For a proof-of-principle demonstrator we will entangle four spatially separated devices, each consisting of two As-dopant atom qubits with all-to-all qubit connectivity, equivalent to a 16-qubit processor. The experimental efforts will be supported by theoretical studies to further develop the most efficient strategies for growing a resilient remote network taking into account realistic experimental parameters such as spin dephasing and signal loss.