High-fidelity Two-qubit Gates Research Articles

High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits

High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits

Acceptor-based qubit in silicon with tunable strain

Long coherence time and compatibility with semiconductor fabrication make spin qubits in silicon an attractive platform for quantum computing. In recent years, hole spin qubits are being developed as they have the advantages of weak coupling to nuclear spin noise and strong spin-orbit coupling (SOC), in constructing high-fidelity quantum gates. However, there are relatively few studies on the hole spin qubits in a single acceptor, which requires only low density of the metallic gates. In particular, the investigation of flexible tunability using controllable strain for fault-tolerant quantum gates of acceptor-based qubits is still lacking. Here, we study the tunability of electric dipole spin resonance (EDSR) of acceptor-based hole spin qubits with controllable strain. The flexible tunability of LH-HH splitting and spin-hole coupling (SHC) with the two kinds of strain can avoid high electric field at the "sweet spot", and the operation performance of the acceptor qubits could be optimized. Longer relaxation time or stronger EDSR coupling at low electric field can be obtained. Moreover, with asymmetric strain, two "sweet spots" are induced and may merge together, and form a second-order "sweet spot". As a result, the quality factor $Q$ can reach $10^{4}$ for single-qubit operation, with high tolerance for the electric field variation. Furthermore, the two-qubit operation of acceptor qubits based on dipole-dipole interaction is discussed for high-fidelity two-qubit gates. The tunability of spin qubit properties in acceptor via strain could provide promising routes for spin-based quantum computing.

Angle-robust two-qubit gates in a linear ion crystal

In trapped-ion quantum computers, two-qubit entangling gates are generated by applying spin-dependent force which uses phonons to mediate interaction between the internal states of the ions. To maintain high-fidelity two-qubit gates under fluctuating experimental parameters, robust pulse-design methods are applied to remove the residual spin-motion entanglement in the presence of motional mode-frequency drifts. Here we propose an improved pulse-design method that also guarantees the robustness of the two-qubit rotation angle against uniform mode-frequency drifts by concatenating pulses with opposite sensitivity of the angle to mode-frequency drifts. We experimentally verify significantly improved robustness of the rotation angle against uniform mode-frequency drifts, as well as observe an improvement in gate fidelity from 97.84(10)% to 98.11(11)%, compared to a single frequency-modulated pulse.

Designing Filter Functions of Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains

High-fidelity two-qubit gates in quantum computers are often hampered by fluctuating experimental parameters. The effects of time-varying parameter fluctuations lead to coherent noise on the qubits, which can be suppressed by designing control signals with appropriate filter functions. Here, we develop filter functions for M{\o}lmer-S{\o}rensen gates of trapped-ion quantum computers that accurately predict the change in gate error due to small parameter fluctuations at any frequency. We then design the filter functions of frequency-modulated laser pulses, and compare this method with pulses that are robust to static offsets of the motional-mode frequencies. Experimentally, we measure the noise spectrum of the motional modes and use it for designing the filter functions, which improves the gate fidelity from 99.23(7)% to 99.55(7)% in a five-ion chain.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors.

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubitgates.

High fidelity two-qubit gates on fluxoniums using a tunable coupler

Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.

Parametric longitudinal coupling between a high-impedance superconducting resonator and a semiconductor quantum dot singlet-triplet spin qubit

Coupling qubits to a superconducting resonator provides a mechanism to enable long-distance entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a controllable spin-photon coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator’s frequency. We measure the energy splitting of the qubit as a function of the drive amplitude and frequency of a microwave signal applied near the resonator antinode, revealing pronounced effects close to the resonator frequency due to longitudinal coupling. By tuning the amplitude of the drive, we reach a regime with longitudinal coupling exceeding 1 MHz. This mechanism for qubit-resonator coupling represents a stepping stone towards producing high-fidelity two-qubit gates mediated by a superconducting resonator.

Numerical optimization of amplitude-modulated pulses in microwave-driven entanglement generation

Microwave control of trapped ions can provide an implementation of high-fidelity two-qubit gates free from errors induced by photon scattering. Furthermore, microwave conductors may be embedded into a scalable trap structure, providing the chip-level integration of control that is desirable for scaling. Recent developments have demonstrated how amplitude modulation of the gate drive can permit a two-qubit entangling operation to become robust against motional mode noise and other experimental imperfections. Here, we discuss a method for the numerical optimization of the microwave pulse envelope to produce gate pulses with noise resilience, considerably faster operation and high energy efficiency.

Toward the Speed Limit of High-Fidelity Two-Qubit Gates.

