Session H35: Semiconducting Qubits: Characterization of Electron and Hole Spin Qubits

Four-qubit quantum processor in isotopically enriched silicon

Quantum processors based on spins in semiconductors are rapidly becoming a strong contender in the race to build a quantum computer. When coupled with micromagnets, these devices offer high fidelity single-qubit [1] and two-qubit [2,3] control while maintaining long coherence times. Until now, silicon spin qubit devices incorporating micromagnets have been limited to one and two qubit demonstrations, even though a one-dimensional extended array of silicon quantum dots has been demonstrated [4]. In this presentation, we will present a four-spin-qubit device architecture. This device is fabricated on an isotopically enriched ²⁸Si/SiGe quantum well and offers four individually addressable spin qubits. Multi-qubit gates can be implemented by gating nearest-neighbor exchange interactions. Preliminary data demonstrating single- and multi-qubit operation will be presented.
[1] Yoneda et al., Nat. Nanotech. 13, 102 (2018)
[2] Zajac et al., Science 359, 439 (2018)
[3] Watson et al., Nature 555, 633 (2018)
[4] Zajac et al., Phys. Rev. Applied 6, 054013 (2016)   

Characterization of gate fidelities in a Si/SiGe two-qubit device

Various candidate implementations for future quantum computers have been investigated over the past twenty years. Silicon spin qubits show great promise [1] for their long coherence times and integration using semiconductor technology but there have been very few quantitative studies of the fidelities of two-qubit gates. Here we characterize the gate fidelities of a C-Phase gate using randomized benchmarking. For single-qubit gates, we perform randomized benchmarking on each spin by itself and also on both spins simultaneously, to probe cross-talk effects. Furthermore, we developed and experimentally verified a new method called character randomized benchmarking [2,3], which combines the advantages of simultaneous and interleaved randomized benchmarking. With this new method, we characterized the fidelity of a C-Phase gate with tighter bounds than those in the traditional approach.

[1] T.F.Watson, et al, Nature 555, 633-637 (2018).
[2] J.Helsen, et al, arxiv:1806.02048.
[3] X.Xue, et al, manuscript in preparation.   

Benchmarking of two-qubit gates for singlet-triplet qubits

We perform benchmarking to evaluate the performance of two-qubit dynamically corrected gates (DCGs) in the singlet-triplet spin qubit system. We execute two types of circuits, i.e. the Deutsch-Jozsa algorithm and Grover algorithm, each of which is carried out with DCGs and gates not immune to noise. The benchmarking process is performed by repeating 100 times of the respective circuit under 1/f noises with different noise exponents ($\alpha$). The average error per execution of one algorithm is compared between DCGs and non-noise-correcting ones, and whether DCGs offer improvement depends on the noise exponent, $\alpha$. We have found that when $\alpha<0.8$ the DCGs would not offer improvements, but DCGs can outperform the non-correcting ones otherwise. The fact that DCGs can offer improvement for a wide range of $\alpha$, on one hand, suggests using DCGs on two-qubit gates can reduce the error, but on the other hand also indicates that quantum algorithms involving two-qubit gates suffer more heavily from noises than those only involving single-qubit gates if no correction to noise is performed.   

Noise correlations in a two-qubit Si/SiGe quantum dot device

Qubits are affected by noise in their environment, but conversely can also be used to probe this noise and study properties such as spectral density and correlations. We use a two-qubit device in a Si/SiGe hetrostructure [1] to investigate noise correlations by studying the decay of two Bell states. These Bell states are insensitive to either correlated or anti-correlated noise, resembling the concept of decoherence-free subspaces, which allows us to extract the uncorrelated, correlated and anti-correlated contributions to the noise affecting the qubits from the decay times for the different initial states. Knowledge about the noise properties makes it possible to design operations that are less sensitive to this noise, and yields information on the noise source, which potentially makes it possible to reduce the noise. We demonstrate this method by artificially adding (anti-) correlated noise and use it characterize the noise in our system.

