Recent advances in semiconductor qubits
Japan standard time (UTC+9)

Tuesday, 9 March 2021, 13:00 – 18:00
15:30-16:00
13:00- Opening

Peter Stano (RIKEN)

13:10-13:40"Optimal frequency estimationand its application to quantumdots”

Kenta Takeda (RIKEN)“Manipulation of three-spinstates in a silicon triple
quantum dot”

13:40-14:10
William Coish (McGill)"First-principles hyperfine andspin-electric coupling forelectron-spin and hole-spin
qubits”

16:00-16:30
Jun Yoneda (Tokyo Tech)"Single electron spin tunnelingin silicon quantum dots”

16:30-17:00Pasquale Scarlino(EPFL)"Hybrid cQED

14:10-14:40

with semiconductor QDs andhigh impedance
superconducting resonators”

Stephano Chesi (CSRC)

17:00-17:30"Superradiant-like dynamicsof nuclear spins by nonadiabatic electron shuttling”

Matthiew Delbecq(LPENS) “Hyperfine

14:40-15:10
Takafumi Fujita (Osaka)"Accelerated electric-dipole
spin resonance in aquantum dot array”

15:10-15:30 Breakcoupling of ultra-clean carbon
nanotube spin qubits in cQED
architecture”

17:30-18:00
Ferdinand Kuemmeth"Navigating(NBI)
high-dimensional gatevoltage spaces of multi-dot
spin qubits”

https://cems.riken.jp/topicalmeeting/009_spinqubits/

Manipulation of three-spin states in a silicon triple quantum dot
Kenta Takeda1
1Quantum Functional System Research Group, RIKEN Center for Emergent Matter Science (CEMS)
kenta.takeda [at] riken.jp

Semiconductor quantum dots are one of the most promising platforms for quantum computing due totheir nanofabrication capability for scaling-up. Recent technical advances have enabled high-fidelity
one- [1,2] and two-qubit [3] gates for spins in quantum dots. The next crucial step toward scaling up
is the demonstration of genuinely multipartite entanglement, an essential resource for quantum error
correction. This requires at least three qubits with full capabilities of control and measurement, a lot
further than individual qubit manipulation. In this talk, we first show individual initialization,measurement, and universal manipulation of three electron spins in a silicon triple quantum dot.
Second, we show generation and characterization of a three-qubit Greenberger–Horne–Zeilinger state,a type of maximally entangled state that is usable to implement a bit-flip or phase-flip quantum error
correcting code. We obtain a state fidelity of 88.0 % by quantum state tomography, which witnesses agenuine three-qubit entanglement. We anticipate that our results will enable exploration of multi-spincorrelations and demonstration of multi-qubit algorithms in scalable silicon-based quantum computing
devices.
[1] J. Yoneda et al., Nat. Nanotechnol. 13, 102–106 (2018).
[2] C. H. Yang et al., Nat. Electron. 2, 151–158 (2019).
[3] W. Huang et al., Nature 569, 532–536 (2019).

First-principles hyperfine and spin-electric coupling forelectron-spin and hole-spin qubits
W. A. Coish
Department of Physics, McGill University, Montreal, QC, Canada

Abstract
Through a combination of first-principles density-functional theory (DFT) and k.p theory, we
have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon [1], and also
in germanium [2]. Our results for electrons are consistent with existing experimental measurements.
For GaAs, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins isstronger and almost purely Ising, while the (weaker) coupling to the Ga nuclear spins has significant
non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strengthof the hyperfine interaction in the valence band is comparable to that in the conduction band andthat the hyperfine tensors are highly anisotropic (Ising) in the heavy-hole subspace. These results
suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence (T2⇤ )times recently measured for heavy holes in silicon quantum dots.
In addition, we have used similar techniques [3] to find the electric-dipole (pseudospin-electric)
coupling between heavy and light holes in GaAs, giving rise to a distinct E-field controllable
Dresselhaus-like spin-orbit coupling for heavy holes in a triangular quantum well, with consequenceson spin splitting, spin coherence/relaxation (T2*/T1) times, spin-electric coupling for cavity-QED,electric-dipole spin resonance, and spin non-conserving tunneling in double quantum dot systems.

[1] P. Philippopoulos, S. Chesi, and W. Coish, First-principles hyperfine tensors for electrons andholes in gaas and silicon, Phys. Rev. B 101, 115302 (2020).
[2] P.

Philippopoulos,

conductor

Hyperfinenanostructures,andPh.D.

spin-orbit
thesis,interactions

McGillUniversityinsemi(2020),

https://escholarship.mcgill.ca/concern/theses/tx31qp42d.
[3] P. Philippopoulos, S. Chesi, D. Culcer, and W. Coish, Pseudospin-electric coupling for holes
beyond the envelope-function approximation, Phys. Rev. B 102, 075310 (2020).

1

Superradiant-like dynamics of nuclear spins by non-adiabatic electron
shuttling
Stefano Chesi1
1Beijing Computational Science Research Center, Beijing 100193, China
stefano.chesi [at] csrc.ac.cn

Superradiant emission of light occurs when, due to quantum coherence, an ensemble of atoms
decays collectively at an enhanced rate. Over the years, several schemes were proposed torealize a superradiant-like dynamics in quantum dots, with the role of atoms played by nuclear
spins and the emitted light by the transport current through the dot [1-4]. Motivated byexperimental progress on electron shuttling through quantum dot arrays, as well as the typicaloperation of single-electron pumps, we propose here a scheme to achieve superradiant-likedynamics through a single-electron quantum dot, whose position is cyclically shuttled between
two external reservoirs. Under suitable conditions, tunneling events are associated withelectron-nuclear flip-flops and drive the superradiant-like dynamics. Our proposal has theadvantage of avoiding optical excitation [3] as well as ferromagnetic contacts [4]. We first
discuss in detail the shuttling process within the approximation of a uniform hyperfine
coupling, which allows us to rely on the exact eigenstates and reveal certain subtleties in thetreatment of the superradiant-like dynamics, missed by previous literature. We then assess theeffect of various imperfections and derive the minimum shuttling time which allows to escape
the adiabatic spin evolution. A related discussion of slow/fast shuttling under the
inhomogeneous field of a nearby micromagnet is also provided.

[1] M. Eto, T. Ashiwa, and M. Murata, J. Phys. Soc. Jpn. 73, 307 (2004).
[2] E. M. Kessler, S. Yelin, M. D. Lukin, J. I. Cirac, and G. Giedke, Phys. Rev. Lett. 104,143601 (2010).
[3] M. J. A. Schuetz, E.M. Kessler, J. I. Cirac, and G. Giedke, Phys. Rev. B 86, 085322 (2012).
[4] S. Chesi and W. A. Coish, Phys. Rev. B 91, 245306 (2015).

Accelerated electric-dipole spin resonance in a quantum dot array
Takafumi Fujita1, 21

2

The Institute of Scientific and Industrial Research (ISIR), Osaka University
Center for Quantum Information and Quantum Biology (QIQB), Osaka University
fujita [at] sanken.osaka-u.ac.jp

Single spin manipulation using the intrinsic spin-orbit interaction is a technique torotate spins without artificial magnetic structures [1], which has been crucial insemiconductor transport experiments and in the earlier period of quantum information
technology. In this talk, we present results on the accelerated electric-dipole spinresonance utilizing a spin-flip tunneling term that appears in a coupled multiple quantum
dot. First, we introduce the single spin tunneling associated with a spin flip in a double
quantum dot [2]. Next, we discuss measurements to utilize this effect in a spin coherent
manner. By setting the microwave frequency on resonance to the magnetic spin splitting
after sufficiently increasing the inter-dot tunnel coupling, the acquired Rabi oscillations
show enhanced speed, which is dependent on microwave amplitude and energy detuning
between the dots. Such concept of spin rotation in a double dot is extended to a triple
quantum dot and we observed a larger speed-up owing to the extended charge oscillation
distance across the three dots.
Since precise spin rotation using this technique relies on a perfect adiabatic charge
shuttling [3], we observed impacts of excited charge states and its decoherence effect thataffected the spin coherence in experiment. We will further discuss the results in detail andpossible paths for utilizing the large tuning variations in a multiple dot for applying tospin rotations in integrated architectures.
[1] K. Nowack, F.H.L. Koppens, Yu.V. Nazarov, L.M.K. Vandersypen, Science 318,1430 (2007).
[2] T. Fujita, P. Stano, G. Allison, K. Morimoto, Y. Sato, M. Larsson, J.-H. Park, A.
Ludwig, A.D. Wieck, A. Oiwa, S. Tarucha, Phys. Rev. Lett. 117, 206802 (2016).
[3] T. Fujita, T.A. Baart, C. Reichl, W. Wegscheider, L.M.K. Vandersypen, npj Quantum
Information 3, 22 (2017).

