Gate fidelity comparison in semiconducting spin qubit implementations affected by control noises

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

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Spin qubits in semiconductor quantum dots are an attractive candidate for scalable quantum information processing. Reliable quantum state transfer and entanglement between spatially separated spin qubits is a highly desirable but challenging goal. Here, we propose a fast and high-fidelity quantum state transfer scheme for two spin qubits mediated by virtual microwave photons. Our general strategy involves using a superadiabatic pulse to eliminate non-adiabatic transitions, without the need for increased control complexity. We show that arbitrary quantum state transfer can be achieved with a fidelity of 95.1% within a 60 ns short time under realistic parameter conditions. We also demonstrate the robustness of this scheme to experimental imperfections and environmental noises. Furthermore, this scheme can be directly applied to the generation of a remote Bell entangled state with a fidelity as high as 97.6%. These results pave the way for fault-tolerant quantum computation on spin quantum network architecture platforms.

In the field of semiconductor quantum dot spin qubits, there is growing interest in leveraging the unique properties of hole-carrier systems and their intrinsically strong spin-orbit coupling to engineer novel spin qubits. In contrast to the weak spin-orbit interaction found in Si, strong spin-orbit coupling in Ge may allow purely electrical spin control using the electric field component of a microwave drive signal applied to a confinement gate, without the need for additional components such as microwave stripline antennas or micromagnets. A crucial aspect in the search for alternative semiconductor qubit host materials is the need to maintain the advantages of existing platforms such as Si: low disorder, long coherence times, extensibility, and semiconductor foundry compatibility. Recent advances in semiconductor heterostructure growth have made available high quality, undoped Ge/SiGe quantum wells that can serve as hosts for hole spin qubits. These quantum wells consist of a pure strained Ge layer flanked by Ge-rich SiGe layers above and below, grown by reduced pressure chemical vapor deposition. Isotopic enrichment is possible if required. The heavy hole charge carriers are characterized by a small effective mass m* ~ 0.08m 0 (about 2.4x lighter than for electrons in Si), high mobility μ ≥ 1E5 cm2/Vs, and highly anisotropic g-factors. The small effective mass should allow relatively large and easily-coupled quantum dots. The next-nearest light hole band is theoretically predicted to be on the order of ~ 100 meV below the heavy hole band. The p-orbital character of the hole wavefunction may provide an advantage in minimizing contact hyperfine interactions with nonzero-spin lattice nuclei. There is both theoretical and experimental evidence of a cubic Rashba-type spin-orbit interaction in this material, whose large strength is manifest as a spin-orbit length on the order of 1 micrometer. An additional advantage over Si is that the two-dimensional band structure of Ge quantum wells does not feature valley states, which can present difficulties for qubit operations. Here, we will describe our ongoing efforts to prepare spin qubits in this platform, including development of gated device architectures, device tuning protocols, and charge-sensing capabilities. Initial work focused on single-layer gate layouts, in which lithographically-defined single and double quantum dots were demonstrated at dilution refrigerator temperatures. Charging energies of ~ 1.7 meV were observed. These devices featured a broad and shallow potential landscape, and only a small number of holes could be confined to a quantum dot. Although adjacent quantum dots could be coupled to one another, this coupling was not easily tuned using this gate design. These limitations in the confinement and control of quantum dots motivated the subsequent adoption of multilayer gate-stack architectures, similar to what has been demonstrated in Si. Our three-layer devices feature gate electrodes designed for accumulation of holes, local depletion to form quantum dots, and selective isolation/screening of electric fields. Device structures feature Ti/Pt gates, ALD oxide dielectrics, and implanted ohmic contacts. Symmetrically constructed devices comprise two gated channels for quantum dot confinement, one to be used as the quantum dot under study and the other operated as a local charge sensor. By monitoring the conductance of the charge sensor as the quantum dot is tuned, we can remotely determine the dot’s occupation number, in principle down to the last hole. Iterative cycles of device fabrication and measurement, combined with numerical modeling, have allowed continuous improvements to the device design. Early three-layer device designs suffered from poor isolation between the upper and lower mirror-symmetric device channels. Numerical modeling showed (and measurements have confirmed) that an additional isolation gate could allow improved autonomy of the two channels while maintaining their electrostatic coupling needed for charge sensing. Ongoing, simulation-informed work to fine-tune the device geometry, as well as efforts toward a qubit demonstration, will be discussed. This work was funded, in part, by the Laboratory Directed Research and Development Program and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in this article do not necessarily represent the views of the US Department of Energy or the United States Government. The work at NTU was supported by the Ministry of Science and Technology (107-2622-8-002-018-). Figure 1