Most implementations of quantum gate operations rely on external control fields to drive the evolution of the quantum system. Generating these control fields requires significant efforts to design the suitable control Hamiltonians. Furthermore, any error in the control fields reduces the fidelity of the implemented control operation with respect to the ideal target operation. Achieving sufficiently fast gate operations at low error rates remains therefore a huge challenge. In this Letter, we present a novel approach to overcome this challenge by eliminating, for specific gate operations, the time-dependent control fields entirely. This approach appears useful for maximizing the speed of the gate operation while simultaneously eliminating relevant sources of errors. We present an experimental demonstration of the concept in a single nitrogen-vacancy center in diamond at room temperature.

Realization of Fast All-Microwave Controlled-Z Gates with a Tunable Coupler

The development of high-fidelity two-qubit quantum gates is essential for digital quantum computing. Here, we propose and realize an all-microwave parametric controlled-Z (CZ) gates by coupling strength modulation in a superconducting Transmon qubit system with tunable couplers. After optimizing the design of the tunable coupler together with the control pulse numerically, we experimentally realized a 100 ns CZ gate with high fidelity of 99.38% ± 0.34% and the control error being 0.1%. We note that our CZ gates are not affected by pulse distortion and do not need pulse correction, providing a solution for the real-time pulse generation in a dynamic quantum feedback circuit. With the expectation of utilizing our all-microwave control scheme to reduce the number of control lines through frequency multiplexing in the future, our scheme draws a blueprint for the high-integrable quantum hardware design.

Coupler-Assisted Controlled-Phase Gate with Enhanced Adiabaticity

High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502; Phys. Rev. Lett. 125, 240503] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast ZZ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near $10^{-5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.

Realization of High-Fidelity Controlled-Phase Gates in Extensible Superconducting Qubits Design with a Tunable CouplerSupported by the National Key R&D Program of China (Grant No. 2017YFA0304300), the Chinese Academy of Sciences, Anhui Initiative in Quantum Information Technologies, Technology Committee of Shanghai Municipality, the National Natural Science Foundation of China (Grants Nos. 11905217, 11774326, and 11905294), the Shanghai Municipal Science and Technology

High-fidelity two-qubit gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design an extensible 5-qubit system in which center transmon qubit can couple to every four near-neighboring qubits via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating central qubit and one near-neighboring qubit. Speckle purity benchmarking and cross entropy benchmarking are used to assess the purity fidelity and the fidelity of the CZ gate. The average purity fidelity of the CZ gate is 99.69±0.04% and the average fidelity of the CZ gate is 99.65±0.04%, which means that the control error is about 0.04%. Our work is helpful for resolving many challenges in implementation of large-scale quantum systems.

3D integration and measurement of a semiconductor double quantum dot with a high-impedance TiN resonator

One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.

C-band single photons from a trapped ion via two-stage frequency conversion

Fiber-based quantum networks require photons at telecommunications wavelengths to interconnect qubits separated by long distances. Trapped ions are leading candidates for quantum networking with high-fidelity two-qubit gates, long coherence times, and the ability to readily emit photons entangled with the ion's internal qubit states. However, trapped ions typically emit photons at wavelengths incompatible with telecommunications fiber. Here, we demonstrate frequency conversion of visible photons, emitted from the S–P dipole transition of a trapped Ba+ ion into the telecommunications C-band. These results are an important step toward enabling a long-distance trapped ion quantum internet.

Crosstalk analysis for single-qubit and two-qubit gates in spin qubit arrays

Scaling up spin qubit systems requires high-fidelity single-qubit and two-qubit gates. Gate fidelities exceeding $98%$ were already demonstrated in silicon-based single and double quantum dots, whereas for the realization of larger qubit arrays, crosstalk effects on neighboring qubits must be taken into account. We analyze qubit fidelities impacted by crosstalk when performing single-qubit and two-qubit operations on neighbor qubits with a simple Heisenberg model. Furthermore, we propose conditions for driving fields to robustly synchronize Rabi oscillations and avoid crosstalk effects. In our analysis, we also consider crosstalk with two neighbors and show that double synchronization leads to a restricted choice for the driving field strength, exchange interaction, and thus gate time. Considering realistic experimental conditions, we propose a set of parameter values to perform a nearly crosstalk-free cnot gate and so open up the pathway to scalable quantum computing devices.

