Session L17: Focus Exchange Based Spin Qubits

Strong photon coupling to the quadrupole moment of an electron in a triple quantum dot

We experimentally couple the photonic excitations of a superconducting microwave resonator to a single electron hosted in a quantum dot charge qubit. The two qubit states with a 4.3 GHz separation arise in a four-electron triple quantum dot formed by locally gating a two-dimensional electron gas in GaAs. We demonstrate strong electron-photon coupling via the quadrupole moment in a parameter regime with negligible dipole coupling. The quadrupolar qubit-photon coupling strength is estimated from the vacuum Rabi mode splitting to be g₀/2π = 150 MHz. The qubit can also be tuned into a regime where it operates as a conventional double quantum dot charge qubit diplole coupled to the resonator. The experiment is motivated by a recent proposal [1,2] which aims at avoiding decoherence by distant charge fluctuations. Using spectroscopy measurements we determine the decoherence rate of the quadrupolar qubit to be γ₂/2π = 32 MHz. Comparing the coupling of charge noise to the conventional dipolar qubit and the quadrupolar qubit, we find that the coherence of the system is limited by short-range charge noise originating from noise sources residing near the triple quantum dot.

[1] M. Friesen, J. Gosh, M.A. Eriksson, and S.N. Coppersmith, Nature Comm. 8, 15923 (2017).
[2] J. Gosh, S.N. Coppersmith, and M. Friesen, Phys. Rev. B 95, 241307 (2017).   

Efficient orthogonal control of tunnel couplings in a quantum dot array

Electrostatically defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and inter-dot tunnel couplings complicates the tuning of the device parameters. To date, cross-talk to the dot potentials is routinely and efficiently compensated using virtual gates, but cross-talk to the tunnel barriers is currently compensated through a slow iterative process, due to exponential dependence of tunnel couplings on gate voltages. Here we show that the crosstalk on tunnel barriers can be compensated using a linear combination of gate voltages, since the exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple dot and define a set of virtual barrier gates as linear combinations of physical gate voltages. We then demonstrate orthogonal control of tunnel couplings in the quadruple dot using these virtual barrier gates. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays.   

Barrier-Controlled Multi-Qubit Exchange

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for coherent qubit manipulation in spin-based quantum computing and quantum information processing. Various other phenomena such as many body localization and time crystals in semiconductor quantum dots also require tunable exchange couplings. However, controlling multiple exchange couplings in large quantum dot arrays proves to be challenging, due to non-linear and non-local dependence of the exchange couplings on the confinement gate voltages. In this work we demonstrate simultaneous control of multiple barrier-induced exchange couplings in a four-qubit processor. We model the dependence of the exchange couplings on all barrier gate voltages, which provides a means of precisely and simultaneously controlling multiple exchange couplings. We demonstrate two-, three-, and four-qubit exchange oscillations, and compare the experimental data to the simulated predictions.   

Coherent Spin-State Transfer via Heisenberg Exchange

Spin qubits in semiconductors are a promising scalable architecture for quantum computing. Long chains of spin qubits have already been realized in different semiconductor platforms but transferring quantum information throughout such chains is still a challenge. Here we present the first experimental demonstration of the coherent transfer of electron spin states back and forth across a chain of four quantum-dot spin qubits using Heisenberg exchange coupling between neighboring electrons, which arises from the overlap of their wavefunctions. We swap the spin states of a pair of electrons via precisely-controlled exchange pulses. Successive SWAP operations between different pairs can transfer a quantum spin state to a distant qubit, without moving any electrons. Because this method is scalable to long chains of spin qubits, coherent spin -state transfer using Heisenberg exchange will be useful in multi qubit operations, measurement-based entanglement swapping and gate teleportation, and error correction in spin-based quantum computers.   

Noise-resilient driven exchange gate for quantum dot spin qubits

Spin qubits in silicon quantum dots are a promising candidate for high-fidelity quantum computation due to long decoherence times and fast operations.