Combining external control with long spin lifetime and coherence is a key challenge for solid state spin qubits. Tunnel coupling with electron Fermi reservoir provides robust charge state control in semiconductor quantum dots, but results in undesired relaxation of electron and nuclear spins through mechanisms that lack complete understanding. Here, we unravel the contributions of tunnelling-assisted and phonon-assisted spin relaxation mechanisms by systematically adjusting the tunnelling coupling in a wide range, including the limit of an isolated quantum dot. These experiments reveal fundamental limits and trade-offs of quantum dot spin dynamics: while reduced tunnelling can be used to achieve electron spin qubit lifetimes exceeding 1 s, the optical spin initialisation fidelity is reduced below 80%, limited by Auger recombination. Comprehensive understanding of electron-nuclear spin relaxation attained here provides a roadmap for design of the optimal operating conditions in quantum dot spin qubits.

Enhancing the precision of measurements in double quantum dot systems via transmission line resonator

Long-distance transfer of quantum information in architectures based on\nquantum dot spin qubits will be necessary for their scalability. One way of\nachieving it is to simply move the electron between two quantum registers.\nPrecise control over the electron shuttling through a chain of tunnel-coupled\nquantum dots is possible when interdot energy detunings are changed\nadiabatically. Deterministic character of shuttling is however endangered by\ncoupling of the transferred electron to thermal reservoirs: sources of\nfluctuations of electric fields, and lattice vibrations. We theoretically\nanalyse how the electron transfer between two quantum dots is affected by\nelectron-phonon scattering, and interaction with sources of $1/f$ and Johnson\ncharge noise in both detuning and tunnel coupling. The electron-phonon\nscattering turns out to be irrelevant in Si quantum dots, while a competition\nbetween the effects of charge noise and Landau-Zener effect leads to an\nexistence of optimal detuning sweep rate, at which probability of leaving the\nelectron behind is minimal. In GaAs quantum dots, on the other hand, coupling\nto phonons is strong enough to make the phonon-assisted processes of interdot\ntransfer dominate over influence of charge noise. The probability of leaving\nthe electron behind depends then monotonically on detuning sweep rate, and\nvalues much smaller than in silicon can be obtained for slow sweeps. However,\nafter taking into account limitations on transfer time imposed by need for\npreservation of electron's spin coherence, minimal probabilities of leaving the\nelectron behind in both GaAs- and Si-based double quantum dots turn out to be\nof the same order of magnitude. Bringing them down below $10^{-3}$ requires\ntemperatures $\\leq \\! 100$ mK and tunnel couplings above $20$ $\\mu$eV.\n

Spin qubits in germanium gate-defined quantum dots have made considerable progress within the last few years, partially due to their strong spin-orbit coupling and site-dependent g-tensors. While this characteristic of the g-factors removes the need for micromagnets and allows for the possibility of all-electric qubit control, relying on these g-tensors necessitates the need to understand their sensitivity to the confinement potential that defines the quantum dots. Here, we demonstrate a S − T_ qubit whose frequency is a strong function of the voltage applied to the barrier gate shared by the quantum dots. We find a g-factor that can be approximately increased by an order of magnitude adjusting the barrier gate voltage only by 12 mV. We show how this strong dependence could potentially be attributed to the dots moving through a variable strain environment in our device. This work not only reinforces previous findings that site-dependent g-tensors in germanium can be utilized for qubit manipulation, but reveals the sensitivity and tunability these g-tensors have to the electrostatic confinement of the quantum dot.

Spin qubits in germanium are a promising contender for scalable quantum computers. Reading out of the spin and charge configuration of quantum dots formed in Ge/Si core/shell nanowires is typically performed by measuring the current through the nanowire. Here, we demonstrate a more versatile approach on investigating the charge configuration of these quantum dots. We employ a high-impedance, magnetic-field resilient superconducting resonator based on NbTiN and couple it to a double quantum dot in a Ge/Si nanowire. This allows us to dispersively detect charging effects, even in the regime where the nanowire is fully pinched off and no direct current is present. Furthermore, by increasing the electro-chemical potential far beyond the nanowire pinch-off, we observe indications for depleting the last hole in the quantum dot by using the second quantum dot as a charge sensor. This work opens the door for dispersive readout and future spin-photon coupling in this system.

