D. T. C. Allcock

Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the pre-existing toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable $D_{5/2}$ qubit manifold of a single trapped $^{40}$Ca$^+$ ion illuminated by 976 nm light that is -44 THz detuned from the dipole-allowed transition to the $P_{3/2}$ manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities $<10^{-4}$ are possible.

Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of $\sim 94\%$ of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44\,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73\% and a SPAM-corrected Bell state fidelity of 98.61\%. When subtracting erasure errors, this fidelity becomes 99.16\%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.

The central challenge of quantum computing is implementing high-fidelity quantum gates at scale. However, many existing approaches to qubit control suffer from a scale-performance trade-off, impeding progress towards the creation of useful devices. Here, we present a vision for an electronically controlled trapped-ion quantum computer that alleviates this bottleneck. Our architecture utilizes shared current-carrying traces and local tuning electrodes in a microfabricated chip to perform quantum gates with low noise and crosstalk regardless of device size. To verify our approach, we experimentally demonstrate low-noise site-selective single- and two-qubit gates in a seven-zone ion trap that can control up to 10 qubits. We implement electronic single-qubit gates with 99.99916(7)% fidelity, and demonstrate consistent performance with low crosstalk across the device. We also electronically generate two-qubit maximally entangled states with 99.97(1)% fidelity and long-term stable performance over continuous system operation. These state-of-the-art results validate the path to directly scaling these techniques to large-scale quantum computers based on electronically controlled trapped-ion qubits.

We experimentally implement circuits of one and two mode operations on two motional modes of a single trapped ion. This is achieved by implementing the required displacement, squeezing, two-mode squeezing, and beamsplitter operations using oscillating electric potentials applied to the trap electrodes. The resulting electric fields drive the modes resonantly or parametrically without the need for optical forces. As a demonstration, we implement SU(2) and SU(1,1) interferometers with phase sensitivities near the Cramér-Rao bound. We report a maximum sensitivity of a SU(2) interferometer within $0.67(5)\,$dB of the standard quantum limit (SQL) as well as a single and two-mode SU(1,1) sensitivity of $5.9(2)\,$dB and $4.5(2)\,$dB below the SQL respectively.

One of the most formidable challenges of scaling up quantum computers is that of control signal delivery. Today's small-scale quantum computers typically connect each qubit to one or more separate external signal sources. This approach is not scalable due to the I/O limitations of the qubit chip, necessitating the integration of control electronics. However, it is no small feat to shrink control electronics into a small package that is compatible with qubit chip fabrication and operation constraints without sacrificing performance. This so-called "wiring challenge" is likely to impact the development of more powerful quantum computers even in the near term. In this paper, we address the wiring challenge of trapped-ion quantum computers. We describe a control architecture called WISE (Wiring using Integrated Switching Electronics), which significantly reduces the I/O requirements of ion trap quantum computing chips without compromising performance. Our method relies on judiciously integrating simple switching electronics into the ion trap chip - in a way that is compatible with its fabrication and operation constraints - while complex electronics remain external. To demonstrate its power, we describe how the WISE architecture can be used to operate a fully connected 1000-qubit trapped ion quantum computer using ~ 200 signal sources at a speed of ~ 40 - 2600 quantum gate layers per second.

We show experimentally that a broad class of interactions involving quantum harmonic oscillators can be made stronger (amplified) using a unitary squeezing protocol. While our demonstration uses the motional and spin states of a single trapped $^{25}$Mg$^{+}$ ion, the scheme applies generally to Hamiltonians involving just a single harmonic oscillator as well as Hamiltonians coupling the oscillator to another quantum degree of freedom such as a qubit, covering a large range of systems of interest in quantum information and metrology applications. Importantly, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, nor does it require a well-defined phase relationship between the squeezing interaction and the rest of the system dynamics, making it potentially useful in instances where certain aspects of a signal or interaction may be unknown or uncontrolled.

We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous, simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counter-rotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground state qubits in commonly-used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in metastable $D_{5/2}$ manifold, showing that gate errors below $10^{-4}$ are achievable for all commonly-used trapped ions.

We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multi-zone 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 localised 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 localisation of the electric field.

We propose a new scheme for individual addressing of trapped ion qubits, selecting them via their motional frequency. We show that geometric phase gates can perform single-qubit rotations using the coherent interference of spin-independent and (global) spin-dependent forces. The spin-independent forces, which can be generated via localised electric fields, increase the gate speed while reducing its sensitivity to motional decoherence, which we show analytically and numerically. While the scheme applies to most trapped ion experimental setups, we numerically simulate a specific laser-free implementation, showing cross-talk errors below $10^{-6}$ for reasonable parameters.

