Flopping mode qubits in double quantum dots (DQDs) allow for coherent spin-photon hybridization and fast qubit gates when coupled to either an alternating external or a quantized cavity electric field. To achieve this, however, electronic systems rely on synthetic spin-orbit interaction (SOI) by means of a magnetic field gradient as a coupling mechanism. Here we theoretically show that this challenging experimental setup can be avoided in heavy-hole (HH) systems in germanium (Ge) by utilizing the sizeable cubic Rashba SOI. We argue that the resulting natural flopping mode qubit possesses highly tunable spin coupling strengths that allow for one- and two-qubit gate times in the nanosecond range when the system is designed to function in an optimal operation mode which we quantify.
We propose and analyze a novel "flopping-mode" mechanism for electric dipole spin resonance based on the delocalization of a single electron across a double quantum dot confinement potential. Delocalization of the charge maximizes the electronic dipole moment compared to the conventional single dot spin resonance configuration. We present a theoretical investigation of the flopping-mode spin qubit properties through the crossover from the double to the single dot configuration by calculating effective spin Rabi frequencies and single-qubit gate fidelities. The flopping-mode regime optimizes th…
Single spin qubits based on phosphorus donors in silicon are a promising candidate for a large-scale quantum computer. Despite long coherence times, achieving uniform magnetic control remains a hurdle for scale-up due to challenges in high-frequency magnetic field control at the nanometre-scale. Here, we present a proposal for a flopping-mode electric dipole spin resonance qubit based on the combined electron and nuclear spin states of a double phosphorus donor quantum dot. The key advantage of utilising a donor-based system is that we can engineer the number of donor nuclei in each quantum do…
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
Coherence of a hole spin flopping-mode qubit in a circuit quantum electrodynamics environment
Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG-Pheliqs（格勒诺布尔阿尔卑斯大学，法国原子能与替代能源委员会，格勒诺布尔理工学院，IRIG-Pheliqs）；QuTech and Kavli Institude of Nanoscience, Delft University of Technology（QuTech与卡弗里纳米科学研究所，代尔夫特理工大学）；Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim（格勒诺布尔阿尔卑斯大学，法国原子能与替代能源委员会，IRIG-MEM-L_Sim）；Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientificas（马德里材料科学研究所，西班牙高等科学研究委员会）；Univ. Grenoble Alpes, CEA, LETI, Minatec Campus（格勒诺布尔阿尔卑斯大学，法国原子能与替代能源委员会，LETI，米纳泰克校区）
Achieving high fidelity control of spin qubits with conventional electron dipole spin resonance (EDSR) requires large magnetic field gradients of about 1 mT/nm, which also couple the qubit to charge noise, and large drive amplitudes of order 1 mV. The flopping-mode is an alternative method to drive EDSR of an electron in a double quantum dot, where the large displacement between both dots increases the driving efficiency. We propose to operate the flopping-mode in the strong-driving regime to use the full magnetic field difference between the two dots. In simulations, the reduced required magn…
Modeling of flopping-mode spin qubits: beyond the two-site model
Imec；KU Leuven（荷语鲁汶大学）；Instituut voor Theoretische Fysica, KU Leuven（荷语鲁伦大学理论物理研究所）；University of Augsburg（奥格斯堡大学）；Center for Advanced Analytics and Predictive Sciences, University of Augsburg（奥格斯堡大学先进分析与预测科学中心）；Department of Electrical Engineering, KU Leuven（荷语鲁汶大学电气工程系）；Department of Physics, University of Antwerp（安特卫普大学物理系）
The effects of alloy disorder on strongly-driven flopping mode qubits in Si/SiGe
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Laboratory for Physical Sciences（物理科学实验室）；Department of Physics, University of Maryland（马里兰大学物理系）；School of Physics, University of New South Wales（新南威尔士大学物理学院）
Hole-spin qubits in germanium beyond the single-particle regime
CNR-Istituto Nanoscienze（意大利国家研究委员会纳米科学研究所）；Università di Milano（米兰大学）；Università degli Studi di Modena e Reggio Emilia（摩德纳和雷焦艾米利亚大学）；University of Basel（巴塞尔大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Delft University of Technology（代尔夫特理工大学）
Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the s…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CEA（法国原子能和替代能源委员会）；IRIG-MEM-L_Sim；Quantum Advanced Research Center (QuARC) - Consejo Superior de Investigaciones Científicas (CSIC)（量子先进研究中心（QuARC）- 西班牙高等科学研究理事会（CSIC））；Instituto de Ciencia de Materiales de Madrid (ICMM) - Consejo Superior de Investigaciones Científicas (CSIC)（马德里材料科学研究所（ICMM）- 西班牙高等科学研究理事会（CSIC））
The possibility of quantum computing with spins in germanium nanoscale transistors has recently attracted interest since it promises highly tuneable qubits that have encouraging coherence times. We here present the first complete theory of the orbital states of Ge donor electrons, and use it to show that Ge could have significant advantages over silicon in the implementation of a donor-based quantum processor architecture. We show that the stronger spin-orbit interaction and the larger electron donor wave functions for Ge donors allow for greater tuning of the single qubit energy than for thos…
The promise of quantum computation with quantum dots has stimulated widespread research. Still, a platform that can combine excellent control with fast and high-fidelity operation is absent. Here, we show single and two-qubit operations based on holes in germanium. A high degree of control over the tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder and by working in a virtual gate space. Spin-orbit coupling obviates the need for microscopic elements and enables rapid qubit control with Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99…
