High-fidelity laser-free universal control of trapped ion qubits

Electromagnetically Induced Transparency Cooling of High-Nuclear-Spin Ions

We report the electromagnetically induced transparency (EIT) cooling of ^{137}Ba^{+} ions with a nuclear spin of I=3/2, which are a good candidate of qubits for future large-scale trapped-ion quantum computing. EIT cooling of atoms or ions with a complex ground-state level structure is challenging due to the lack of an isolated Λ system, as the population can escape from the Λ system to reduce the cooling efficiency. We overcome this issue by leveraging an EIT pumping laser to repopulate the cooling subspace, ensuring continuous and effective EIT cooling. We cool the two radial modes of a single ^{137}Ba^{+} ion to average motional occupations of 0.08(5) and 0.15(7), respectively. Using the same laser parameters, we also cool all the ten radial modes of a five-ion chain to near their ground states. Our approach can be adapted to atomic species possessing similar level structures. It allows engineering of the EIT Fano-like spectrum, which can be useful for simultaneous cooling of modes across a wide frequency range, aiding in large-scale trapped-ion quantum information processing.

Fast Photon-Mediated Entanglement of Continuously Cooled Trapped Ions for Quantum Networking

We entangle two cotrapped atomic barium ion qubits by collecting single visible photons from each ion through in vacuo 0.8 NA objectives, interfering them through an integrated fiber beam splitter and detecting them in coincidence. This projects the qubits into an entangled Bell state with an observed fidelity lower bound of F>94%. We also introduce an ytterbium ion for sympathetic cooling to remove the need for recooling interruptions and achieve a continuous entanglement rate of 250  s^{-1}.

Low cross-talk optical addressing of trapped-ion qubits using a novel integrated photonic chip

Individual optical addressing in chains of trapped atomic ions requires the generation of many small, closely spaced beams with low cross-talk. Furthermore, implementing parallel operations necessitates phase, frequency, and amplitude control of each individual beam. Here, we present a scalable method for achieving all of these capabilities using a high-performance integrated photonic chip coupled to a network of optical fibre components. The chip design results in very low cross-talk between neighbouring channels even at the micrometre-scale spacing by implementing a very high refractive index contrast between the channel core and cladding. Furthermore, the photonic chip manufacturing procedure is highly flexible, allowing for the creation of devices with an arbitrary number of channels as well as non-uniform channel spacing at the chip output. We present the system used to integrate the chip within our ion trap apparatus and characterise the performance of the full individual addressing setup using a single trapped ion as a light-field sensor. Our measurements showed intensity cross-talk below ~10-3 across the chip, with minimum observed cross-talk as low as ~10-5.

Individual Addressing and State Readout of Trapped Ions Utilizing Radio-Frequency Micromotion

Excess "micromotion" of trapped ions due to the residual radio-frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.

Multi-site integrated optical addressing of trapped ions

One of the most effective ways to advance the performance of quantum computers and quantum sensors is to increase the number of qubits or quantum resources in the system. A major technical challenge that must be solved to realize this goal for trapped-ion systems is scaling the delivery of optical signals to many individual ions. In this paper we demonstrate an approach employing waveguides and multi-mode interferometer splitters to optically address multiple 171Yb+ ions in a surface trap by delivering all wavelengths required for full qubit control. Measurements of hyperfine spectra and Rabi flopping were performed on the E2 clock transition, using integrated waveguides for delivering the light needed for Doppler cooling, state preparation, coherent operations, and detection. We describe the use of splitters to address multiple ions using a single optical input per wavelength and use them to demonstrate simultaneous Rabi flopping on two different transitions occurring at distinct trap sites. This work represents an important step towards the realization of scalable integrated photonics for atomic clocks and trapped-ion quantum information systems.

Penning micro-trap for quantum computing

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, because of high-fidelity quantum gates and long coherence times1-3. However, the use of radio-frequencies presents several challenges to scaling, including requiring compatibility of chips with high voltages4, managing power dissipation5 and restricting transport and placement of ions6. Here we realize a micro-fabricated Penning ion trap that removes these restrictions by replacing the radio-frequency field with a 3 T magnetic field. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the quantum charge-coupled device architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

Ion trap with in-vacuum high numerical aperture imaging for a dual-species modular quantum computer

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10(1)% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

Engineering Artificial Atomic Systems of Giant Electric Dipole Moment

The electric dipole moment (EDM) plays a crucial role in determining the interaction strength of an atom with electric fields, making it paramount to quantum technologies based on coherent atomic control. We propose a scheme for engineering the potential in a Paul trap to realize a two-level quantum system with a giant EDM formed by the motional states of a trapped electron. We show that, under realistic experimental conditions, our system exhibits enhanced EDMs compared to those attainable with Rydberg atoms, serving as a complementary counterpart in the megahertz (MHz) resonance-frequency range. Furthermore, we show that such artificial atomic dipoles can be efficiently initialized, read out, and coherently controlled, thereby providing a potential platform for quantum technologies such as ultrahigh-sensitivity electric-field sensing.

