Trapped-Ion Quantum Logic with Global Radiation Fields

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.

Quantum Phase Transitions for an Integrable Quantum Rabi-like Model with Two Interacting Qubits

A two-interacting-qubit quantum Rabi-like model with vanishing transverse fields on the qubit pair is studied. Independently of the coupling regime, this model can be exactly and unitarily reduced to two independent single-spin quantum Rabi models, where the spin-spin coupling plays the role of the transverse field. This transformation and the analytical treatment of the single-spin quantum Rabi model provide the key to prove the integrability of our model. The existence of different first-order quantum phase transitions, characterized by discontinuous two-spin magnetization, mean photon number, and concurrence, is brought to light.

Integrable quantum many-body sensors for AC field sensing

Quantum sensing is inevitably an elegant example of the supremacy of quantum technologies over their classical counterparts. One of the desired endeavors of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with a limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing.

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.

Microwaves in Quantum Computing

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers.

Bottom-Gate Approach for All Basic Logic Gates Implementation by a Single-Type IGZO-Based MOS Transistor with Reduced Footprint

Logic functions are the key backbone in electronic circuits for computing applications. Complementary metal-oxide-semiconductor (CMOS) logic gates, with both n-type and p-type channel transistors, have been to date the dominant building blocks of logic circuitry as they carry obvious advantages over other technologies. Important physical limits are however starting to arise, as the transistor-processing technology has begun to meet scaling-down difficulties. To address this issue, there is the crucial need for a next-generation electronics era based on new concepts and designs. In this respect, a single-type channel multigate MOS transistor (SMG-MOS) is introduced holding the two important aspects of processing adaptability and low static dissipation of CMOS. Furthermore, the SMG-MOS approach strongly reduces the footprint down to 40% or even less area needed for current CMOS logic function in the same processing technology node. Logic NAND, NOT, AND, NOR, and OR gates, which typically require a large number of CMOS transistors, can be realized by a single SMG-MOS transistor. Two functional examples of SMG-MOS are reported here with their analysis based both on simulations and experiments. The results strongly suggest that SMG-MOS can represent a facile approach to scale down complex integrated circuits, enabling design flexibility and production rates ramp-up.

Robust and Resource-Efficient Microwave Near-Field Entangling ^{9}Be^{+} Gate

Microwave trapped-ion quantum logic gates avoid spontaneous emission as a fundamental source of decoherence. However, microwave two-qubit gates are still slower than laser-induced gates and hence more sensitive to fluctuations and noise of the motional mode frequency. We propose and implement amplitude-shaped gate drives to obtain resilience to such frequency changes without increasing the pulse energy per gate operation. We demonstrate the resilience by noise injection during a two-qubit entangling gate with ^{9}Be^{+} ion qubits. In the absence of injected noise, amplitude modulation gives an operation infidelity in the 10^{-3} range.

Shuttling of Rydberg Ions for Fast Entangling Operations

We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using the high electric polarizability of the Rydberg electronic states in combination with mutual Coulomb coupling of ions that establishes common modes of motion. After laser initialization of ions to a superposition of ground and Rydberg states, the entanglement operation is driven purely by applying a voltage pulse that shuttles the ion crystal back and forth. This operation can achieve entanglement on a sub-μs timescale, more than 2 orders of magnitude faster than typical gate operations driven by continuous-wave lasers. Our analysis shows that the fidelity achieved with this protocol can exceed 99.9% with experimentally achievable parameters.

Compensation of the trap-induced quadrupole interaction in trapped Rydberg ions

The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.

Trapped-Ion Spin-Motion Coupling with Microwaves and a Near-Motional Oscillating Magnetic Field Gradient

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.

Versatile laser-free trapped-ion entangling gates

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 eitherσ ^ ϕ ⊗ σ ^ ϕ orσ ^ z ⊗ σ ^ 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. Theσ ^ z ⊗ σ ^ z gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

Resilient Entangling Gates for Trapped Ions

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 path towards relaxing ion cooling requirements in practical realizations of quantum computing and simulation.

Robust Entanglement Gates for Trapped-Ion Qubits

High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits; however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the renowned Mølmer-Sørensen gate by using multitone drives. We experimentally implemented several of the proposed gates on ^{88}Sr^{+} ions trapped in a linear Paul trap and verified their resilience.

High-Fidelity Preservation of Quantum Information During Trapped-Ion Transport

A promising scheme for building scalable quantum simulators and computers is the synthesis of a scalable system using interconnected subsystems. A prerequisite for this approach is the ability to faithfully transfer quantum information between subsystems. With trapped atomic ions, this can be realized by transporting ions with quantum information encoded into their internal states. Here, we measure with high precision the fidelity of quantum information encoded into hyperfine states of a ^{171}Yb^{+} ion during ion transport in a microstructured Paul trap. Ramsey spectroscopy of the ion's internal state is interleaved with up to 4000 transport operations over a distance of 280  μm each taking 12.8  μs. We obtain a state fidelity of 99.9994( _{-7}^{+6})% per ion transport.

Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of sqrt[N], with N being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson-mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of π/2, independently of the number of pulses applied. We experimentally demonstrate the robustness of our entangling gate with fast dynamical decoupling to σ_{z} noise using ions in a Paul trap.

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Ions trapped in a quadrupole Paul trap have been considered one of the strong physical candidates to implement quantum information processing. This is due to their long coherence time and their capability to manipulate and detect individual quantum bits (qubits). In more recent years, microfabricated surface ion traps have received more attention for large-scale integrated qubit platforms. This paper presents a microfabrication methodology for ion traps using micro-electro-mechanical system (MEMS) technology, including the fabrication method for a 14 µm-thick dielectric layer and metal overhang structures atop the dielectric layer. In addition, an experimental procedure for trapping ytterbium (Yb) ions of isotope 174 (174Yb+) using 369.5 nm, 399 nm, and 935 nm diode lasers is described. These methodologies and procedures involve many scientific and engineering disciplines, and this paper first presents the detailed experimental procedures. The methods discussed in this paper can easily be extended to the trapping of Yb ions of isotope 171 (171Yb+) and to the manipulation of qubits.

Blueprint for a microwave trapped ion quantum computer

The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion-based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation-based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error-threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects.