Session K39: Semiconductor Qubits V

Phase correction code on spin qubits

An important requirement for realizing a useful quantum computer are large numbers of fault-tolerant qubits.  Spin qubits, based on quantum dots in semiconductor materials such as silicon and germanium, are a promising platform because they resemble transistors and therefore have great potential for scalability. However, implementing error correction codes, to achieve fault tolerance, have not been shown on spin qubits yet.

Recently, we have shown a two-by-two spin qubit array in a Ge/SiGe heterostructure on a silicon wafer[1]. As a next step, we explore the possibilities of this four qubit device. Apart from the CZ gate, we demonstrate a CS gate and a native resonance SWAP gate. We use the CZ and CS gate to construct a Toffoli-like three-qubit gate. Additionally, we show that we can project the state of a data qubit unto an ancilla qubit and back. By applying echo pulses on the ancilla qubit, we can extend the coherence of the data qubit. Moreover, we can implement a majority vote phase correction code on three qubits, projecting the result unto the data qubit. These experiments are milestones for semiconductor spin qubits, since they form the first steps towards error correction on this platform.

[1] Hendrickx, et al. A four-qubit germanium quantum processor. Nature 591, 580–585 (2021).   

Exchange gate between hole spin qubits with Rashba spin-orbit coupling

Hole spin qubits in semiconductor quantum dots have seen rapid progress in recent years. We focus on the Rashba spin-orbit (SO) coupling, which has been used to implement electric dipole spin resonance (EDSR) without microstructures to create local magnetic fields for single-qubit gate operations. We theoretically study the exchange interaction between localized holes in a double quantum dot system in the planar semiconductor heterostructure, elucidating the effects of the Rashba spin-orbit coupling. Effective Hamiltonian of the system and optimal conditions for two-qubit gates based on the exchange interaction between hole spin qubits with the SO coupling are presented.   

A single hole spin with enhanced coherence in natural silicon

Spin quantum bits in semiconductor appear to be one of the most promising technologies for the development of the quantum processor. Although electrons are the focus of modern research, holes exhibit many interesting physical properties. In particular, spin-orbit interaction allows a fully electrical  control of the hole spin qubit state. As a drawback, any external electric perturbation is likely to induce decoherence. Here we demonstrate for a single hole qubit in silicon the existence of sweet spots at which the qubit is decoupled from charge noise while keeping an efficient electrical driving. We first realize spin single-shot readout of the first hole accumulated in a natural silicon quantum dot made from an semi-industrial 300mm CMOS foundry. Subsequently, we characterize the hole spin g-tensor and its susceptibility to electric fields by coherent manipulation depending on the external magnetic field orientation. It reveals optimal operation points at which the longitudinal spin-electric susceptibility is minimal. At these sweet-spots, we measure an Hahn-Echo decay time $T2^echo = 100us while maintaining Rabi frequencies in the MHz range . This work opens new perspectives for quantum processing based on spin-orbit qubits.   

Electric-dipole spin resonance for light-holes in germanium quantum well

Holes in Germanium (Ge) quantum wells (QW) have recently attracted a great deal of attention due to their numerous attractive properties for the realization of quantum processors. In contrast to electrons, holes are affected significantly by the large spin-orbit coupling in Ge, enabling fast all-electrical spin-manipulation schemes such as electric-dipole spin resonance (EDSR). A novel type of two-dimensional hole gas consisting of light-holes can be achieved by applying a significant amount of tensile train (>1%) to the QW. A light-hole based quantum device also benefits of a more efficient photon-to-spin interface. This work discusses the properties of light-hole spins in highly tensile strained Ge QWs, whose strain is caused by coherent growth onto highly relaxed germanium-tin buffer layers. A perturbative framework describing Rabi-flopping of a light hole spin in a parabolic isotropic gate-defined quantum dot is derived from 8-band k·p theory. A quantitative analysis of the Rabi frequency versus physical parameters shows that light-holes can be manipulated 2 to 3 orders of magnitude faster than heavy-holes. The framework explicitly takes in account the spread of the envelope wavefunctions into the barriers and is suitable for any out-of-plane confining potential.   

Anisotropy of hole spin qubits in a silicon fin field-effect transistor

Hole spin qubits in silicon quantum dots have a great potential for scaling up quantum circuits, due to the small footprint of the devices and their industry compatibility.

We investigate hole spin qubits integrated in silicon fin field-effect transistors, which represent today’s industry standard transistor geometry. While our devices feature both industry quality and compatibility, they are fabricated in a flexible way to accelerate their development [Geyer et al., Appl. Phys. Lett. 118, 104004 (2021)]. Recently, we have demonstrated qubit operation above 4K and fast, all-electric gate operations with high fidelity [Camenzind et al., arXiv:2103.07369 (2021)].

Here, we explore the mechanisms of hole-spin driving by mapping out the dependence of the qubit parameters (g-factor, Rabi frequency, dephasing time) on the magnetic field orientation. We identify two distinct driving mechanisms: g-tensor and iso-Zeeman spin resonance [Crippa et al., Phys. Rev. Lett. 120, 137702 (2018)] and alter their contribution by applying the microwave signal to different gate electrodes. The anisotropy of the g-factor and the Rabi frequency is well explained by theory. Further, we identify sweet spots in the magnetic field orientation for fast spin manipulation that maintain a high spin coherence.   

Combining n-MOS Charge Sensing with p-MOS Silicon Hole Double Quantum Dots in a CMOS platform

Silicon hole quantum dots are an interesting complement to conventional electron quantum dots as a way to realise scalable spin qubits. The strong spin-orbit interaction in holes allows all-electric spin control [1]. Recent calculations also suggest it is possible to engineer a “sweet spot” for holes, where environmental decoherence is minimised, while simultaneously allowing rapid spin control [2]. However, the fabrication of p-type devices is not as developed as n-type. As such, disorder and device instability are challenges in p-type devices, and isolation of a single hole in a planar silicon quantum dot was demonstrated only recently [3].

CMOS devices combine both n-type and p-type capabilities within the same chip to offer a route to integrate a high performance, stable electron charge sensor into a hole qubit device. The concept was recently demonstrated using a single electron transistor and a single hole transistor [4] - but a question remains whether a qubit with an ambipolar charge sensor can be fabricated. In this work, we fabricate an n-type charge sensor adjacent to a p-type double quantum dot. We show that this geometry allows sensing of the p-type double quantum dot system down to the last hole. We also demonstrate control of parameters that are essential to qubit operation, including control of the reservoir tunnel rates which can allow latched spin readout [5], as well as control of the interdot coupling rate which is essential for exchange qubit operation. These results show the feasibility of ambipolar CMOS charge sensing qubits.

[1] Crippa et al., Phys. Rev. Lett. (2018)

[2] Liles et al., arXiv. (2021)

[3] Liles et al., Nat. comms. (2018)

[4] Almeida et al., Phys. Rev. B (2020)

[5] Boganet al., Commun. Phys. (2019)   

Quantum Coherence in Germanium Hole Spin Qubits

The ability to reliably store quantum information is an underpinning assumption for the operation of a quantum computer. This ability is compromised when qubits exchange energy with external systems in a process known as decoherence. In spin qubit systems, decoherence can be quantified by the time the transeverse component of a spin state takes to dephase (T2). For hole spin qubits in planar germanium (Ge/SiGe), pure dephasing times (T2*) have been limited to a few hundred nanoseconds.

 

Here we study the magnetic field dependence of T2* for hole qubits in Ge/SiGe. We find a 1/B dependence suggesting charge noise is the dominant decohering process, and observe T2* as high as 1.8 μs at 0.1 T, extendable to 500 μs using refocussing techniques. Furthermore, we  observe the decohering effect of the residual 73Ge nuclear spins on hole spin qubits. We confirm that hole spin qubits are sensitive to the nuclear spin bath, and extract the amplitude of the fluctuating Overhauser field to be 34.4 kHz, that we predict to limit spin dephasing times to T2*,hf = 6.54 μs. These results simultaneously represent a milestone in spin coherence in hole qubits, while also demonstrating their sensitivity to hyperfine coupling, providing concrete evidence of the necessity of isotopic purification.   

Electrical control of the g-tensor of the first holein a silicon MOS quantum dot

The spin state of a single hole in a semiconductor device provides a promising platform for a wide range of spin based quantum devices. A primary advantage of using holes, rather than electrons, is the intrinsically strong coupling of hole spins to electric fields. This strong spin-electric coupling allows rapid all-electrical control over the hole spin state, which is advantageous for many spin based devices, such as spin qubits [1-2]. However, due to the complexity of hole spin physics, gaps remain in our understanding of the mechanisms that enable electrical control of hole spins.

 

In this work, we report measurements and simulations of the g-tensor of a single hole that is confined in a silicon planar MOS quantum dot [3]. We show that thermal contraction of the metal gates in this MOS device produces a non-uniform strain profile, resulting in nanometre-scale variations in the hole-spin character. We show that local electric fields can be used to displace the hole relative to the non-uniform strain profile, therefore allowing a new mechanism for electric modulation of the hole g-tensor. Using this mechanism, we demonstrate tuning of the hole g-factor by up to 500%. In addition, we observe a potential sweet spot where dg_(110)/dV = 0, offering a possible configuration to suppress spin decoherence caused by electrical noise [4]. These results open a path towards a previously unexplored technology: engineering of non-uniform strains to optimise spin-based devices

 

[1] - Maurand, R., et al. Nature communications 7.1 (2016): 1-6.

[2] - Hendrickx, Nico W., et al. Nature 591.7851 (2021): 580-585.

[3] - Liles, S. D., et al. arXiv preprint arXiv:2012.04985 (2020).

[4] - Wang, Zhanning, et al. npj Quantum Information 7.1 (2021): 1-8   

Towards hole-spin qubits in Si pMOSFETs within a planar CMOS foundry technology

Hole spins in semiconductor quantum dots represent a viable route for the implementation of electrically controlled qubits. In particular, the qubit implementation based on Si pMOSFETs offers great potentialities in terms of integration with the control electronics and long-term scalability.

Moreover, the future down scaling of these devices will possibly improve the performance of both the classical (control) and quantum components of such monolithically integrated circuits. Here we use a multi-scale approach to simulate a hole-spin qubit in a down scaled Si-channel pMOSFET, whose structure is based on a commercial 22nm fully-depleted silicon-on-insulator device. Our calculations show the formation of well-defined hole quantum dots within the Si channel, and the possibility of a general electrical control, with Rabi frequencies of the order of 100 MHz for realistic field values. A crucial role of the channel aspect ratio is also demonstrated, as well as the presence of a favorable parameter range for the qubit manipulation.   

All-electrical control of hole singlet-triplet spin qubits at low leakage points

We study the effect of the spin-orbit interaction on heavy holes confined in a double quantum dot in the presence of a magnetic field of arbitrary direction. Rich physics arise as the two hole states of different spin are not only coupled by the spin-orbit interaction but additionally by the effect of site-dependent anisotropic g tensors. It is demonstrated that these effects may counteract in such a way as to cancel the coupling at certain detunings and tilting angles of the magnetic field. This feature may be used in singlet-triplet qubits to avoid leakage errors and implement an electrical spin-orbit switch, suggesting the possibility of task-tailored two-axes control. Additionally, we investigate systems with a strong spin-orbit interaction at weak magnetic fields. By exact diagonalization of the dominant Hamiltonian we find that the magnetic field may be chosen such that the qubit ground state is mixed only within the logical subspace for realistic system parameters, hence reducing leakage errors and providing reliable control over the qubit.   

Electron and Hole Spin Qubits Variability in Si MOS Devices

Semiconductor spin qubits may show significant device-to-device variability in the presence of spin-orbit coupling mechanisms. Interface roughness, charge traps, layout or process inhomogeneities indeed shape the real space wave functions, hence the spin properties. It is, therefore, important to understand how reproducible the qubits can be in order to assess strategies to cope with this disorder. Here we model the variability of the Larmor/Rabi frequencies and spin lifetimes due to roughness and charge traps at the Si/SiO2 interface in metal-oxide-semiconductor devices. We consider both electron qubits (with synthetic spin-orbit coupling fields created by micro-magnets) and hole qubits (with intrinsic spin-orbit coupling). We highlight, in particular, the relations between the characteristic sizes of the disordered dots and their Larmor and Rabi frequencies. We show that the hole qubits are typically more sensitive to interface roughness than electron qubits due to the smaller hole confinement mass. Yet the main source of variability is charged traps, which can scatter the Rabi frequencies of both electron and hole qubits over one order of magnitude in realistic device layouts. We analyze the implications for the design of spin qubits and for the choice of materials.   

Hole spin qubits in Si and Ge quantum dots: Ultrafastgates and noise resilient qubits

Hole spin qubits in Si and Ge quantum dots are frontrunner platforms for scalable quantum computers. In these systems, the spin-orbit interactions permit efficient and ultrafast all-electric qubit control, but, at the same time, enhance the susceptibility of the qubit to charge noise. We show that in planar Ge/SiGe heterostructures and in Si fin field-effect transistors (FinFETs), these interactions can be fully tuned by the design of the quantum dot and by external electric fields [1], enabling sweet spots where the charge noise can be completely removed [2]. Remarkably, in Si FInFETs, also the noise caused by hyperfine interactions with nuclear spins -another leading source of decoherence in spin qubits- can be suppressed at these sweet spots [3], greatly enhancing the coherence of these qubits, and reducing the need for expensive isotopically purified materials.