Demonstrations of single qubit gates with fidelities up to 99.9% have been shown [1,2].
Recent demonstrations of two-qubit gates show fidelities of 92-98% [2,3]. These two-qubit gate implementations are not robust against low-frequency charge noise, which couples in via the exchange interaction, causing a limited fidelity. We propose a simple yet effective scheme that is resilient against low-frequency charge noise. We use a combination of analytic calculations and numerical simulations under realistic conditions to obtain estimated gate fidelities greater than 99%, which allow for fault-tolerant two qubit gates. We directly compare these realizations with existing proposals and will present our experimental efforts towards achieving this goal.


[1] Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)
[2] Huang et al., Nature (London) 569, 532 (2019)
[3] Xu et al., Phys. Rev. X 9, 021011 (2019)   

Interplay of exchange and superexchange in triple quantum dots

Recent experiments on semiconductor quantum dots have demonstrated the ability to utilize a large quantum dot to mediate superexchange interactions and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. We will describe our theoretical efforts to understand the controllability of superexchange interactions in these systems. We focus on a triple-dot system arranged in a triangular configuration and use configuration interaction calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the geometry and detuning of the mediating dot are varied. We also study how the strength and sign of the superexchange coupling depends on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.
  

Coherent manipulation of three-spin states in a Si/SiGe triple quantum dot

Quantum dot arrays provide a promising platform for quantum information processing. In Si-based devices, recent technological advances make it possible to implement single- and two-qubit operations with high fidelities. A three-qubit system is a next step toward scaling up and it is particularly important for realizing a quantum error-correcting code. In this work, we demonstrate coherent manipulation of three individual spins in a Si/SiGe triple quantum dot by site-selective electric dipole spin resonance. Spins in the left and right dots are read out by a spin-selective tunneling technique while the center spin is measured by reading out the left spin subsequently to a controlled-rotation operation. We also report our recent progress on controlled-controlled-rotation where the resonance frequency of the center spin depends on both left and right spin states.

[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).   

Full Permutation Dynamical Decoupling in an Encoded Triple-Dot Qubit

Dynamical decoupling (DD) sequences can mitigate decoherence induced by slowly varying interactions between a qubit and a bath by using appropriately timed qubit rotations. For an exchange only qubit encoded in the spins of three electrons, dynamical decoupling can be achieved by applying a series of full-SWAP operations on the constituent spins which fully permute their locations across the three dots [1]. Using gate-defined quantum dots in an enriched Si/SiGe device, we demonstrate that repeated applications of the full permutation sequence can echo low frequency charge and magnetic noise, resulting a dynamically decoupled coherence time of 100s of microseconds. We find that the first order DD sequence is susceptible to rotations about the Y-axis of the Bloch sphere, driven by either real magnetic field gradients or spin-orbit pseudo-gradients. Initializing the qubit along the Y axis renders the experiment insensitive to these errors, as implied by measurements of qubit leakage in this configuration. The resulting experiment is only sensitive to high-frequency noise sources and is similar to noise spectroscopy. We compare our results to simulations which include various types of high-frequency charge noise.
1. J R West and B H Fong New J. Phys. 14 083002 (2012)   

Highly tunable exchange-only singlet-only qubit in a GaAs triple quantum dot

Quantum-dot based exchange-only spin qubits offer fast manipulation and full electric control but decohere rapidly in the presence of Zeeman field gradients, such as those resulting from the hyperfine interaction with randomly polarized nuclear-spin ensembles in the dots. A solution is to encode the qubit in the decoherence-free subspace spanned by two four-particle singlet states in a quadruple-dot setup [1].

Here we propose an implementation of this singlet-only qubit in a triple quantum dot with a (1,4,1) charge occupation. In the central multi-electron dot, the interplay between Coulomb interaction and an out-of-plane magnetic field creates an energy spectrum with a tunable singlet-triplet splitting and this feature can be exploited to create a six-particle singlet-only qubit with a qubit splitting that can straightforwardly be tuned over several μeV by adjusting the external magnetic field. We confirm the full exchange-based electric control of the qubit and demonstrate its superior coherence properties due to its singlet-only nature.

