Session B29: Semiconductor Qubits - Spin Qubit Read-out I

Live

Silicon is considered a promising candidate for realizing large qubit processors [1], making quantum dots in silicon nanowire transistors, fabricated in industrial cleanrooms on 300-mm wafers, particularly attractive [2]. We perform gate-based reflectometry measurements of various charge states in a foundry-fabricated two-dimensional quadruple quantum dot. From a wiring perspective, the low number of control channels (one gate-electrode per dot and global top and back gates) is desirable, provided that tunnel couplings are adjustable to allow controlled single-electron movements [3] and single-shot reflectometry readout.
Using native and virtual gate voltages, we demonstrate charge sensing and dispersive read-out down to the last electron in each dot, and show an adjustability of interdot tunneling rates using the top gate. We support our findings with k x p modeling and simulations based on a constant interaction model, and experimentally demonstrate single-shot detection of interdot charge transitions with unity signal-to-noise ratios at bandwidths exceeding 1 MHz.
[1] Vandersypen et al., npj Quant.Inf. 3, 34 (2017)
[2] Maurand et al., Nat.Comm. 7, 13575 (2016)
[3] Ansaloni et al., arXiv:2004.00894 (2020)   

Live

We report the measurement of the electron spin orientation in a singly-occupied gate-defined quantum dot, fabricated using CMOS compatible processes at the 300 mm wafer-scale [1]. For readout, we employ spin-dependent tunnelling [2] combined with a low-footprint single-lead quantum dot charge sensor, measured using radiofrequency gate reflectometry [3]. We demonstrate spin readout, obtaining valley splittings in the range 0.5-0.7 meV and a maximum electron spin relaxation time (T₁) of 9 ± 3 s at 1 Tesla. These long lifetimes indicate that the silicon nanowire geometry and fabrication processes possess considerable promise for qubit devices, while this spin-readout method is well-suited to scalable architectures. We will discuss progress towards integrating such spin-readout with quantum-limited amplifiers [4].

[1] Nat. Commun. 7, 13575 (2016)
[2] Nature 430, 431 (2004)
[3] Nat. Commun. 6, 6084 (2015)
[4] Phys. Rev. Lett. 124, 67701 (2020)   

Live

Silicon spin qubits have achieved high-fidelity one- and two-qubit gates [1,2] and promise an industrial route to fault-tolerant quantum computation. A significant next step for the development of scalable multi-qubit processors is the operation of foundry-fabricated, extendable two-dimensional (2D) quantum-dot arrays.
In this talk I will present our recent results on the control of a foundry-fabricated 2x2 array of silicon quantum dots in the few-electron regime, achieving single-electron occupation in each of the four gate-defined dots [3]. By exploiting the second dimension as well as single electron control, we induce the spatial exchange of electron pairs within the array. In principle, this discrete exchange operation is protected against charge noise, owing to Coulomb blockade, and may find use in permutational quantum computing [4].

[1] T. F. Watson et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633 (2018).
[2] D. M. Zajac et al. Resonantly driven CNOT gate for electron spins. Science 359, 439 (2018).
[3] F. Ansaloni et al., arXiv:2004.00894 (2020).
[4] S. P. Jordan, Permutational Quantum Computing. Quantum Information and Computation 10, 470 (2010).   

Live

An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at the atomic level is detrimental to qubit uniformity. Here we investigate two spin qubits confined in a silicon double quantum-dot artificial molecule. Each quantum dot has a robust shell structure and, when operated at an occupancy of 5 or 13 electrons, has single spin-½ valence electron in its p- or d-orbital, respectively. These higher electron occupancies screen atomic-level disorder. The larger multielectron wavefunctions also enable significant overlap between neighbouring qubit electrons, while making space for an interstitial exchange-gate electrode. We implement a universal gate set using the magnetic field gradient of a micromagnet for electrically-driven single qubit gates, and a gate-voltage-controlled inter-dot barrier to perform two-qubit gates by pulsed exchange coupling. We use this gate set to demonstrate a Bell state preparation between multielectron qubits with fidelity 90.3%, confirmed by two-qubit state tomography using spin parity measurements.   

Live

To implement quantum error-correction, readout must be performed much faster than the coherence time, up to ~100 μs for spins in silicon [1]. With that goal in mind, here we demonstrate the readout of an inter-dot charge transition, the basis of parity readout, in 50 ns with a SNR of 3.3. We do so using dispersive gate sensing with a CMOS split-gate nanowire transistor. This fast readout is achieved firstly by maximising the coherent coupling rate between the microwave photons and the charge dipole. We measure a coupling of 183 MHz owing to the large inter-dot lever arm (0.72) of our asymmetric split-gate device, and the high impedance (560 Ω) of our readout cavity, which comprises of an off-chip superconducting spiral [2] that is inductively coupled to the microwave feedline. Secondly, this inductive coupling is tuned so that the cavity linewidth is similar to the state-dependent shift in the resonant frequency, the regime of optimal state visibility [3].