Ultrahigh-fidelity spatial mode quantum gates in high-dimensional space by diffractive deep neural networks

While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate's performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.

Sideband cooling of a trapped ion in strong sideband coupling regime

Conventional theoretical studies on the ground-state laser cooling of a trapped ion have mostly focused on the weak sideband coupling (WSC) regime, where the cooling rate is inverse proportional to the linewidth of the excited state. In a recent work [New J. Phys.23, 023018 (2021)10.1088/1367-2630/abe273], we proposed a theoretical framework to study the ground state cooling of a trapped ion in the strong sideband coupling (SSC) regime, under the assumption of a vanishing carrier transition. Here we extend this analysis to more general situations with nonvanishing carrier transitions, where we show that by properly tuning the coupling lasers a cooling rate proportional to the linewidth can be achieved. Our theoretical predictions closely agree with the corresponding exact solutions in the SSC regime, which provide an important theoretical guidance for sideband cooling experiments.

Fast, High-Fidelity Addressed Single-Qubit Gates Using Efficient Composite Pulse Sequences

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for ^{43}Ca^{+} hyperfine "atomic clock" qubits in a cryogenic (100 K) surface trap. For a single qubit, we benchmark an error of 1.5×10^{-6} per Clifford gate (implemented using 600 ns π/2 pulses). For 2 qubits in the same trap zone (ion separation 5  μm), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error 3.4×10^{-5} per addressed π/2 gate. The scheme scales theoretically to larger numbers of qubits in a single register.

Optically Driven Both Classical and Quantum Unary, Binary, and Ternary Logic Gates on Co-Decorated Graphene Nanoflakes

Nanospintronics holds great potential for providing high-speed, low-power, and high-density logic and memory elements in future computational devices. Here, using ab initio many-body theory, we suggest a nanoscale framework for building quantum computation elements, based on individual magnetic atoms deposited on graphene nanoflakes. We show the great possibilities of this proposal by exemplarily presenting four quantum gates, namely, the unary Pauli-X, Pauli-Y, Pauli-Z, and Hadamard gates, as well as the universal classical ternary Toffoli gate, which preserves information entropy and is therefore fully reversible and minimally energy consuming. All our gates operate within the subpicosecond time scale and reach fidelities well above 90%. We demonstrate the ability to control the spin direction and localization, as well as to create superposition states and to control the quantum phase of states, which are indispensable ingredients of quantum computers. Additionally, being optically driven, their predicted operating speed by far beats that of modern quantum computers.

Coherent Control of Trapped-Ion Qubits with Localized Electric Fields

We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multizone trap by simultaneously applying an electric field and a spin-dependent gradient. Both the phase and amplitude of the effective single-qubit rotation depend on the electric field, which can be localized to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic-field gradients in a surface-electrode ion trap, and measure the localization of the electric field.

Robust Quantum Memory in a Trapped-Ion Quantum Network Node

We integrate a long-lived memory qubit into a mixed-species trapped-ion quantum network node. Ion-photon entanglement first generated with a network qubit in ^{88}Sr^{+} is transferred to ^{43}Ca^{+} with 0.977(7) fidelity, and mapped to a robust memory qubit. We then entangle the network qubit with a second photon, without affecting the memory qubit. We perform quantum state tomography to show that the fidelity of ion-photon entanglement decays ∼70 times slower on the memory qubit. Dynamical decoupling further extends the storage duration; we measure an ion-photon entanglement fidelity of 0.81(4) after 10 s.

A high-fidelity quantum matter-link between ion-trap microchip modules

System scalability is fundamental for large-scale quantum computers (QCs) and is being pursued over a variety of hardware platforms. For QCs based on trapped ions, architectures such as the quantum charge-coupled device (QCCD) are used to scale the number of qubits on a single device. However, the number of ions that can be hosted on a single quantum computing module is limited by the size of the chip being used. Therefore, a modular approach is of critical importance and requires quantum connections between individual modules. Here, we present the demonstration of a quantum matter-link in which ion qubits are transferred between adjacent QC modules. Ion transport between adjacent modules is realised at a rate of 2424 s^-1 and with an infidelity associated with ion loss during transport below 7 × 10^-8. Furthermore, we show that the link does not measurably impact the phase coherence of the qubit. The quantum matter-link constitutes a practical mechanism for the interconnection of QCCD devices. Our work will facilitate the implementation of modular QCs capable of fault-tolerant utility-scale quantum computation.

