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

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.

Rapid exchange cooling with trapped ions

The trapped-ion quantum charge-coupled device (QCCD) architecture is a leading candidate for advanced quantum information processing. In current QCCD implementations, imperfect ion transport and anomalous heating can excite ion motion during a calculation. To counteract this, intermediate cooling is necessary to maintain high-fidelity gate performance. Cooling the computational ions sympathetically with ions of another species, a commonly employed strategy, creates a significant runtime bottleneck. Here, we demonstrate a different approach we call exchange cooling. Unlike sympathetic cooling, exchange cooling does not require trapping two different atomic species. The protocol introduces a bank of "coolant" ions which are repeatedly laser cooled. A computational ion can then be cooled by transporting a coolant ion into its proximity. We test this concept experimentally with two 40Ca+ ions, executing the necessary transport in 107 μs, an order of magnitude faster than typical sympathetic cooling durations. We remove over 96%, and as many as 102(5) quanta, of axial motional energy from the computational ion. We verify that re-cooling the coolant ion does not decohere the computational ion. This approach validates the feasibility of a single-species QCCD processor, capable of fast quantum simulation and computation.

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9-12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19-22, we achieve a Bell state fidelity of [Formula: see text], which improves to [Formula: see text] when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits7,22-24.

Raman Scattering Errors in Stimulated-Raman-Induced Logic Gates in ^{133}Ba^{+}

^{133}Ba^{+} is illuminated by a laser that is far detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental atomic physics limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering.

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.

Native qudit entanglement in a trapped ion quantum processor

Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.

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.

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.

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.

Transport-Enabled Entangling Gate for Trapped Ions

We implement a 2-qubit entangling Mølmer-Sørensen interaction by transporting two cotrapped ^{40}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 produce Bell states with fidelities commensurate to those of stationary gates performed in the same system. This result establishes the feasibility of actively incorporating ion transport into quantum information entangling operations.

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

Universal control of multiple qubits-the ability to entangle qubits and to perform arbitrary individual qubit operations1-is a fundamental resource for quantum computing2, simulation3 and networking4. Qubits realized in trapped atomic ions have shown the highest-fidelity two-qubit entangling operations5-7 and single-qubit rotations8 so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams9-12 or by moving ions with respect to laser beams13-15, but at lower fidelities. Laser-free entangling methods16-20 may offer improved scalability by harnessing microwave technology developed for wireless communications, but so far their performance has lagged the best reported laser-based approaches. Here we demonstrate high-fidelity laser-free universal control of two trapped-ion qubits by creating both symmetric and antisymmetric maximally entangled states with fidelities of [Formula: see text] and [Formula: see text], respectively (68 per cent confidence level), corrected for initialization error. We use a scheme based on radiofrequency magnetic field gradients combined with microwave magnetic fields that is robust against multiple sources of decoherence and usable with essentially any trapped ion species. The scheme has the potential to perform simultaneous entangling operations on multiple pairs of ions in a large-scale trapped-ion quantum processor without increasing control signal power or complexity. Combining this technology with low-power laser light delivered via trap-integrated photonics21,22 and trap-integrated photon detectors for qubit readout23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.