[1] Veldhorst, M. et al., Nat. Nanotechnol. 9, 981-985 (2014)
[2] Ahmed, I. et al., Phys. Rev. Applied 10, 014018 (2018)
[3] Gambetta, J. et al., Phys. Rev. A. 77, 012112 (2008)   

Live

To read the state of silicon spin qubits, the mechanism that has provided highest fidelity is spin-to-charge conversion via Pauli spin blockade [1]. However, given the valley degree of freedom in silicon quantum dots, which can lead to complex energy spectra, accurate identification of the spin states involved in Pauli spin blockade is a key requirement for reliable readout and operation of silicon spin qubits.

Here, we expand the standard description of Pauli spin blockade in a double quantum dots (DQD) to include multiparticle states with large total spin angular momentum S. Using gate-based dispersive readout and magnetospectroscopy, we show successive steps of spin blockade and spin-blockade lifting involving spin states up to S=3 as well as the formation of a novel spin-quintet state [2]. Furthermore, we demonstrate the use of this technique for discerning whether the valleys involved in DQD interdot transitions are of equal or different quantum number.

[1] Harvey-Collard et al, Phys. Rev. X 8, 021046 (2018)
[2] Lundberg et al, Phys. Rev. X 10, 041010 (2020)   

Live

My talk on high-frequency reflectometry measurements has two parts, explaining its use to tune gate voltages into desired charge configurations of quantum-dot arrays, and to perform simultaneous single-shot readout of multiple qubits.

For gate-voltage tuning, the traditional dense raster scans of charge stability diagrams cannot be scaled to larger arrays with many gate electrodes, due to the prohibitively large number of pixels contained in naive high-dimensional gate-voltage cubes. To mitigate this challenge, we developed sparse acquisition methods in which the boundaries of Coulomb-blockade polytopes are reconstructed from a discrete set of time stamps, each triggered by a simple thresholding circuit that detects abrupt changes in the reflectometry signal without ever digitizing it. We combine this method with an active-learning algorithm and a large-margin classifier to adaptively propose and execute new line searches in gate-voltage space. We implement this approach on a 2x2 array of quantum dots implemented in fully-depleted silicon-on-insulator devices.

For the simultaneous single-shot readout of four singlet-triplet qubits, implemented in gate-controlled gallium-arsenide heterostructures, we utilize frequency multiplexing and four radiofrequency resonators with distinct resonance frequencies, each monitoring via time-resolved reflectometry the state of a sensor dot associated with a qubit. I will explain the simultaneous and interlaced detection of exchange-rotation and Overhauser-dephasing operations, as well as various coherent spin-exchange processes within the quantum dot array that reveal mechanisms related superexchange, electron-electron correlations, and negative (multi-electron) exchange coupling.   

Live

Spin qubits in silicon are great candidates for scalable quantum information processors due to their long coherence time combined with compatibility with industrial CMOS fabrication lines [1]. The spin-readout is obtained by spin-to-charge conversion using a nearby SET. This require multiple additional leads and limits the scalability of the system. RF-reflectometry measurement provides a compact alternative [2,3] as only one lead is necessary to control and read the qubit [4]. The critical part for this measurement is to obtain an impedance matching, at low temperature, between the resonant circuit and the RF-line. This is due to the temperature dependence of each of the tank circuit components and the sample-to-sample capacitance variability. In this talk, we report a charge-sensing measurement of a CMOS device with optimized reflectometry setup and discuss the use of tunable capacitors to target high sensitivity RF-measurement for spin qubit readout.

[1] M. Veldhorst, et al., Nat. Nano. 9, 981–985 (2014)
[2] B. J. Villis, et al., Appl. Phys. Lett. 104, 233503 (2014)
[3] I. Ahmed, et al., Appl. Phys. Lett. 10, 014018 (2018)
[4] P. Pakkiam, et al., Phys. Rev., 8, 041032 (2018)   

