Noise resilience of quantum information processing is a crucial precondition to reach the fault-tolerance threshold. While resilience to many types of noise can be achieved through suitable control schemes, resilience to amplitude noise seems to be elusive within the common harmonic approximation for the bus mode of trapped ions. We show that weak an-harmonicities admit control schemes that achieve amplitude noise-resilience consistent with state-of-the-art experimental requirements, and that the required an-harmonicities can be achieved with current standards of micro-structured traps or even the intrinsically an-harmonic Coulomb interaction. This approach applies broadly to any platform that employs a bosonic bus as a qubit coupler.
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 present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) \times 10^{-3}$. We analyze the expected errors in the MS gate and find that pop…
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…
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…
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 …
To achieve scalable quantum computing, improving entangling-gate fidelity and its implementation-efficiency are of utmost importance. We present here a linear method to construct provably power-optimal entangling gates on an arbitrary pair of qubits on a trapped-ion quantum computer. This method leverages simultaneous modulation of amplitude, frequency, and phase of the beams that illuminate the ions and, unlike the state of the art, does not require any search in the parameter space. The linear method is extensible, enabling stabilization against external parameter fluctuations to an arbitrar…
The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multi-dimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used Molmer-Sorensen entangling gate opera…
We implement a two-qubit entangling Mølmer-Sørensen interaction by transporting two co-trapped $^{40}\mathrm{Ca}^{+}$ ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a constant Doppler shift during the transport which uses fine temporal adjustment of the moving confinement potential. The fixed interaction duration of the ions transported through the laser beam as well as the dynamically changing ac Stark shift require alterations to the calibration procedures used for a stationary gate. We use the interaction to pr…
Efficiently entangling pairs of qubits is essential to fully harness the power of quantum computing. Here, we devise an exact protocol that simultaneously entangles arbitrary pairs of qubits on a trapped-ion quantum computer. The protocol requires classical computational resources polynomial in the system size, and very little overhead in the quantum control compared to a single-pair case. We demonstrate an exponential improvement in both classical and quantum resources over the current state of the art. We implement the protocol on a software-defined trapped-ion quantum computer, where we rec…
Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算联合中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Department of Electrical and Computer Engineering, University of Washington（华盛顿大学电气与计算机工程系）
The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields, or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
Large-scale multimode entangling-gate synthesis in trapped-ion systems
State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Center for Trapped Ion Quantum Science, Institute for Basic Science（基础科学研究院捕获离子量子科学中心）
Arbitrary parallel entangling gates with independent calibration on a trapped ion quantum computer
Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；National Quantum Laboratory (QLab), University of Maryland（马里兰大学国家量子实验室）；Department of Physics, University of Maryland（马里兰大学物理系）；Duke Quantum Center and Department of Physics, Duke University（杜克大学量子中心及物理系）
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a `bichromatic' interaction picture, we show that either ${\hatσ_ϕ\otimes\hatσ_ϕ}$ or ${\hatσ_{z}\otimes\hatσ_{z}}$ geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluct…
We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here…
Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals. The strong dipole-dipole interactions in polar molecule and Rydberg atom systems all…
The conventional approach to perform two-qubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling gate operation presents a big technical challenge, as such the required laser source is not available off-the-shelf. For this, we have engineered an ultrafast entangling gate source based on a frequency comb. The source generate…
Universität Innsbruck（因斯布鲁克大学）；Universidad Autónoma de Madrid（马德里自治大学）；Instituto de Física Teórica (UAM-CSIC)（理论物理研究所（UAM-CSIC））；Universität Siegen（锡根大学）；Alpine Quantum Technologies（阿尔卑斯量子技术公司）
Constructing a large scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground state cooled, our method provides a …
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.
Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at leas…
Our goal is to provide a new approach to the construction of geometry-induced entanglement between a pair of $Λ$ type atoms in a system consists of $N$ identical atoms by means of nonadiabatic quantum holonomies. By employing the quantum Zeno effect, we introduce a tripod type interaction Hamiltonian between two selected atoms trapped in an optical cavity, which allows arbitrary geometric entangling power. This would be a substantial step toward resolving the feasibility of realizing universal nonadiabatic holonomic entangling two-qubit gates.
Quantum computers are expected to achieve a significant speed-up over classical computers in solving a range of computational problems. Chains of ions held in a linear Paul trap are a promising platform for constructing such quantum computers, due to their long coherence times and high quality of control. Here we report on the construction of a small, five-qubit, universal quantum computer using $^{88}\text{Sr}^{+}$ ions in an RF trap. All basic operations, including initialization, quantum logic operations, and readout, are performed with high fidelity. Selective two-qubit and single-qubit ga…
Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. We propose and implement a pairwise-parallel gate scheme on a trapped-ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped-ion chain. We demonstrate the utility of this scheme by creating a GHZ state in one step using parallel gates with one overlapping qubit. We also show its advantage for circuits by implementing a digital quantum simulation of the dynamics of an in…
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, …
Drive-Through Quantum Gate: Non-Stop Entangling a Mobile Ion Qubit with a Stationary One
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；National University of Singapore（新加坡国立大学）；Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Trapped-Ion Quantum Computing Laboratory, Hon Hai Research Institute, Foxconn（鸿海研究院会离子阱量子计算实验室）
We study a class of entangling gates for trapped atomic ions and demonstrate the use of numeric optimization techniques to create a wide range of fast, error-robust gate constructions. Our approach introduces a framework for numeric optimization using individually addressed, amplitude and phase modulated controls targeting maximally and partially entangling operations on ion pairs, complete multi-ion registers, multi-ion subsets of large registers, and parallel operations within a single register. Our calculations and simulations demonstrate that the inclusion of modulation of the difference p…
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…
Demonstration of a dressed-state phase gate for trapped ions
我们演示了Bermudez等人提出的捕获离子纠缠门方案。[Phys. Rev. A 85，040302（2012）]。强载流子和单边带跃迁的同时激发使得能够确定性地产生纠缠态。该方法适用于磁场不敏感状态，对热激发是鲁棒的，包括从量子位退相误差的动态解耦，并且与具有捕获离子的一些其他纠缠门相比，在实验实现中提供了简化。我们实现了0.974（4）的贝尔态保真度，并确定了主要的误差来源。