Donor electron spins in semiconductors make exceptional quantum bits because of their long coherence times and compatibility with industrial fabrication techniques. Despite many advances in donor-based qubit technology, it remains difficult to selectively manipulate single donor electron spins. Here, we show that by replacing the prevailing semiconductor host material (silicon) with germanium, donor electron spin qubits can be electrically tuned by more than an ensemble linewidth, making them compatible with gate addressable quantum computing architectures. Using X-band pulsed electron spin re…
The prospect of building quantum circuits using advanced semiconductor manufacturing positions quantum dots as an attractive platform for quantum information processing. Extensive studies on various materials have led to demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium. However, interconnecting larger numbers of qubits in semiconductor devices has remained an outstanding challenge. Here, we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable c…
A key challenge in quantum computation is the implementation of fast and local qubit control while simultaneously maintaining coherence. Qubits based on hole spins offer, through their strong spin-orbit interaction, a way to implement fast quantum gates. Strikingly, for hole spins in one-dimensional germanium and silicon devices, the spin-orbit interaction has been predicted to be exceptionally strong yet highly tunable with gate voltages. Such electrical control would make it possible to switch on demand between qubit idling and manipulation modes. Here, we demonstrate ultrafast and universal…
Dopant-based quantum computing implementations often require the dopants to be situated close to an interface to facilitate qubit manipulation with local gates. Interfaces not only modify the energies of the bound states but also affect their symmetry. Making use of the successful effective mass theory we study the energy spectra of acceptors in Si or Ge taking into account the quantum confinement, the dielectric mismatch and the central cell effects. The presence of an interface puts constraints to the allowed symmetries and lead to the splitting of the ground state in two Kramers doublets [J…
High-fidelity geometric quantum gates exceeding 99.9% in germanium quantum dots
University of Science and Technology of China（中国科学技术大学）；CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学量子信息科学与技术卓越中心）；Institute of Microelectronics, Chinese Academy of Sciences（中国科学院微电子研究所）；Beijing Superstring Academy of Memory Technology（北京超弦存储技术研究院）；School of Physical Science and Technology, Guangxi University（广西大学物理科学与技术学院）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克与卡弗里纳米科学研究所）
The electric dipole spin resonance (EDSR) combining strong spin-orbit coupling (SOC) and electric-dipole transitions facilitates fast spin control in a scalable way, which is the critical aspect of the rapid progress made recently in germanium (Ge) hole-spin qubits. However, a puzzle is raised because centrosymmetric Ge lacks the Dresselhaus SOC, a key element in the initial proposal of the hole-based EDSR. Here, we demonstrate that the recently uncovered finite k-linear Rashba SOC of 2D holes offers fast hole spin control via EDSR with Rabi frequencies in excellent agreement with experimental…
The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of …
In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material scie…
We theoretically investigate the properties of holes in a Si$_{x}$Ge$_{1-x}$/Ge/ Si$_{x}$Ge$_{1-x}$ quantum well in a perpendicular magnetic field that make them advantageous as qubits, including a large ($>$100~meV) intrinsic splitting between the light and heavy hole bands, a very light ($\sim$0.05$\, m_0$) in-plane effective mass, consistent with higher mobilities and tunnel rates, and larger dot sizes that could ameliorate constraints on device fabrication. Compared to electrons in quantum dots, hole qubits do not suffer from the presence of nearby quantum levels (e.g., valley states) that…
An anomalous energy splitting of spin triplet states at zero magnetic field has recently been measured in germanium quantum dots. This zero-field splitting could crucially alter the coupling between tunnel-coupled quantum dots, the basic building blocks of state-of-the-art spin-based quantum processors, with profound implications for semiconducting quantum computers. We develop an analytical model linking the zero-field splitting to spin-orbit interactions that are cubic in momentum. Such interactions naturally emerge in hole nanostructures, where they can also be tuned by external electric fi…
Hole spins confined in semiconductor quantum dot systems have gained considerable interest for their strong spin-orbit interactions (SOIs) and relatively weak hyperfine interactions. Here we experimentally demonstrate a tunable SOI in a double quantum dot in a Germanium (Ge) hut wire (HW), which could help enable fast all-electric spin manipulations while suppressing unwanted decoherence. Specifically, we measure the transport spectra in the Pauli spin blockade regime in the double quantum dot device.By adjusting the interdot tunnel coupling, we obtain an electric field tuned spin-orbit length…
