Robust and fast microwave-driven quantum logic for trapped-ion qubits

Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, where is the difference in qubit frequencies.

We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 10% fluctuations. We also find that the optimized scheme can also reduce errors caused by higher-order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows a new route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.

We demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies 72.3 and 136.3 MHz. The gate is activated by a 61.6-ns-long pulse at a frequency between noncomputational transitions |10⟩−|20⟩ and |11⟩−|21⟩, during which the qubits complete only four and eight Larmor periods, respectively. The measured gate error of (8±1)×10−3 is limited by decoherence in the noncomputational subspace, which will likely improve in the next-generation devices. Although our qubits are about 50 times slower than transmons, the two-qubit gate is faster than microwave-activated gates on transmons, and the gate error is on par with the lowest reported. Architectural advantages of low-frequency fluxoniums include long qubit coherence time, weak hybridization in the computational subspace, suppressed residual ZZ-coupling rate (here 46 kHz), and the absence of either excessive parameter-matching or complex pulse-shaping requirements.6 MoreReceived 4 November 2020Accepted 17 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.021026Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCapacitanceChargeEntanglement productionJosephson effectQuantum computationQuantum controlQuantum gatesQuantum information with solid state qubitsSuperconductivityQuantum InformationInterdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

Ultracold trapped atomic ions excited into highly energetic Rydberg states constitute a promising platform for scalable quantum information processing. Elementary building blocks for such tasks are high-fidelity and sufficiently fast entangling two-qubit gates, which can be achieved via strong dipole–dipole interactions between microwave-dressed Rydberg ions, as recently demonstrated experimentally (Zhang et al 2020 Nature 580 345). We theoretically investigate the performance of three protocols leading to controlled-phase gate operations. Starting from a microscopic description of Rydberg ions in a linear Paul trap, we derive an effective Hamiltonian that faithfully captures the essential dynamics underlying the gate protocols. We then use an optimization scheme to fine-tune experimentally controllable parameters like laser detuning and Rabi frequency to yield maximal gate fidelity under each studied protocol. We show how non-adiabatic transitions resulting from fast laser driving relative to the characteristic time scales of the system detrimentally affect the fidelity. Despite this, we demonstrate that in the realistic scenario of Rydberg ions with finite radiative lifetimes, optimizing the best found gate protocol enables achievement of fidelities as high as 99.25 % for a gate time of 0.2 μ s . This considerably undercuts entangling gate durations between ground state ions, for which gate times are typically limited by the comparably slower time scales of vibrational modes. Overall, this places trapped Rydberg ions into the regime where fast high-accuracy quantum computing and eventually quantum error correction become possible.

A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.

Microwave-driven quantum logic gates in trapped-ion systems offer a scalable and laser-free alternative to optical control, with the potential for robust integration into surface-electrode trap architectures. In this work, we present a systematic design guideline for planar ion traps optimized for fast two-qubit microwave gates using chip-integrated conductors. We investigate two electrode configurations, one employing a single microwave line for driving σ transitions, and another with two symmetric lines for π transitions. Through finite-element simulations, we analyze ion height, magnetic field gradients, heating effects, and gate durations under realistic cryogenic conditions. Our results show that both configurations can achieve two-qubit gate times in the order of 10 μs for Be+9 and Ca+40 ions.

Because of its geometric nature, holonomic quantum computation is fault tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantum computation in a liquid NMR quantum information processor. Two noncommuting one-qubit holonomic gates, rotations about x and z axes, and the two-qubit holonomic CNOT gate are realized by evolving the work qubits and an ancillary qubit nonadiabatically. The successful realizations of these universal elementary gates in nonadiabatic holonomic quantum computation demonstrates the experimental feasibility of this quantum computing paradigm.

We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broadband optical pulses to rotate electron spins and provide the clock signal to the system. Nonlocal two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.

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 multi-qubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.