[1] T.F. Watson et al., Nature 555, 633 (2018)   

Magnetic-Field Effects on Error and Leakage in Randomized Benchmarking of a Si/SiGe Triple-dot Qubit

The exchange-only, triple-dot qubit is fully controllable through voltage-based modulation of the exchange interaction between neighboring dot pairs, requiring no magnetic gradients or magnetic resonance. Nevertheless, several magnetic effects play important roles in errors and leakage of the qubit under operation, whether by dephasing for an idle qubit or during a multi-pulse experiment such as randomized benchmarking. This talk discusses the magnetic-field-dependent impacts of three types of magnetic gradients: magnetic screening gradients due to the Meissner effect in superconducting gates, interface-spin-orbit effects, and contact hyperfine interactions including the full vector of nuclear magnetization. While Meissner and spin-orbit gradients are suppressed by operating near zero magnetic field, we find that gradients oriented in directions transverse to the field, in particular the flip-flop terms of the hyperfine component, play a more dominant role. Isolating the effects of magnetic gradients on qubit performance is aided by modifications to the randomized benchmarking protocol that allow reliable extraction of the proportion of total error due to leakage, which is a signature of magnetic gradient effects in exchange-only qubits.   

Analyzing the fidelity of a singlet-triplet spin-orbit qubit in silicon using gate set tomography

It has been recently demonstrated that spin-orbit effects observed in silicon quantum dots are much larger than what is expected for bulk silicon [1-3]. These spin-orbit effects can be used to achieve all-electrical universal control of a double quantum dot singlet-triplet qubit without the need for any external components, such as micromagnets or microwave resonators, to produce a magnetic field gradient [4]. In this work, we use gate set tomography to analyze the fidelity of these gates. We also explore the possibility of using AC control, both in the weak and strong driving regimes, to improve the fidelity of qubit operations.

This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the DOE’s National Nuclear Security Administration under contract DE-NA0003525

References
1. Jock et al., Nat. Commun. 9, 1768 (2018)
2. Tanttu et al., arXiv:1807.10415 (2018)
3. Harvey-Collard et al., arXiv:1808.07378 (2018)
4. Harvey-Collard et al., IEEE IEDM 36.5.1 (2017)   

Measurements of capacitive coupling in two double dots in Si/SiGe for application in two qubit gates

We present measurements of a Si/SiGe quantum dot device made with overlapping self-oxidized Al gates. The device includes a linear array of four quantum dots and two auxiliary dots for charge sensing. The dots have a lithographic pitch of 130 nm and are separated from the gates by a 30 nm SiGe spacer and 5 nm of aluminum oxide deposited by ALD. We measure the charge noise in all six dots and observe a power spectral density that is approximately 1/f in the 1-200 Hz range with a chemical potential noise amplitude of 1-2 μeV/Hz^1/2 at 1 Hz. We tune the device to form two tunnel-coupled double dots and observe the capacitive coupling with both double dots at the (0,1)-(1,0) polarization line. We measure a detuning shift of ~8 GHz due to the change in polarization of the adjacent double dot, demonstrating the potential of the system for coherent two-qubit coupling via capacitive interaction.   

Detuning dependence of capacitive coupling for quantum dot hybrid qubits

Implementation of robust two-qubit entangling gates is necessary in order to form a universal set of multi-qubit operations. We derive the coupling form between two capacitively coupled qubits, each consisting of three electrons in a double quantum dot (i.e., two hybrid qubits), and show how the effective coupling behaves as a function of detuning. By pulsing the detuning adiabatically, we show how two-qubit entangling operations can be performed on relatively fast 100ns timescales. The entangling operations are then simulated in the presence of experimentally measured quasistatic noise. The fidelities are typically only around 90%, pointing to the need for further improvement via shaped-pulse optimization.
  

Induced quantum dot probe for qubit and material characterization

We propose a non-destructive means of characterizing quantum dot parameters across a semiconductor wafer by inducing a quantum dot on the material system of interest with a separate probe chip that can also house the measurement circuitry. We show that a single wire can create the dot, determine if an electron is present, and be used to measure critical device parameters. Adding more wires enables more complicated setup and measurements. As one application for this concept we consider silicon metal-oxide-semiconductor and silicon/silicon-germanium quantum dot qubits relevant to quantum computing and show how to measure low-lying excited states (so-called `valley' states) in a novel way. The approach provides a simple and flexible method for characterization applicable to various quantum systems.   