[1] A. Sala and J. Danon, Phys. Rev. B 95, 241303(R) (2017)   

Correcting Distortion of Base-band Exchange Pulses in Quantum Dot Qubits

Repeatedly identical control waveforms are necessary for high fidelity qubit control. In triple-dot exchange-only spin qubits, full Bloch-sphere control is achieved via baseband voltage pulses alone. This makes them sensitive to the effects of pulse distortion extending from kHz to GHz frequencies. Here we present a technique to correct the known distortion of our arbitrary waveform generators. The application of this correction lead to a reduction of single qubit infidelity from 0.5% to 0.2% as measured by the “blind randomized benchmarking” protocol [1]. Additionally, we will cover an extension to this routine where we are able to estimate and potentially correct residual pulse distortion using coherent qubit control experiments.
[1] R. W. Andrews, et al. Nat Nanotechnol. 14, 747 (2019).   

Long-Distance Charge Transport in a Single Electron Conveyor Device in (Al,Ga)As

For the realization of scalable quantum computing architectures enabling topological error correction, a transfer of the qubit information over distances of at least a few microns is required for making space for signal vias and allowing for tiling of qubit registers with classical control-circuits. Instead of coupling qubits by employing surface acoustic waves, we chose a one-dimensional, gate-defined conveyor belt-like device layout where electrons are moved between qubit sites by translating the potential minima in which the electrons are trapped. Here, the direction and the velocity of the electron transport are not limited by the crystal’s properties.

In this talk, I will present a device designed to allow the shuttling of electrons over 7 µm with only four voltage signals, whereby in principle arbitrary distances are feasible. We employed high-yield, multi-layer electron beam lithography in order to fabricate the required 100 metallic gates. I will show results on pumping charges from one reservoir to the other by filling each potential minimum in the conveyor with up to five electrons. We observed charge transport which is independent of a bias voltage and linear in frequency.   

Computer-automated tuning procedures for semiconductor quantum dot arrays

As with any quantum computing platform, semiconductor quantum dot devices require sophisticated hardware and controls for operation. The increasing complexity of quantum dot devices necessitates the advancement of automated data collection and control software. By automating the analysis of charge stability diagrams, we can easily create tools to tune charge occupancy and interdot tunnel couplings in our quantum dot arrays. We use an image analysis toolbox developed in Python to automate the calibration of virtual gates, a process that previously involved a large amount of user intervention. Moreover, we show that straightforward feedback protocols can be used to simultaneously tune multiple tunnel couplings in a triple quantum dot¹.

[1] A.R. Mills et al., Appl. Phys. Lett. 115, 113501 (2019)   

Designing CPHASE Gates with Arbitrary Phase by Structural Modification of the Fong-Wandzura Sequence

We design efficient arbitrary CPHASE gates for exchange-only spin-based quantum computation in which quantum gates are carried out by sequences of exchange pulses acting on qubits encoded using three or more spins. The construction we present is motivated by our analytic derivation [1] of the Fong-Wandzura sequence [2], the shortest known pulse sequence for an exact CNOT gate (for a linear array of spins). This earlier derivation is based on a type of elevation of a simple five-pulse sequence consisting only of SWAP or trivial pulses, which captures the essential structure of the Fong-Wandzura sequence. In the present construction, we introduce and evaluate a modified simple five-pulse sequence consisting of four SWAP pulses and one pulse of arbitrary duration. We then show how this sequence can be elevated in a fashion similar to that of our Fong-Wandzura derivation, to yield a leakage-free entangling two-qubit sequence that carries out a gate operation locally equivalent to arbitrary CPHASE.

[1] D. Zeuch and N. E. Bonesteel, Physical Review A 93 (2016).
[2] B. H. Fong and S. M. Wandzura, Quantum Information & Computation 11 (2011).