Session G49: Novel Spin Qubits

Tin as a nuclear spin qubit in silicon

Nuclear spin qubits in silicon are renowned for long coherence times and superb control fidelity, as demonstrated by donor-based systems such as implanted phosphorous.  Isoelectronic species are an intriguing alternative to donors.  Having no strong confining potential, a nuclear spin qubit can interact with an electron through a hyperfine interaction that is fully controlled by electrodes of gate-defined quantum dots (QDs).  Such electrostatic control can be used to shuttle electrons from one nuclear spin qubit to another with relative ease to mediate entanglement between distant nuclear spins.  In this talk we will discuss the potential of isoelectronic nuclear spins qubits, with an emphasis on tin [PRX Quantum 3, 040320 (2022)]. Our density-functional-theory calculations indicate an enhanced hyperfine interaction in tin relative to other isoelectronic candidates resulting in promising qubit performance.  A hyperfine-induced electron-nuclear controlled-phase (e-n-CPhase) gate operation in the tin system is predicted to be exceptionally resilient to charge or voltage noise and diabatic spin flips are suppressed with a modest magnetic field.  The only other significant source of anticipated e-n-CPhase error is from extraneous nuclear spins which may be mitigated through enrichment (to eliminate nuclear spins) and/or compensation (by tracking the slow drift in nuclear spin noise).  We predict the effectiveness of combining these mitigation strategies by calculating spin-cluster correlation expansions.  Comparing our model with experiments at 800 ppm ²⁹Si bolsters confidence in our predictions.  In addition, our experimental effort to demonstrate this unique qubit technology is ramping up, confirming the viability of tin implantation and demonstrating coherent electron shuttling.  These results lay the groundwork for realizing the promise of a QD-coupled tin qubit platform.   

Probing the single-particle valley relaxation time in bilayer graphene quantum dots

Graphene and bilayer graphene (BLG) have emerged as interesting and promising host materials for qubits. Thanks to its tunable band gap, bilayer graphene allows for electrostatic confinement of charge carriers in quantum dots (QDs), similar as done in conventional III-V semiconductors. Additional to the spin degree of freedom, BLG exhibits a valley pseudospin, which distinguishes between its two energetically degenerate but inequivalent band structure minima (valleys) K and K'. The finite Berry curvature at these high symmetry points gives rise to a valley-dependent magnetic moment allowing for manipulation and control of the valley degree of freedom. Complementary to spintronics, the control over the valley enables valleytronics, where the valley degree of freedom is used as platform for quantum information processing. To assess the potential of valley qubits in BLG, it is necessary to investigate the relaxation time T₁ of an excited valley state, as it limits the lifetime of the encoded quantum information.

Here, we report single-particle valley relaxation times of up to 7 μs in a BLG quantum dot, sufficiently long to utilize a valley state for coherent manipulation. The observed dependency of T₁ on the perpendicular magnetic field can be described qualitatively and quantitatively by a model considering T₁ to be limited by electron-phonon coupling. We identify coupling to acoustic phonons via bond length change and via the deformation potential as the limiting mechanisms.   

Simulating spin-valley locking in the transport spectroscopy of bilayer graphene quantum dots

Spin-valley qubits in 2D-material quantum dots are being actively pursued as platforms for quantum information manipulation. Keeping in mind recent experiments [1-2], we present a detailed simulation of the transport spectroscopy [3] of bilayer graphene single quantum dots, considering the spin-valley physics in detail. Using a first-principles based Hamiltonian, we perform detailed quantum transport simulations of the Coulomb diamonds, in the presence of an arbitrarily aligned magnetic field. Extrapolating from the transport simulations, we establish the occurence of spin-valley locking. Furthermore, we elucidate the role of defects, intra and inter-valley Coulomb interaction on the signatures of spin-valley locking, thereby leading to machine learning ready extrapolation [4] of the associated g-factors. 

[1] L. Banszerus et.al.,  Nat. Comms., 12, 5250 (2021). 