Optimal frequency estimation and its application to quantum dots
Peter Stano
RIKEN Center for Emergent Matter Science, JapanI present results on optimal phase estimation of a qubit [1]. I use them to show how toextend the coherence of the current spin-qubit devices against slow noise (nuclear spin-noisein GaAs or quasi-static charge-noise in Si).
I start with the broad appeal of phase estimation, as the essence of all known quantum
algorithms. I explain the relation and point out differences of the estimation of a parameter ofa solid-state qubit and the existing phase estimation protocols which had been developed inoptics, as a homodyne-with-feedback detection. I formulate optimal estimation as aminimization problem and discuss the figures of merit. I discuss the pros and cons ofminimizing the entropy versus the variance of the estimated quantity distribution and therelation to the maximum-likelihood estimation. I then describe the classes of minimization
strategies: local versus global and online versus offline. I finally present our algorithm which
generates the optimal solution within the local(greedy)+offline class and I prove its uniqueness.
I illustrate the construction and behavior of the optimal strategy with numerical examples
applied to singlet-triplet qubit in GaAs. I point out how some estimation patterns, usuallyadopted ad-hoc, naturally emerge in our construction. I show that our method can be used torefine any given class of estimation strategies, for example, the (Kitaev) Quantum Phase
Estimation Algorithm (QPEA). I conclude by illustrating the power of noise estimation inboosting the coherence of spin qubits as seen in recent experiments [2-5].

[1] A. Gutierrez-Rubio, P. Stano, D. Loss, Optimal frequency estimation and its application to noisein quantum dots, arxiv:2004.12049.
[2] T. Nakajima, et al, Coherence of a driven electron spin qubit actively decoupled from quasi-static
noise, Phys. Rev. X 10 011060 (2020).
[3] T. Nakajima, et al., Quantum non-demolition measurement of an electron spin qubit,Nat. Nanotech. 14 555, (2019).
[4] A. Noiri, et al., A fast quantum interface between different spin qubit encodings,
Nat. Commun. 9, 5066 (2018).
[5] M. R. Delbecq, Quantum dephasing in a gated GaAs triple quantum dot due to non-ergodic noise,
Phys. Rev. Lett. 116, 046802 (2016).

Single electron spin tunneling in silicon quantum dots
Jun Yoneda1
1Tokyo Tech Academy for Super Smart Society, Tokyo Institute of Technology, Tokyo,152-8552 Japan
yoneda.j.aa [at] m.titech.ac.jp

The ability to faithfully transfer a quantum bit of information (or qubit) in thequantum computing architecture offers viable routes for scalability and fault tolerancewith increased connectivity. Conversely, qubit transfer may introduce dephasing, loss,
and state leakage which stationary qubits are meticulously engineered against. Siliconbased quantum dot qubits have demonstrated immense promise in terms of coherence,high control fidelity, and large-scale fabrication. However, it has remained to be seen
whether one can transport the qubit with fidelities at the fault-tolerant level in thisstructure. In this presentation, we show that single electron tunneling can implement
highly coherent spin qubit transport in an isotopically-enriched silicon quantum-dot array.
Using Ramsey interferometry and quantum state tomography techniques, we assess theimpact of tunneling on the spin qubit coherence in detail and report a polarization transfer
fidelity of 99.97% and an average coherent transfer fidelity of 99.4%. This transfer
method can be extended to longer quantum-dot chains by sequencing it from one site to
the next in a bucket-brigade manner, offering micron-scale on-chip quantum links forsilicon spin-qubit architectures.
[1] J. Yoneda, W. Huang, M. Feng, C. H. Yang, K. W. Chan, T. Tanttu, W. Gilbert, R. C.
C. Leon, F. E. Hudson, K. M. Itoh, A. Morello, S. D. Bartlett, A. Laucht, A. Saraiva,
A. S. Dzurak, arXiv 2008.04020 (2020).