We develop an architecture for distributed quantum computation using quantum bus of plasmonic circuits and spin qubits in self-assembled quantum dots. Deterministic quantum gates between two distant spin qubits can be reached by using an adiabatic approach in which quantum dots couple with highly detuned plasmon modes in a metallic nanoring. Plasmonic quantum bus offers a robust and scalable platform for quantum optics experiments and the development of on-chip quantum networks composed of various quantum nodes, such as quantum dots, molecules, and nanoparticles.

In the last 20 years, silicon quantum dots have received considerable attention from academic and industrial communities for research on readout, manipulation, storage, near-neighbor and long-range coupling of spin qubits. In this paper, we introduce how to realize a single spin qubit from Si-MOS quantum dots. First, we introduce the structure of a typical Si-MOS quantum dot and the experimental setup. Then, we show the basic properties of the quantum dot, including charge stability diagram, orbital state, valley state, lever arm, electron temperature, tunneling rate and spin lifetime. After that, we introduce the two most commonly used methods for spin-to-charge conversion, i.e., Elzerman readout and Pauli spin blockade readout. Finally, we discuss the details of how to find the resonance frequency of spin qubits and show the result of coherent manipulation, i.e., Rabi oscillation. The above processes constitute an operation guide for helping the followers enter the field of spin qubits in Si-MOS quantum dots.

Synthesized spin-orbit coupling (SSOC) is crucial for the operation of spin qubits in silicon quantum dot, as it address the challenge posed by the inherently weak intrinsic spin-orbit coupling (ISOC) in silicon. Here, we investigate the anisotropic properties of single spin qubit in silicon metal-oxide-semiconductor (Si-MOS) quantum dot and provide experimental evidence for the control of SSOC. Additionally, we experimentally demonstrate that tuning the operating point away from the conventional configuration can enhance the quality factor of the spin qubit. These findings lay a foundation for the realization of high-quality tunable spin-orbit qubits.

We study effects of spin-orbit interaction on quantum states in multiple low-dimensional systems. In the first part we investigate coupling of hybrid qubit with other broadly used types of qubit like singlet-triplet or single spin qubit in quantum dots. In the second part we investigate effects of strong in-plane magnetic field on g-factor renormalization in lateral quantum dots in GaAs, exploiting the symmetry of the underlying lattice. In the third part we analyze the topological phase transition in Majorana nanowires and we show that edge spin along the direction of the external magnetic field can be used as a probe of this elusive transition.

High-fidelity control and unprecedented long dephasing times in silicon-based single spin qubits have recently confirmed the prospects of solid-state quantum computation. We investigate the feasibility of using a micro-magnet stray field for all-electrical, addressable spin qubit control in a Si/SiGe double quantum dot. For a micro-magnet geometry optimized for high Rabi-frequency, addressability, and robustness to fabrication misalignment as previously demonstrated by Yoneda et al. [Phys. Rev. Lett. 113, 267601 (2014)], we simulate the qubit decoherence due to magnetic stray-field fluctuations, which may dominate in nuclear spin-free systems, e.g., quantum dots in Si/SiGe, Si-MOS structures and (bilayer) graphene. With calculated Rabi-frequencies of 15 MHz, a qubit addressability error below 10−3 is achievable. Magnetic fluctuations from a micro-magnet limits the spin relaxation time to T1 ≳ 3 s, while pure spin dephasing is negligible. Our results show that micro-magnets are a promising tool for spin qubit computation in nuclear spin-free systems.

The realization of a coherent interface between distant charge or spin qubits in semiconductor quantum dots is an open challenge for quantum information processing. Here, we demonstrate both resonant (real) and nonresonant (virtual) photon-mediated coherent interactions between double quantum-dot charge qubits separated by several tens of micrometers. We present clear spectroscopic evidence of the resonant collective enhancement of the coupling of two qubits and the resonator. With both qubits in resonance with each other but detuned from the resonator, we observe exchange coupling between the qubits mediated by virtual photons. In both instances, pronounced bright and dark states governed by the symmetry of the qubit-field interaction are found. Our observations are in excellent quantitative agreement with master-equation simulations. The extracted two-qubit coupling strengths significantly exceed the linewidths of the combined resonator-qubit system, which indicates that this approach is viable for creating photon-mediated two-qubit gates in quantum-dot-based systems.