Robust Two-Qubit Gates for Trapped Ions Using Spin-Dependent Squeezing

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 sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.

99.92%-Fidelity cnot Gates in Solids by Noise Filtering

Inevitable interactions with the reservoir largely degrade the performance of entangling gates, which hinders practical quantum computation from coming into existence. Here, we experimentally demonstrate a 99.920(7)%-fidelity controlled-not gate by suppressing the complicated noise in a solid-state spin system at room temperature. We found that the fidelity limited at 99% in previous works results from considering only static classical noise, and, thus, in this work, a complete noise model is constructed by also considering the time dependence and the quantum nature of the spin bath. All noises in the model are dynamically corrected by an exquisitely designed shaped pulse, giving the resulting error below 10^{-4}. The residual gate error is mainly originated from the longitudinal relaxation and the waveform distortion that can both be further reduced technically. Our noise-resistant method is universal and will benefit other solid-state spin systems.

Crosstalk Suppression in Individually Addressed Two-Qubit Gates in a Trapped-Ion Quantum Computer

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual Xσ[over ^]_{ϕ} interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians.

Universal Fidelity Reduction of Quantum Operations from Weak Dissipation

Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation, resulting in a small error probability per operation. Here, we find a simple formula for the fidelity reduction of any desired quantum operation, where the ideal evolution is confined to the computational subspace. Interestingly, this reduction is independent of the specific operation; it depends only on the operation time and the dissipation. Using our formula, we investigate the situation where dissipation in different parts of the system has correlations, which is detrimental for the successful application of quantum error correction. Surprisingly, we find that a large class of correlations gives the same fidelity reduction as uncorrelated dissipation of similar strength.

QDataSet, quantum datasets for machine learning

The availability of large-scale datasets on which to train, benchmark and test algorithms has been central to the rapid development of machine learning as a discipline. Despite considerable advancements, the field of quantum machine learning has thus far lacked a set of comprehensive large-scale datasets upon which to benchmark the development of algorithms for use in applied and theoretical quantum settings. In this paper, we introduce such a dataset, the QDataSet, a quantum dataset designed specifically to facilitate the training and development of quantum machine learning algorithms. The QDataSet comprises 52 high-quality publicly available datasets derived from simulations of one- and two-qubit systems evolving in the presence and/or absence of noise. The datasets are structured to provide a wealth of information to enable machine learning practitioners to use the QDataSet to solve problems in applied quantum computation, such as quantum control, quantum spectroscopy and tomography. Accompanying the datasets on the associated GitHub repository are a set of workbooks demonstrating the use of the QDataSet in a range of optimisation contexts.

Measurement(s)	Simulations of one- and two-qubit quantum systems evolving in the presence and absence of noise and distortion
Technology Type(s)	Simulated measurement using Python packages
Sample Characteristic - Organism	Simulated quantum systems
Sample Characteristic - Environment	Quantum systems in noisy and noiseless environments

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

High-Fidelity Indirect Readout of Trapped-Ion Hyperfine Qubits

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a ^{9}Be^{+} qubit ion is mapped to a ^{25}Mg^{+} readout ion using laser-driven Raman transitions. By partitioning the ^{9}Be^{+} ground-state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of 1.2_{-0.6}^{+1.1}×10^{-4} and 0_{-0}^{+1.9}×10^{-5} with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.

Temporal Quantum Memory and Non-Locality of Two Trapped Ions under the Effect of the Intrinsic Decoherence: Entropic Uncertainty, Trace Norm Nonlocality and Entanglement

The engineering properties of trapped ions and their capacity to engender numerous quantum information resources determine many aspects of quantum information processing. We devise a setup of coherent and even coherent fields acting on two trapped ions to generate quantum memory, non-locality, and entanglement. Various effects, such as intrinsic decoherence, Lamb–Dicke regime, and dipole–dipole interaction are investigated. The inter-coupling of trapped ions, as well as the generation and dynamics of correlations between them, are analyzed. Using quantum memory assisted entropic uncertainty, trace-norm measurement induced non-locality, and concurrence, we find that the coherent and even coherent fields successfully generate non-local correlations in trapped-ions, with the latter being more resourceful for the dynamics and preservation of the non-local correlations. Furthermore, we observe that the entropic uncertainty and the trace norm induced non-locality present symmetrical dynamics. The dipole–dipole interaction improves correlation’s generation, robustness, and entropic uncertainty suppression.

Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620  μm. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

High-Fidelity Bell-State Preparation with ^{40}Ca^{+} Optical Qubits

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35  μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.