We present a scalable uniform technique for construction of highly conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine-learning architecture with a convolutional neural network, we illustrate a fast, robust, and precise quantum state tomography for continuous variables, through the experimentally measured data generated from the balanced homodyne detectors. Compared with the maximum likelihood estimation method, which suffers from time-consuming and overfitting problems, a well-trained machine fed with squeezed vacuum and squeezed thermal states can complete the task of reconstruction of the density matrix in less than one second. Moreover, the resulting fidelity remains as high as 0.99 even when the antisqueezing level is higher than 20dB. Compared with the phase noise and loss mechanisms coupled from the environment and surrounding vacuum, experimentally, the degradation information is unveiled with machine learning for low and high noisy scenarios, i.e., with the antisqueezing levels at 12dB and 18dB, respectively. Our neural network enhanced quantum state tomography provides the metrics to give physical descriptions of every feature observed in the quantum state with a single scan measurement just by varying the local oscillator phase from 0 to 2π and paves a way of exploring large-scale quantum systems in real time.

Global control strategies for arrays of qubits are a promising pathway to scalable quantum computing. A continuous-wave global field provides decoupling of the qubits from background noise. However, this approach is limited by variability in the parameters of individual qubits in the array. Here we show that by modulating a global field simultaneously applied to the entire array, we are able to encode qubits that are less sensitive to the statistical scatter in qubit resonance frequency and microwave amplitude fluctuations, which are problems expected in a large-scale system. We name this approach the SMART (sinusoidally modulated, always rotating, and tailored) qubit protocol. We show that there exist optimal modulation conditions for qubits in a global field that robustly provide improved coherence times. We discuss in further detail the example of spins in silicon quantum dots, in which universal one- and two-qubit control is achieved electrically by controlling the spin-orbit coupling of individual qubits and the exchange coupling between spins in neighboring dots. This paper provides a high-fidelity qubit operation scheme in a global field, significantly improving the prospects for scalability of spin-based quantum computer architectures.

Trapped ion hardware has made significant progress recently and is now one of the leading platforms for quantum computing. To construct two-qubit gates in trapped ions, experimental manipulation approaches for ion chains are becoming increasingly prevalent. Given the restricted control technology, how implementing high-fidelity quantum gate operations is crucial. Many works in current pulse design optimization focus on ion–phonon and effective ion–ion couplings while ignoring the first-order derivative terms expansion impacts of these two terms brought on by experiment defects. This paper proposes a novel robust quantum control optimization method in trapped ions. By introducing the first-order derivative terms caused by the error into the optimization cost function, we generate an extremely robust Mølmer–Sørensen gate with infidelity below 10−3 under a drift noise range of ±10 kHz, the relative robustness achieves a tolerance of ±5%, compared to the 200-kHz frequency spacing between phonon modes, and for time noise drift, the tolerance reached to 2%. Our work reveals the vital role of the first-order derivative terms of coupling in trapped ion pulse control optimization, especially the first-order derivative terms of ion–ion coupling. It provides a robust optimization scheme for realizing more efficient entangled states in trapped ion platforms.

For maintaining the stability of voltage and frequency, the droop control is often adopted when micro-grid is in islanding operational mode. Although this method can control the fluctuation of voltage and frequency, when the loads change, its implementation effect is weak In order to solve the mentioned problem, an improved dynamic self-adjusting droop control strategy is proposed: on the basis of the traditional one, PI control of voltage and frequency is introduced to control flow. The principle and implementation steps of this method are analyzed. Finally, the operating characteristics of overloading connection, overloading cutting-off and loads disturbance are simulated and discussed based on an islanding mode built in Matlab/Simulink. The results show the proposed method can control the voltage and frequency more effectively and faster than traditional droop control, and can enhance the stability of micro-grid in islanding operational mode.

We have measured flux-noise correlations in a tunable superconducting flux\nqubit. The device consists of two loops that independently control the qubit's\nenergy splitting and tunnel coupling. Low frequency flux noise in the loops\ncauses fluctuations of the qubit frequency and leads to dephasing. Since the\nnoises in the two loops couple to different terms of the qubit Hamiltonian, a\nmeasurement of the dephasing rate at different bias points provides a way to\nextract both the amplitude and the sign of the noise correlations. We find that\nthe flux fluctuations in the two loops are anti-correlated, consistent with a\nmodel where the flux noise is generated by randomly oriented unpaired spins on\nthe metal surface.\n