[2] R. Krishnan et. al., Nano. Lett., 23, 6171 (2023). 

[3] A. Mukherjee and B. Muralidharan, 2D Materials, 10, 035006 (2023). 

[4] A. Das et.al., ArXiv: 2308.04937 (2023).    

Characterizing spin-valley-blockades in the bilayer graphene system

Advancements in the transport spectroscopy of 2D-material quantum-dot platforms have sparked an interest in spin-valley qubits. In this context, the Pauli blockades observed in quantum dot structures play a pivotal role in enabling the initialization and manipulation of multi-qubit systems. Concentrating on multi-quantum dot structures within the bilayer graphene framework and guided by experimental findings, we have develop multifaceted computational models, that capture the transport characteristics as a function of gate voltages as well as the physics of the underlying material. Besides accurately simulating the occurrence of Pauli blockades, our simulations have notably unveiled two remarkable phenomena: (i) the presence of multiple resonances within a bias triangle, and (ii) the manifestation of multiple spin-valley blockades. Harnessing our model to train a machine learning algorithm, we have devised an automated approach for the real-time identification of multiple Pauli blockade regimes. Through numerical forecasts and validation against test data, we pinpoint both the locations and the number of Pauli blockades likely to arise. The comprehensive and integrated computational models developed in this study thus lay a foundation for future experiments in the field of transport spectroscopy in other 2D-material platforms for the experimental realization of spin-valley qubits.

    

Characterizing the effective g-tensor of hole qubits in planar germanium quantum wells

Electron holes in germanium quantum wells show a promising alternative to producing spin qubits due to their potential for fast all-electrical control mediated by the presence of a strong and tunable spin-orbit interaction. However, the same mechanism leads to a potential drawback as it also increases the qubit's sensitivity to nearby charge fluctuations. In this work, we use a nonsymmetrized multiband k·p theory to investigate the dependence of the qubit's effective g-tensor to experimentally relevant parameters such as strain and electric and magnetic field strength and orientation. We use this information to identify potential operational sweetspots where the effect of charge noise is optimized.   

Boundary conditions for a hole spin qubit in a Ge quantum dot

Hole spin in a semiconductor quantum dot is an intriguing candidate for qubit because of its strong intrinsic spin-orbit coupling, which enables fast electrical control and thus potential scalability. However, hole spin qubits are more complicated than conduction electron spin qubits because of the strong mixing of heavy and light holes, and a multi-band theory is required to study hole spins accurately.

 

One main difficulty of studying holes in a realistic heterostructure is the coupled boundary conditions, which are a direct result of the multi-band theory. In this talk, we will introduce a perturbative treatment to address this boundary condition problem. We study a planar quantum dot in a SiGe-Ge quantum well within the formalism of effective-mass approximation, and examine how the choice of boundary conditions affect the splitting of hole spins.   

Oral: Sweet spots and sweet lines in Ge/GeSi hole spin qubits

We theoretically investigate sweet spots and sweet lines in Ge/GeSi hole spin qubit heterostructures with different symmetries (disk-shaped, squeezed and displaced hole quantum dots, under homogeneous and inhomogeneous strains). We monitor Rabi frequencies, coherence times and quality factors as a function of magnetic field orientation and look for the optimal driving configuration. We establish, in particular, a general classification of the geometrical nature of sweet magnetic field orientations where the Larmor frequency of the hole spin decouples from electrical noise. We show that the optimal operation point practically results from the interplay between the sweet spots and lines of different classes of relevant perturbations. In general, the optimal magnetic field orientation (best quality factor) is near the plane of the heterostructure, but can wiggle around in the presence of shear strains. Our results provide guidelines to find high-coherence operation points for hole spin qubits, and for the design of devices more resilient to noise.   

A study of symmetry-protected topology of surfaces of maximum entanglement in Si, Ge and GaAs for spin-qubit architectures

Progress on spin qubits depends on a fundamental and precise understanding of electron and hole g factors and their anisotropy.