Live

The manipulation fidelity of a single-electron spin qubit gate-confined in a ²⁸Si/SiGe quantum dot has recently been drastically improved by nuclear isotope purification [1]. Here, we characterize a ²⁸Si/SiGe device with an embedded nanomagnet, a large valley splitting (> 0.2 meV [2]), and a remaining ²⁹Si concentration of only 60 ppm in the strained silicon quantum well layer, which is grown by molecular beam epitaxy. We identify the combination of charge noise and gradient magnetic field as the dominant source of low frequency qubit detuning noise. The power spectral density (PSD) of the charge noise explains the frequency-dependence of the detuning noise PSD, as well as the observation of a decreasing time-ensemble spin dephasing time with increasing measurement time over several hours [3]. We also comment on the role of the remaining nuclear spins in the SiGe barrier on the qubit dephasing and the origin of the observed large valley splitting.
[1] J. Yoneda, et al., Nat. Nanotechnol. 13, 102 (2018).
[2] A. Hollmann et al., arXiv:1907.04146.
[3] T. Struck et al., arXiv:1909.11396.   

Live

The spin of electrostatically confined electrons in semiconductor heterostructures has proven to be a promising candidate for hosting long-lived quantum information. Single and two spin qubit realizations rely on manipulation using (engineered) magnetic fields, but universal control using exclusively pairwise Heisenberg exchanges becomes possible when encoding the qubit in the spin-1/2 subspace of three electrons. While such qubits have proven to be operable with high fidelity [1], an issue is the presence of the spin-3/2 leakage subspace which tends to be occupied under sustained operation and has to be actively depopulated via so called Leakage Reduction Units.
We show, based on group-theoretic reasoning, that 2 ancillary spins are sufficient to perform such leakage reduction and present sequence accomplishing this task within 14 exchange gates, less than half than previously reported [2].
We further discuss the resilience with respect to noise as well as the possibility and implications of flagging leakage via such gadgets.

[1] R. W. Andrews et al., Nat. Nanotechnol. 14, 747–750 (2019)
[2] B. H. Fong and S. M. Wandzura, Quantum Inf. Comput. 11 1003-1018 (2011)   

Live

Markovian models of qubit dynamics break down for charge qubits coupled to 1/f noise and for spin qubits coupled to slow nuclear-spin baths. For spin/charge qubits also coupled to a cavity, it can be difficult to directly extract time-domain coherence dynamics because the AC control fields used to prepare and measure these qubits have the potential to excite the cavity mode. In this talk, we present a way of extracting the coherence dynamics of a qubit coupled to a cavity purely from frequency-dependent measurements of the cavity response in cavity quantum electrodynamics (QED). In contrast to a more standard equation-of-motion approach, we make neither a Markov approximation nor a weak-coupling approximation for the qubit-bath dynamics. Using this approach, we calculate the spectroscopic response of a spin qubit coupled to nuclear spins. This response shows pronounced non-Lorentzian features, indicative of non-Markovian dynamics, arising from a many-spin collective mode. We also consider the case of a qubit coupled to a single bosonic mode corresponding to, e.g., a mechanical degree of freedom, phonon, or cavity mode. In this instance, strong coupling gives rise to higher harmonics in the qubit coherence spectrum.   

On Demand

High fidelity scalable readout is one of the key requirements for quantum computers with more than just a few qubits. Charge sensing dots are in this regard the most sensitive sensors for spin qubit readout. The most widespread readout technique is based on RF reflectometry, satisfying the requirement of high fidelity, but requires bulky, power-hungry components and is not well scalable. A more scalable alternative is to use transistors in close proximity to the qubit [1,2].
For best performance a high output swing of the sensor is desirable. We present experimental results in GaAs of an asymmetric sensing dot (ASD), improving the sensor response by a factor of 13, compared to conventional charge sensing dots. We perform charge sensing using a current biased ASD and observe a (3.0±0.2)mV swing, in response to a (1,1)→(2,0) transition in a nearby double dot.
The improved voltage swing is due to a device design with a strongly decoupled drain reservoir from the sensor dot, mitigating negative feedback effects.
[1] M. J. Curry et al., APL 2015
[2] L. A. Tracy et al., APL 2016   

On Demand

A quantum non-demolition (QND) single-shot qubit readout is crucial for large-scale quantum computing, and unlike conventional counterparts, can serve as a state preparation process with its error extinguishable by repetition. Here we discuss the state preparation fidelity of a cumulative QND readout of an electron spin qubit in a silicon quantum dot with its neighboring electron spin used as an ancilla [1]. By repeating the single QND readout process, a qubit spin state is prepared in the state correlated to the readout outcomes with a state dependent fidelity. Furthermore, a series of readout outcomes can be converted to the likelihood ratio of successful state preparation, which allows one to select events with a higher preparation fidelity. Combined with real-time signal processing, such protocols offer alternative routes for high-fidelity state preparation.

[1] J. Yoneda et al, Nat. Commun. 11, 1144 (2020).