Session E35: Exchange-Based Spin Qubits

Spin qubits made of quantum dots and donors in silicon

In this talk, I will present our recent work on control and readout of electron spin qubits in silicon MOS. Valley splitting is an issue that can induce control variability or limit readout fidelity. We show how this splitting is tunable in MOS devices [1], and introduce a shell-filling trick to overcome potential readout challenges. Readout fidelity has lagged behind that of control. We demonstrate that an enhanced latching mechanism can be used to improve the signal and lifetime of the spin-blockade readout while preserving its speed, achieving single-shot readout fidelities of > 99.86% [2]. The best spin qubit in the solid state is the nuclear spin of donors, but it is difficult to couple it to other qubits. We show coherent coupling of a donor to a quantum dot, a milestone for nuclear spin quantum computing [3]. We also study spin-orbit interaction for electrons in silicon quantum dots. We show that it is sufficiently large to drive a singlet-triplet qubit, allowing universal control without external elements [4]. We study the mechanisms behind this interaction and find three different effects [5]. Our work identifies crystallographic and magnetic field anisotropies that can be used to enhance or suppress these effects.

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. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government.

[1] Gamble et al., App. Phys. Lett. 109, 253101 (2016)
[2] Harvey-Collard et al., Phys. Rev. X (2018)
[3] Harvey-Collard et al., Nat. Comm. 8, 1029 (2017)
[4] Jock et al., Nat. Comm. 9, 1768 (2018)
[5] Harvey-Collard et al., arXiv:1808.07378 (2018)   

Decoherence of a donor-dot hybrid qubit in Si

A recent proposal for a scalable donor-based quantum computer scheme promises excellent coherence properties and fast qubit couplings [1]. The system consists of two types of qubits per donor: a flip-flop qubit consisting of the electron and nuclear spins, and a charge qubit of the donor electron tunneling between the donor and an interface quantum dot. The proposal identifies a parameter regime where flip-flop qubit dephasing due to electrical noise is strongly suppressed.

We study the decoherence properties of the flip-flop qubit when positioned near this sweet spot. In particular, we study the effect of charge noise that is coupled to the flip-flop qubit via the dependence of the hyperfine interaction and the electron gyromagnetic ratio on the charge qubit state. We find that zero frequency noise is indeed suppressed at the sweet spot. In the meantime, finite-frequency contributions from the qubit coupling to the excited charge states come into play at shorter time scales, although their effects average out over longer times. We also explore the decoherence dependence on external control parameters such as the applied magnetic field and tunnel coupling between the donor and dot.

[1] G. Tosi et al., Nature Comms 8, 450 (2017).   

Probing exchange interaction for gate-defined double quantum dots

The exchange interaction J is vital for gating in electron-spin qubits. Therefore, understanding its behavior is crucial for high-fidelity gating, especially at low J where an inability to turn it off completely may impact the fidelity of parallel qubit operations. Historically, the exchange interaction (controlled via detuning ε between dots) measured in experiment, J(ε) ∝ exp(−ε/ ε₀) [1-2], has deviated from Hubbard-based predictions, J(ε) ∝ 1/|ε|.
We present measurements of J down to values below 1MHz by controlling the nuclear magnetic field gradient ΔB_z in a GaAs double quantum dot. When ΔB_z becomes comparable to J the visibility of the S-T₀ precession is reduced. Fitting the relation between oscillation amplitude and frequency allows the extraction of J(ε). In combination with Ramsey-like experiments we measure J(ε) over three orders of magnitude.
Our results can be reproduced by a microscopic model including excited states in each dot and state-dependent tunnel coupling. Some parameters in the Hamiltonian, e.g. ground-state tunneling, excited-state tunneling, S-T₀ splitting, can be measured independently and are found to be reasonably consistent with the model.
[1] O. E. Dial et al., Phys. Rev. Lett. 14, 146804 (2013)
[2] T. F. Watson et al., arXiv:1708.04214 (2017)   

Computational modeling of exchange splitting in Si/SiO2 double quantum dots

One and two qubit operations have been demonstrated using electrons trapped in quantum dots at the interface of isotopically purified Si/SiO₂ materials. We present a computational study of Si/SiO₂ based double quantum dot qubits which could help in scaling the device design. Exchange splitting between the lowest singlet and triplet states, which plays an important role in two qubit operations, is calculated using the full configuration interaction (FCI) method. The single electron wavefunctions used in FCI are calculated using 20-band sp³d⁵s* tight binding (TB) Hamiltonian, which accurately represents the conduction-band X valley and spin orbit coupling in quantum dots. The electrostatic potential needed in TB is calculated using self-consistent effective-mass Schrodinger-Poisson (S-P) simulations on finite element meshes resembling the actual device geometry. Energy spectrum of S-P and TB simulations shows a good match at low detuning between the dots. At high detuning close to the (1,1)-(0,2) transition, where the two qubit operations take place, higher X-valleys along x, y and z axes are found to play a role in the exchange splitting, which could impact the response to charge noise.   

Achieving A High Fidelity Controlled-NOT Gate Between A Pair Of Exchanged-Coupled Silicon Double-Quantum-Dot Hybrid Qubits

It has been shown that operating qubits by varying exchange couplings while operating at sweet spots against detuning noise can improve gate fidelities. For double-quantum-dot hybrid qubits, this requires keeping the system in the large-detuning regime where dephasing is greatly suppressed. Here we show that, in a pair of exchange-coupled double-quantum-dot hybrid qubits, it is possible to exploit the large-detuning regime to achieve a sizeable exchange interaction between the qubits while suppressing leakage and dephasing, yielding a high-fidelity controlled phase gate with a gate time less than 1 ns. We find that the fidelity of a CNOT gate can be above 99.9%, in the presence of charge noise typical for semiconductor devices.   

Quadrupolar exchange-only spin qubit

We propose a quadrupolar exchange-only (QUEX) spin qubit that is highly robust against charge noise and nuclear spin dephasing, the dominant decoherence mechanisms in quantum dots [1]. Building on ideas developed for the exchange-only qubit [2], the hybrid qubit [3], and the exchange-only singlet-only spin qubit [4], the QUEX the qubit consists of four electrons trapped in three quantum dots, and operates in a decoherence-free subspace to mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise, the qubit can be completely operated at an extended charge noise sweet spot that is first-order insensitive to electrical fluctuations. Due to on site exchange mediated by the Coulomb interaction, the qubit energy splitting is electrically controllable and can amount to several GHz even in the "off" configuration, making it compatible with conventional microwave cavities. A symmetric readout and initialization protocol can be used to perform fast and high fidelity measurements.
[1] M. Russ, J. R. Petta, and G. Burkard, PRL 121, 177701 (2018)
[2] D. P. DiVincenzo et al., Nature 408, 339 (2000)
[3] Z. Shi et al., Phys. Rev. Lett. 108, 140503 (2012)
[4] A. Sala and J. Danon, Phys. Rev. B 95, 241303 (2017)   

Strong Microwave Photon Coupling to the Electron Quadrupole Moment

The implementation of circuit quantum electrodynamics (cQED) allows coupling of distant qubits by microwave photons hosted in on-chip resonators. Typically, the qubit-photon interaction is realized by coupling the photons to the electrical dipole moment of the qubit. A recent proposal [1] suggests storing the quantum information in the quadrupole moment of an electron in a triple quantum dot. This type of qubit is expected to have an improved coherence since the qubit does not have a dipole moment and is consequently better protected from electric noise. We report the experimental realization of such a quadrupole qubit hosted in a triple quantum dot in a GaAs/AlGaAs heterostructure. A high-impedance microwave resonator is capacitively coupled to the middle of the triple dot to realize interaction with the qubit quadrupole moment. We demonstrate strong quadrupole qubit-photon coupling with a qubit-photon coupling strength of g / 2π ≈ 130 MHz and a qubit decoherence rate of γ₂ / 2π ≈ 30 MHz. Furthermore, we observe improved coherence properties of the qubit when operating in the parameter space where the dipole coupling vanishes.

[1] M. Friesen et al., Nature Comm. 8, 15923 (2017)   

Suppression of Leakage for a Charge Quadrupole Qubit in Triangular Geometry

The relatively weak coupling between spin states in spin qubits has spurred a revival of interest in charge qubits, which promises stronger coupling between multiple charge qubits due to stronger long-range Coulomb interaction. Among the proposed charge qubits, charge quadrupole (CQ) qubit is suggested to provide a relatively robust quantum computation by virtue of the logical bases residing in a decoherence free subspace such that leakage state decouples from the manifold [1]. Conventionally, CQ qubit is realized with an electron residing in a lateral triple quantum dot device, yet any fluctuation in tunneling and detuning control causes significant leakage. We propose a strategy to mitigate such destructive coupling by simply implementing the CQ qubit in a triangular triple quantum dot, where the tunneling between the two dots on the edge strongly suppresses leakage, eliminating the need of complex pulse sequences. The reduction of leakage is demonstrated from molecular orbital calculation, in corporation with numerical simulations.

