在量子水平上对混合物理系统的精确控制对于许多基于量子的技术的实现是重要的。在量子信息处理（QIP）和量子网络领域，各种提议讨论了混合架构的可能性，其中将特定任务委托给最合适的子系统。例如，在量子网络中，将信息从具有良好存储器属性的子系统传送到在网络中的节点之间传输信息时更有效的另一个子系统可能是有利的。对于被捕获的离子，由不同种类形成的混合系统引入了额外的自由度，可以利用这些自由度来扩展和细化系统的控制。不同元素的离子以前曾在QIP实验中用于交感冷却，通过耗散产生纠缠，以及一个物种与另一个物种的量子非破坏（QND）测量。在这里，我们展示了不同元素的离子之间的纠缠量子门，它可以作为QIP，量子网络，精密光谱学，计量学和量子模拟的重要组成部分。通过激光束诱导的状态相关力产生的有效自旋-自旋相互作用，实现了$^9$ Be $^+$离子和$^{25}$ Mg $^+$离子之间的几何相位门。结合单量子比特门和同种纠缠门，这种混合元素纠缠门在这样的混合系统上为通用QIP提供了一套完整的门。使用一系列这样的门，我们演示了一个受控非（CNOT）门和交换门。我们进一步证明了这些门对热激发的鲁棒性，并在量子逻辑光谱（QLS）中显示出改进的检测。我们还观察到一个强烈的违反CHSH型贝尔不等式纠缠态组成的不同的离子物种。
英文摘要：
Precision control over hybrid physical systems at the quantum level is important for the realization of many quantum-based technologies. In the field of quantum information processing (QIP) and quantum networking, various proposals discuss the possibility of hybrid architectures where specific tasks are delegated to the most suitable subsystem. For example, in quantum networks, it may be advantageous to transfer information from a subsystem that has good memory properties to another subsystem that is more efficient at transporting information between nodes in the network. For trapped-ions, a hybrid system formed of different species introduces extra degrees of freedom that can be exploited to expand and refine the control of the system. Ions of different elements have previously been used in QIP experiments for sympathetic cooling, creation of entanglement through dissipation, and quantum non-demolition (QND) measurement of one species with another. Here, we demonstrate an entangling quantum gate between ions of different elements which can serve as an important building block of QIP, quantum networking, precision spectroscopy, metrology, and quantum simulation. A geometric phase gate between a $^9$Be$^+$ ion and a $^{25}$Mg$^+$ ion is realized through an effective spin-spin interaction generated by state-dependent forces induced with laser beams. Combined with single-qubit gates and same-species entangling gates, this mixed-element entangling gate provides a complete set of gates over such a hybrid system for universal QIP. Using a sequence of such gates, we demonstrate a Controlled-NOT (CNOT) gate and a SWAP gate. We further demonstrate the robustness of these gates against thermal excitation and show improved detection in quantum logic spectroscopy (QLS). We also observe a strong violation of a CHSH-type Bell inequality on entangled states composed of different ion species.
We describe the optimal realization of entangling quantum gates for trapped ions mediated by a dissipative bus mode. With suitably shaped control pulses one can substantially decrease ion-phonon entanglement while maintaining the mediated interaction.
Dynamical decoupling techniques are the method of choice for increasing gate fidelities. While these methods have produced very impressive results in terms of decreasing local noise and increasing the fidelities of single qubit operations, dealing with the noise of two qubit gates has proven more challenging. The main obstacle is that the noise time scale is shorter than the two qubit gate itself so that refocusing methods do not work. We present a measurement and feedback based method to refocus two qubit gates which cannot be refocused by conventional methods. We analyze in detail this metho…
Entangling operations are a necessary tool for large-scale quantum information processing, but experimental imperfections can prevent current schemes from reaching sufficient fidelities as the number of qubits is increased. Here it is shown numerically how multi-toned generalizations of standard trapped-ion entangling gates can simultaneously be made robust against noise and mis-sets of the frequencies of the individual qubits. This relaxes the degree of homogeneity required in the trapping field, making physically larger systems more practical.