Hybrid Circuit Quantum Electrodynamics withSemiconductor QDs and Superconducting Resonators
P. Scarlino
Institute of Physics, EPFL, Lausanne, Switzerland
Semiconductor qubits rely on thecontrol of charge and spin degrees offreedom of electrons or holes confinedin quantum dots (QDs). Typically,
semiconductor qubit-qubit coupling isshort range, effectively limiting qubit
distance to the spatial extent of thewavefunction of the confined particle(a few hundred nanometers). This is a significant
Figure1: a DQD charge system strongly
constraint towards scaling of the QD-based
coupled to a SQUID array resonator [1].
architectures to reach dense 1D or 2D arrays of QDs.
Inspired by techniques originally developed for circuit QED, we recently demonstrated thestrong coupling limit of individual electron charges [1,2] confined in GaAs quantum dots, byusing the enhancement of the electric component of the vacuum fluctuations of a resonatorwith impedance beyond the typical 50 Ohm of standard coplanar waveguide technology (Fig.1).
By making use of this hybrid technology, we recently
realized a proof of concept experiment, where thecoupling between a transmon and a double QD (DQD)
is mediated by virtual microwave photon excitations ina high impedance SQUID array resonator, which acts
as a quantum bus enabling long-range coupling
between dissimilar qubits [3]. Similarly, we achievedcoherent coupling between two DQD charge qubitsseparated by approximately ~50 um [4]. In thedispersive
regime,wespectroscopicallyobserved qubit-qubit coupling as an avoided- Figure2: a Triple QD resonant exchange spincrossing in the energy spectrum of the DQD qubit strongly coupled to a NbTiN resonator [5].
charge qubits. The methods and techniquesdeveloped in these works are transferable to QD devices based on other material systems andwill be beneficial for spin based hybrid systems [5] (see Fig.2).

References[1] A. Stockklauser*, P. Scarlino*, et al., Phys. Rev. X 7, 011030 (2017).
[2] P. Scarlino*, D. J. van Woerkom*, et al., Phys. Rev. Lett. 122, 206802 (2019).
[3] P. Scarlino*, D. J. van Woerkom*, et al., Nat. Comm. 10, 3011 (2019).
[4] D. J. van Woerkom*, P. Scarlino*, et al., Phys. Rev. X 8, 041018 (2018).
[5] A. Landig*, J. Koski*, et al., Nature 560, 179-184 (2018).

Hyperfine coupling of ultra-clean carbon nanotube spin qubits in cQED
architecture
Matthieu Delbecq1
1

Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne
Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France

Semiconducting spin qubits are promising candidates for manipulating quantum information becauseof their long coherence times and potential for scalability. For years, the development ofsemiconducting spin qubits was hindered by a large dephasing due to the hyperfine coupling of theelectron spin to surrounding nuclear spins of the host material. Impressive improvements of thedephasing time were recently achieved by switching to materials with less (natural silicon Si) toalmost no (isotopically purified 28Si) nuclear spins, compared to GaAs which has a 100%concentration. Interestingly, carbon nanotubes (CNT) have a lower concentration of nuclear spins
than natural silicon and can also be isotopically purified. In addition they should theoretically present
a hyperfine coupling smaller than in Si by a factor 5 to 20, which would boost the dephasing by thisamount compared to Si. However, since the first realization of a CNT spin qubit in 2013, the hyperfine
coupling was found to be 103 to 104 times larger than theoretically predicted. We developed a highvacuum stapling technique that allows for the realization of ultra-clean CNT devices in microwave
cavities. Similarly to previous implementations, the spin qubit is realized in a double quantum dot
with non-collinear ferromagnetic contacts [1]. The CNT stapling technique results in a much cleaner
spectrum as well as a much higher tunability of the device thanks to the clean environment. We
observe the largest dephasing time reported in CNT spin qubits (T2*~600 ns), reducing thediscrepancy with the theoretical value of the hyperfine coupling to a factor ~50 [2]. Possible
explanations for the remaining discrepancy comprise Luttinger liquid interactions, effects of thecavity field and a remaining large charge noise, all of which can be investigated and dealt with infuture devices.
[1] J. J. Viennot et al., Science 349, 408 (2015).
[1] T. Cubaynes et al., Npj Quantum Inf. 5, 47 (2019).

Navigating high-dimensional gate-voltage spaces of multidot spin qubits
Ferdinand Kuemmeth

Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen

The voltage tuning of few-qubit devices is traditionally done by hand by human experts,
using low-dimensional charge stability maps as visual aids for navigating in control-voltage
space. Large arrays of spin qubits will require automatic tune-up by computers. For gatevoltage tuning, the traditional dense raster scans of charge stability diagrams cannot bescaled to larger arrays with many gate electrodes, due to the prohibitively large number ofpixels contained in naive high-dimensional gate-voltage cubes.
To mitigate this challenge we are developing autonomous sparse acquisition methods inwhich the boundaries of Coulomb-blockade polytopes are reconstructed by suitablealgorithms from a discrete set measurements. We test our approach on simulated convex
charge stability diagrams as well as actual multi-dot arrays implemented in fully-depleted
silicon-on-insulator devices. The charge state boundaries learned by our algorithm for a 2x2
array of quantum dots is in good agreement with two-dimensional diagnostic raster scansmeasured by traditional methods on the same device.