[1] M. Friesen, J. Ghosh, M. Eriksson, and S. Coppersmith, Nature Communications 8, 15923 (2017).   

A High-Fidelity Gateset for Exchange-Coupled Singlet-Triplet Qubits

A key ingredient for a quantum computer is the accurate manipulation of qubits in order to generate high-fidelity gates. For S-T₀ qubits in semiconductor quantum dots, which allow purely electric control with moderate bandwidth requirements, single-qubit gates with fidelities above the error correction threshold were demonstrated, whereas two-qubit operations have not reached the required fidelity [1-2].
Here, we numerically optimize a complete two-qubit gate set under realistic experimental constraints, exploiting exchange coupling while also accounting for capacitive coupling. We obtain fidelities of 99.9% for GaAs, while about 99.99% are achieved with vanishing magnetic field noise as in Si. We suppress leakage to 10⁻⁵ by choosing high inter-qubit magnetic field gradients.
For optimized parallel single-qubit gates, we find that inter-qubit capacitive coupling needs to be considered to avoid undesired entanglement, but is mitigated by interleaved operation. Realistic levels of residual inter-qubit exchange coupling are compensated for by our gates.
We will also report on progress of the realization of such gates in a GaAs device with two exchange-coupled S-T₀ qubits.
[1] Unpublished results relating to Cerfontaine et al., arXiv:1606.01897
[2] Nichol et al., npj Quantum Inf. 3 (2017)   

Fast high-fidelity entangling gates in Si double quantum dots

High-fidelity two-qubit gates remain a challenge for spin qubits in quantum dots, partly due to the exchange coupling’s sensitivity to charge noise and relatively longer gate times. Here we show that, by using simple smooth pulses to control the amplitude of the oscillating magnetic field, entangling gates locally equivalent to control-NOT and control-Z gates can be implemented in times as low as 26 ns and with fidelities up to 99.99%. Moreover, we provide the particular single-qubit gates necessary to make the two-qubit gates exactly equal to the CNOT and CZ gates.   

Robust implementation of one-qubit gates despite always-on exchange coupling in silicon double quantum dots

In a silicon two-qubit device, bandwidth constraints on exchange coupling and limitations on ESR power are important obstacles for the realization of strictly local gates, which are themselves necessary components of robust non-local gating schemes [1]. Here we show that, even in the presence of an exchange coupling stronger than one-qubit Rabi frequencies, spins can be addressed separately to implement a particular class of one-qubit gates optionally surrounded by exchange gates, and the crosstalk between them can be eliminated stroboscopically. We also show how to make such gates robust against quasistatic charge- and hyperfine-noise.

[1] U. Güngördü, J. P. Kestner, Phys. Rev. B 98, 165301 (2018)   

Adiabatic two-qubit gates of capacitively coupled quantum dot hybrid qubits

Semiconductor quantum dot qubits have progressed greatly over the past several years, with two-qubit gates realized by several groups. So far, the fidelities reported for these gates are still below the error correction threshold. Here, we model a system consisting of two capacitively-coupled quantum dot hybrid qubits, and optimize the adiabatic electrical pulses used to entangle these qubits. We find a simple pulse that yields a CZ gate with greater than 99% fidelity in the presence of a quasistatic charge noise distribution with standard deviation 1 µeV. Further, we introduce the concept of a “dynamical sweet spot” which can be used to develop pulses that decrease the infidelity by a factor of >5.   

Minimal non-orthogonal gate decomposition for qubits with limited control

How an arbitrary unitary transformation can be decomposed into minimum number of elementary rotations, subject to particular physical constraints, is a fundamental and practical question. Here, we consider two important scenarios. The first one is when rotation axes are allowed to vary in a range of a plane, which corresponds to the Singlet-Triplet (ST) qubit in quantum-dot systems; the second one is when rotation axes can only along two fixed directions, corresponding to the Exchange-Only (EO) qubits. For both scenarios, we provide the criteria for determining the minimal number of pieces and explicit gate construction procedure for each unitary gate. Our results analytically explain the four-gate decomposition of EO qubits, previously determined numerically by Divincenzo et al. Moreover, our approaches can reduce both gate time and gate fidelity dramatically for ST qubits, compared with Ramon sequence and its variant.