We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.
We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity…
On the local equivalence of trapped-ion two-qudit gates
P.N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Russian Quantum Center（俄罗斯量子中心）；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
Fast entangling gates have been proposed for trapped ions that are orders of magnitude faster than current implementations. We present here a detailed analysis of the challenges involved in performing a successful fast gate. We show that the RWA is a stable approximation with respect to pulse numbers: the timescale on which we can neglect terms rotating at the atomic frequency is negligibly affected by the number of pulses in the fast gate. In contrast, we show that the laser pulse instability does give rise to a pulse-number dependent effect; the fast gate infidelity is compounded with the nu…
Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensiti…
Entangling gates in trapped-ion quantum computing have primarily targeted stationary ions with initial motional distributions that are thermal and close to the ground state. However, future systems will likely incur significant non-thermal excitation due to, e.g., ion transport, longer operational times, and increased spatial extent of the trap array. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Molmer-Sorenson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shar…
Amplitude noise which inflicts a random two qubit term is one of the main obstacles preventing the implementation of a high fidelity two-body gate below the fault tolerance threshold. This noise is difficult to refocus as any refocusing technique could only tackle noise with frequency below the operation rate. Since the two qubit gate speed is normally the slowest rate in the system, it constitutes the last bottleneck towards an implementation of a gate below the fault tolerant threshold. Here we propose to use composite pulses as a dynamical decoupling approach, in order to reduce two qubit g…
Essentially all known quantum gates rely on a weak-coupling approximation resulting in linear dynamics. With the explicit example of trapped ions, we show how high-fidelity quantum gates can be achieved outside such an approximation, and we derive readily implementable driving fields to realize gates with extremely high fidelities for ions well outside the Lamb-Dicke regime with motional temperatures achievable by only Doppler cooling.
Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, …
RF-induced micromotion in trapped ion systems is typically minimised or circumvented to avoid off-resonant couplings for adiabatic processes such as multi-ion gate operations. Non-adiabatic entangling gates (so-called `fast gates') do not require resolution of specific motional sidebands, and are therefore not limited to timescales longer than the trapping period. We find that fast gates designed for micromotion-free environments have significantly reduced fidelity in the presence of micromotion. We show that when fast gates are designed to account for the RF-induced micromotion, they can, in …
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling wi…
The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. The motion has been considered as a classical oscillator in analyzing the influence. Here we treat the motion of the atom as a quantum oscillator. The population on the vibrational states of the atom are considered in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate is dramatically limi…
Fast entangling gates for trapped ions offer vastly improved gate operation times relative to implemented gates, as well as approaches to trap scaling. Gates on neighbouring ions only involve local ions when performed sufficiently fast, and we find that even a fast gate between distant ions with few degrees of freedom restores all the motional modes given more stringent gate speed conditions. We compare pulsed fast gate schemes, defined by a timescale faster than the trap period, and find that our proposed scheme has less stringent requirements on laser repetition rate for achieving arbitrary …
We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped ion hyperfine qubits. The protocol consists of sequences of $π$-pulses acting on ions that are oriented along an externally applied magnetic field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magn…
We present an efficient approach to optimising pulse sequences for implementing fast entangling two-qubit gates on trapped ion quantum information processors. We employ a two-phase procedure for optimising gate fidelity, which we demonstrate for multi-ion systems in linear Paul trap and microtrap architectures. The first phase involves a global optimisation over a computationally inexpensive cost function constructed under strong approximations of the gate dynamics. The second phase involves local optimisations that utilise a more precise ODE description of the gate dynamics, which captures th…
We report the implementation of a perceptron quantum gate in an ion-trap quantum computer. In this scheme, a perceptron's target qubit changes its state depending on the interactions with several qubits. The target qubit displays a tunable sigmoid switching behaviour becoming a universal approximator when nested with other percetrons. The procedure consists on the adiabatic ramp-down of a dressing-field applied to the target qubit. We also use two successive perceptron quantum gates to implement a XNOR-gate, where the perceptron qubit changes its state only when the parity of two input qubits …