The majority of microfabricated ion traps in use for quantum information processing are of the 2D 'surface-electrode' type or of the 3D 'wafer' type. Surface-electrode traps greatly simplify fabrication and hold the promise of allowing trapped-ion quantum computers to scale via standard semiconductor industry fabrication techniques. However, their geometry constrains them to having much lower trapping efficiency, depth, and harmonicity compared to 3D geometries. Conversely 3D geometries offer superior trap performance but fabrication is more complex, limiting potential to scale. We describe new 'trench' geometries that exist in the design space between these two paradigms. They still allow for a simple, planar electrode layer but with much more favourable trapping properties. We propose such traps could be 3D-printed over a 2D wafer with microfabricated components already integrated into it, thus retaining all the integration techniques and scaling advantages of surface-electrode traps. As a proof of principle we use 2-photon direct laser writing lithography to print the required electrode structures with the proposed geometry.

Quantum computers, much like their classical counterparts, will likely benefit from flexible qubit encodings that can be matched to different tasks. For trapped ion quantum processors, a common way to access multiple encodings is to use multiple, co-trapped atomic species. Here, we outline an alternative approach that allows flexible encoding capabilities in single-species systems through the use of long-lived metastable states as an effective, programmable second species. We describe the set of additional trapped ion primitives needed to enable this protocol and show that they are compatible with large-scale systems that are already in operation.

We report precision measurements of the nuclear magnetic moment of \textsuperscript{43}Ca\textsuperscript{+}, made by microwave spectroscopy of the 4s $^2$S$_{1/2}$ $\left|F=4, M=0\right\rangle \rightarrow \left|F=3, M=1\right\rangle$ ground level hyperfine clock transition at a magnetic field of $\approx$ 146 G, using a single laser-cooled ion in a Paul trap. We measure a clock transition frequency of $f = 3199941076.920 \pm 0.046$ Hz, from which we determine $μ_I / μ_{\rm{N}} = -1.315350(9)(1)$, where the uncertainty (9) arises from uncertainty in the hyperfine $A$ constant, and the (1) arises from the uncertainty in our measurement. This measurement is not corrected for diamagnetic shielding due to the bound electrons. We make a second measurement which is less precise but agrees with the first. We use our $μ_I$ value, in combination with previous NMR results, to extract the change in shielding constant of calcium ions due to solvation in D$_2$O: $Δσ= -0.00022(1)$.

Universal control of multiple qubits -- the ability to entangle qubits and to perform arbitrary individual qubit operations -- is a fundamental resource for quantum computation, simulation, and networking. Here, we implement a new laser-free scheme for universal control of trapped ion qubits based on microwave magnetic fields and radiofrequency magnetic field gradients. We demonstrate high-fidelity entanglement and individual control by creating symmetric and antisymmetric two-qubit maximally entangled states with fidelities in the intervals [0.9983, 1] and [0.9964, 0.9988], respectively, at 68% confidence, corrected for state initialization error. This technique is robust against multiple sources of decoherence, usable with essentially any trapped ion species, and has the potential to perform simultaneous entangling operations on many pairs of ions without increasing control signal power or complexity.

Strong and precisely-controlled interactions between quantum objects are essential for quantum information processing, simulation, and sensing, and for the formation of exotic quantum matter. A well-established paradigm for coupling otherwise weakly-interacting quantum objects is to use auxiliary bosonic quantum excitations to mediate the interactions. Important examples include photon-mediated interactions between atoms, superconducting qubits, and color centers in diamond, and phonon-mediated interactions between trapped ions and between optical and microwave photons. Boson-mediated interactions can in principle be amplified through parametric driving of the boson channel; the drive need not couple directly to the interacting quantum objects. This technique has been proposed for a variety of quantum platforms, but has not to date been realized in the laboratory. Here we experimentally demonstrate the amplification of a boson-mediated interaction between two trapped-ion qubits by parametric modulation of the trapping potential. The amplification provides up to a 3.25-fold increase in the interaction strength, validated by measuring the speedup of two-qubit entangling gates. This amplification technique can be used in any quantum platform where parametric modulation of the boson channel is possible, enabling exploration of new parameter regimes and enhanced quantum information processing.