We evaluate tight-binding analytical expressions to calculate the g-tensor of electron and hole spins for group IV and III-V semiconductors with focus on crystalline Si, Ge and GaAs -- the leading hosts for gate-controlled spin qubits. Recalling that the electron g-factor for bulk Si is +2 but -0.44 for bulk GaAs indicates the need to diagnose the occurrence of large variations in g. Mathematically, these values are the singular values of the asymmetric g tensor. Using the determinant of g,  det(g), as a diagnostic, we see large regions of k-space, for many bands in these semiconductors, where det(g) has an inverted sign. The topology of the surfaces where det(g) = 0 is particularly intricate in the case of the first conduction bands of Si and the second conduction band of Ge. We observe that these surfaces can be as complex as Fermi surfaces and share similar characteristics. We show that, considering just the spin contribution $g_S$ to the g tensor, surfaces where $det(g_S)=0$, which also commonly occur, indicate the occurrence of maximal spin-orbital entanglement in the Bloch states.   

Observation of microsecond lived quantum states in carbon-based circuits

We manipulate the quantum state of a carbon nanotube double quantum dot with ferromagnetic contacts embedded in a microwave cavity. By performing quantum manipulations such as Rabi oscillations, Ramsey fringes and spin echoes, we demonstrate coherence times of the order of 1 μs, 2 orders of magnitude larger that what has been measured so far in any carbon quantum circuit and 1 order of magnitude larger than Si based quantum dots in comparable environment. This hold promises for pure isotopically purified ¹²C spin quantum bits in circuit quantum electrodynamics.   

Sweet Spot Combining Qubit Coherence and Speed

Strong spin-orbit interaction (SOI) has attracted major interest in quantum dot spin qubits, as it enables ultrafast, scalable and compact qubit devices. However, the SOI not only facilitates all electrical driving, but at the same time couples the qubit to charge noise, leading to dephasing. This seems to suggest that stronger SOI leads to faster qubit operation but only at the cost of coherence.

Here, we provide experimental evidence in a Ge/Si core/shell nanowire demonstrating a qubit which reaches its most coherent point of operation exactly when its speed is the fastest, coinciding with vanishing derivatives of its g-factor with respect to all gates. Such a compromise-free sweet spot combining qubit speed and coherence requires a strong SOI with a maximum in coupling strength. Here, this is likely provided by strong and gate tunable direct-Rashba SOI in the 1D confinement of the Ge/Si nanowire employing iso-Zeeman driving from a remote gate. Our results overturn the conventional paradigm that fast operation speeds imply reduced qubit lifetimes.

Additionally, were were able to find a charge configuration of the double dot for which both spins can be individually addressed at different microwave frequencies, allowing the implementation of exchange-based conditional spin rotations at 1.5 K.   

Mechanism of high-temperature quantum dot operation in isoelectronic-trap-assisted tunnel FETs

Silicon spin qubit is one of the promising candidates as a building block of quantum computers. Recently, Si tunnel-FET (TFET)-type qubits have successfully operated at high temperatures up to 10 K, which employs the electronic state of the isoelectronic trap (IET) impurity as a quantum dot. To investigate the mechanism of their high-temperature operation, as a first step, we develop a device simulator reproducing their single-electron transistor (SET) operation. In this presentation, we report the device simulation clarifying the high-temperature SET operation mechanism.

This device operates as a SET with tunneling between the source and drain intermediated with the IET state. Firstly, short gate length must be employed such that tunneling distances are sufficiently short. Secondly, the quantum dot should be located far from the source and drain, to avoid Coulomb repulsion between a charged quantum dot and surrounding electrons hindering the charge up of the quantum dot. This requirement becomes stricter at high temperatures because the number of surrounding electrons increases. Thirdly, the localized IET state is preferred to produce a small quantum dot. This causes a deep potential distribution when the quantum dot is charged up, resulting in large charging energy. Satisfying these three requirements enables high-temperature SET operation of the devices.