Device-level modeling of hole quantum dot qubits in germanium

Holes in Ge quantum wells in Ge/SiGe heterostructures have a number of promising properties that have made them the target of growing interest for qubit applications. These include strong intrinsic spin-orbit coupling, the absence of valley degeneracy, and small effective masses. In this talk, we will describe ongoing work towards developing comprehensive models of these systems to facilitate the design and optimization of devices and the rationalization of experiments. We make use of electrostatic/strain modeling to compute the potential landscape and capacitances of a given device structure. The potential landscape is fed into a multi-band effective mass theory, with other parameters drawn from first principles models, to extract a qubit Hamiltonian. We will report on work describing ongoing quantum dot experiments and make projections pertaining to qubit tunability and performance.   

EDSR of a single heavy hole in a lateral GaAs/AlGaAs quantum dot qubit

Single holes are attractive as spin qubits due to their advantageous properties which include a reduced hyperfine interaction, a strong spin-orbit coupling for sub-nanosecond spin rotations, and the absence of valley complications.
Here we report single hole electric dipole spin resonance (EDSR) measurements over the 20-50 GHz range taking advantage of the strong spin-orbit coupling. The experiment was performed in a GaAs double quantum dot device described in [1] tuned in such way that only one of the dots contained a single heavy hole with the Fermi level of the adjacent lead positioned in between Zeeman split spin states. In this situation one hole is initialized in the lowest spin level and the current is blocked. A small microwave voltage is applied to a plunger gate to mediate EDSR rotating the hole spin from the lower to the upper spin level allowing the hole to tunnel to the lead. The spin resonance is detected as an increase in current when the resonant condition is fulfilled. The second dot is used as an auxiliary tool to tune the g-factor via a strong spin-dependent tunnel coupling[1]. We show that g-factor can be tuned in the range of 30% by a small change of the voltage applied to the auxiliary dot plunger gate.
[1] A. Bogan et al., Phys. Rev. Lett. 120, 207701 (2018).   

Origins and enhancement of hole spin-mixing in InAs quantum dot molecules

Hole spins in self-assembled InAs quantum dots molecules (QDMs) are a strong candidate for qubit architecture due to their all-optical operation and enhanced tunability via voltage bias across the two dots. In order to capitalize on the all-optical operation and the enhanced tunability, we exploit the spin-mixing provided by the “molecule-like” coupled hole states. Through an atomistic tight-binding model and perturbative field analysis, we discuss the origin of spin-mixing and compare it with previous models using effective Hamiltonians. We then apply our understanding to the case where the GaAs inter-dot region is alloyed with a dilute amount of Bi. Replacing As atoms with the heavier Bi atoms enhances spin-orbit effects and, in turn, increases spin-mixing. However, it complicates the model, as atomistic alloying effects have to be considered, something not explored by prior models. Finally, we briefly discuss the practical operation of InAs/GaBiAs QDM qubits with the enhanced spin-mixing.   

Controlling hole spin in quantum dots: Rashba or not Rashba

Hole spins in semiconductor quantum dots (QD) are promising qubits. Zeeman-split states form two-level systems with splitting determined by the physical spin of the hole. Due to strong spin-orbit coupling, hole spin orientation is locked to the QD axis for magnetic fields B away from the Voigt configuration. However, in Voigt configuration, the hole spin displays significant texture across the dot but is weakly polarized. Application of an electric field parallel or antiparallel to B in the Voigt configuration restores the hole spin. This spin control can be related to the QD geometry. The question remains whether this can be explained as a Rashba effect originating from interface fields or is inherent to an atomistic description of hole spins in QDs. Tight-binding theory is used to study GaAs/AlAs QDs with a graded alloy describing the QD interface to minimize Rashba effects of sharp interfaces. The results are compared with results for QDs with sharp interfaces. Several examples illustrate how a graded interface influences the spin locking seen for QDs with sharp interfaces and how this changes spin texture and spin polarization in the Voigt configuration. The results are used to assess the contribution of Rashba effects.