We report high-fidelity state readout of a trapped ion qubit using a trap-integrated photon detector. We determine the hyperfine qubit state of a single $^9$Be$^+$ ion held in a surface-electrode rf ion trap by counting state-dependent ion fluorescence photons with a superconducting nanowire single-photon detector (SNSPD) fabricated into the trap structure. The average readout fidelity is 0.9991(1), with a mean readout duration of 46 $μ$s, and is limited by the polarization impurity of the readout laser beam and by off-resonant optical pumping. Because there are no intervening optical elements between the ion and the detector, we can use the ion fluorescence as a self-calibrated photon source to determine the detector quantum efficiency and its dependence on photon incidence angle and polarization.

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.

Detection of the weakest forces in nature and the search for new physics are aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. Here we demonstrate a widely applicable technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal "squeezing" interactions before and after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implement this protocol with a trapped-ion mechanical oscillator and measure an increase of up to 17.5(3) decibels in sensitivity to small displacements.

We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.

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 fluctuations. The ${\hatσ_{z}\otimes\hatσ_{z}}$ gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field.

We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43Ca+ ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent "atomic clock" qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ion's radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed.

Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing. Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here, we use a deterministic quantum logic gate to generate a "hybrid" entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally-entangled state of one Ca-40 qubit and one Ca-43 qubit, held 3.5 microns apart in the same ion trap, with 99.8(6)% fidelity. We test the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations, or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors due to photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential pre-requisite for general-purpose quantum computing.

We describe an ex-situ surface-cleaning procedure that is shown to reduce motional heating from ion-trap electrodes. This precleaning treatment, to be implemented immediately before the final assembly and vacuum processing of ion traps, removes surface contaminants remaining after the electrode-fabrication process. We incorporate a multi-angle ion-bombardment treatment intended to clean the electrode surfaces and interelectrode gaps of microfabricated traps. This procedure helps to minimize redeposition in the gaps between electrodes that can cause electrical shorts. We report heating rates in a stylus-type ion trap prepared in this way that are lower by one order of magnitude compared to a similar untreated stylus-type trap using the same experimental setup.

We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.

We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zone, while a similar set of electrodes is used to null the residual microwave field in a neighbouring zone. The geometry is chosen to reduce the residual field to the 0.5% level without nulling fields; with nulling, the crosstalk may be kept close to the 0.01% level for realistic microwave amplitude and phase drift. Using standard photolithography and electroplating techniques, we have fabricated a proof-of-principle electrode array with two trapping zones. We discuss requirements for the microwave drive system and prospects for scalability to a large two-dimensional trap array.

We describe and implement a method to restore the state of a single qubit, in principle perfectly, after it has partially collapsed. The method resembles the classical Hahn spin-echo, but works on a wider class of relaxation processes, in which the quantum state partially leaves the computational Hilbert space. It is not guaranteed to work every time, but successful outcomes are heralded. We demonstrate using a single trapped ion better performance from this recovery method than can be obtained employing projection and post-selection alone. The demonstration features a novel qubit implementation that permits both partial collapse and coherent manipulations with high fidelity.

We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the 2S1/2 to 2P1/2 transition as usual, but repump via the 2P3/2 level. By filtering out light on the cooling transition and detecting only the fluorescence from the 2P_3/2 to 2S1/2 decays, we suppress the scattered laser light background count rate to 1 per second while maintaining a signal of 29000 per second with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam.

Laser-cleaning of the electrodes in a planar micro-fabricated ion trap has been attempted using ns pulses from a tripled Nd:YAG laser at 355nm. The effect of the laser pulses at several energy density levels has been tested by measuring the heating rate of a single 40Ca+ trapped ion as a function of its secular frequency. A reduction of the electric-field noise spectral density by ~50% has been observed and a change in the frequency dependence also noticed. This is the first reported experiment where the "anomalous heating" phenomenon has been reduced by removing the source as opposed to reducing its thermal driving by cryogenic cooling. This technique may open the way to better control of the electrode surface quality in ion microtraps.

We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap electrodes, and the heating rate for a single trapped ion. The performance of this trap is found to be comparable with others of the same size scale.

We describe the fabrication and characterization of a new surface-electrode Paul ion trap designed for experiments in scalable quantum information processing with Ca+. A notable feature is a symmetric electrode pattern which allows rotation of the normal modes of ion motion, yielding efficient Doppler cooling with a single beam parallel to the planar surface. We propose and implement a technique for micromotion compensation in all directions using an infrared repumper laser beam directed into the trap plane. Finally, we employ an alternate repumping scheme that increases ion fluorescence and simplifies heating rate measurements obtained by time-resolved ion fluorescence during Doppler cooling.