Full configuration interaction simulations of exchange-coupled donors in silicon using multi-valley effective mass theory

Donor spins in silicon have achieved record values of coherence times and single-qubit gate fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic gates, where the most natural coupling is the exchange interaction. To aid the efficient design of scalable donor-based quantum processors, we model the two-electron wave function using a full configuration interaction method within a multi-valley effective mass theory. We exploit the high computational efficiency of our code to investigate the exchange interaction, valley population, and electron densities for two phosphorus donors in a wide range of lattice positions, orientations, and as a function of applied electric fields. The outcomes are visualized with interactive images where donor positions can be swept while watching the valley and orbital components evolve accordingly. Our results provide a physically intuitive and quantitatively accurate understanding of the placement and tuning criteria necessary to achieve high-fidelity two-qubit gates with donors in silicon.

Single-tone pulse sequences and robust two-tone shaped pulses for three silicon spin qubits with always-on exchange

Quantum computation requires high-fidelity single-qubit and two-qubit gates on a scalable platform. Silicon spin qubits are a promising platform toward realization of this goal. In this paper we show how to perform single-qubit and CZ gates in a linear chain of three spin qubits with always-on exchange coupling, which is relevant for certain dot- and donor-based silicon devices. We also show how to make the CZ gate robust against both charge noise and pulse length error using a two-tone pulse shaping method. The robust pulse maintains a fidelity of 99.99% at 3.5% fluctuations in exchange or pulse amplitude, which is an improvement over the uncorrected pulses where this fidelity can only be maintained for fluctuations in exchange up to 2% or up to 0.2% in amplitude.

Realization of High-Fidelity CZ and ZZ -Free iSWAP Gates with a Tunable Coupler

High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is essential for addressing coherent leakage to the coupler and parasitic longitudinal ($ZZ$) interactions during two-qubit gates. Here, we present a systematic approach that goes beyond the dispersive approximation to exploit the engineered level structure of the coupler and optimize its control. Using this approach, we experimentally demonstrate CZ and $ZZ$-free iSWAP gates with two-qubit interaction fidelities of $99.76 \pm 0.07$% and $99.87 \pm 0.23$%, respectively, which are close to their $T_1$ limits.

Charge noise suppression in capacitively coupled singlet-triplet spin qubits under magnetic field

Charge noise is the main hurdle preventing high-fidelity operation, in particular that of two-qubit gates, of semiconductor-quantum-dot-based spin qubits. While certain sweet spots where charge noise is substantially suppressed have been demonstrated in several types of spin qubits, the existence of one for coupled singlet-triplet qubits is unclear. We theoretically demonstrate, using full configuration-interaction calculations, that a range of nearly sweet spots appear in the coupled singlet-triplet qubit system when a strong enough magnetic field is applied externally. We further demonstrate that ramping to and from the judiciously chosen nearly sweet spot using sequences based on the shortcut to adiabaticity offers maximal gate fidelities under charge noise and phonon-induced decoherence. These results should facilitate realization of high-fidelity two-qubit gates in singlet-triplet qubit systems.

Recent progress in atomistic modelling and simulations of donor spin qubits in silicon

Electron or nuclear spins associated with dopant atoms, such as phosphorus impurities in silicon (Si:P), have been shown to form excellent qubits with promising potential for scale-up towards a fault-tolerant quantum computer architecture. The remarkable progress in the design and characterisation of Si:P qubits and quantum gates has been led by recent experimental demonstrations. Equally importantly, advances in theoretical modelling and simulations over a number of years have underpinned the experimental efforts through the fundamental understanding of dopant physics and by providing crucial interpretation of the experimental evidence. This brief review article provides highlights of our research on developing atomistic theoretical methods and their application to the understanding, characterisation and scale-up of Si:P qubits in silicon. We have established a state-of-the-art theoretical framework which is capable of performing electronic structure simulations over millions of atoms. This includes a comprehensive set of central-cell corrections within atomistic tight-binding theory to simulate dopant energy spectra and electronic wave functions with high precision. When integrated with Bardeen’s tunnelling formalism and Chen’s derivative rule, the theoretical simulations were able to reproduce the measured spatially resolved scanning tunnelling microscope (STM) images of dopant wave functions, providing an unprecedented access to the dopant physics in silicon. A systematic examination of the STM image features (brightness and symmetry) allowed pinpointing of the dopant atom positions in silicon lattice with an exact atom precision and for dopant depths up to 5 nm below the silicon surface. The scale-up of the metrology technique was demonstrated by training a machine learning algorithm such as convolutional neural network. For the design and implementation of high-fidelity two-qubit quantum gates, we investigated exchange interaction between dopant pairs and showed that the application of a small lattice strain could provide a full control in the presence of one-lattice site donor position variations. The state-of-the-art computational capability developed by our team is a culmination of more than five years of research efforts – it has been well-benchmarked against several different experimental measurements and is expected to play an important role in design and characterisation of quantum gates and scale-up architectures in the coming years.