Session Q74: Semiconducting Qubits I

The emergence of the strong dispersive regime of circuit quantum electrodynamics with spins

Circuit quantum electrodynamics with spins, or spin-circuit QED for short, is perceived as a platform for scaling up semiconductor spin qubits by enabling long-range interaction between spin qubits and dispersive spin readout.

Here, I will present our latest work on spin-spin coupling through virtual microwave photons, an essential step towards resonator-mediated two-qubit gates. Previous work has demonstrated the coupling of spin qubits resonantly with the superconducting cavity, in the so-called strong coupling regime. While this is a very important first step, it is also not sufficient to allow an entangling two-qubit gate between distant spins. Using a high-impedance resonator to increase the charge-photon and spin-photon coupling, we achieve spin-spin interaction in the dispersive regime, which means that the resonator mode is only virtually populated; it is the regime where two-qubits gates are possible. We also observe photon-number splitting of the spin resonance frequency, an effect by which every resonator photon shifts the qubit frequency by more than its linewidth. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. I will then also present the latest developments on measurements in the time-domain performed on the same sample.

Next, I will introduce our recent work on resolving transitions in the Jaynes-Cummings ladder. We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multi-photon transitions by increasing the probe power and using two-tone spectroscopy.   

Towards an Exchange-Only Compatible Spin-Photon Interface in Si/SiGe

Coherent coupling of spin qubits to microwave photons has in recent years been demonstrated in Si/SiGe teasing the possibility of long-range two-qubit gates [1, 2]. In most demonstrations, spin-photon coupling is engineered by placement of micromagnets on top of the quantum dot gate stack creating an always-on charge-spin hybridization. Gradient magnetic fields, however, are fundamentally incompatible with exchange-only qubit operation as they induce state leakage out of the decoherence-free subsystem. An alternative approach that is compatible with exchange-only operation is to use large simultaneous exchange pulses to create a bias-dependent electric dipole moment in the “XRX” regime [3]. In this talk we discuss the integration and characterization of Single Layer Etch Defined Gate Electrode (SLEDGE) devices, which rely on vias to separate front-end from back-end interconnects, with superconducting microwave resonators using flip-chip bonding [4].

[1] F. Borjans et al. Nature 577 195-198 (2020)

[2] P.H. Collard et al. PRX 12, 021026 (2022)

[3] A. Pan et al. Quantum Sci. Technol. 5, 034005 (2020)

[4] W. Ha et al. Nano Lett. 22, 1443 (2021)   

On-chip filters for high-impedance superconducting resonators in the hybrid cQED device architecture

In hybrid quantum dot (QD)-cQED systems, superconducting microwave resonators are used as mediators for non-local qubit interactions. High-impedance resonators are desirable, as the increased impedance enhances the charge-photon coupling rate and moves the system deeper into the strong spin-photon coupling regime. However, higher impedance can cause significant microwave leakage through the dc bias lines used to form the QDs. On-chip LC filters on each gate line have been shown to improve the quality factor of the high-Z resonator [1,2]. Last year, we reported direct current resistivity measurements and microwave investigations of niobium nitride (NbN) films of different thicknesses. We measured a large kinetic inductance of LK ∼ 41.2 pH/sq and sheet resistance of R_s ~ 274 Ohm/sq for 15 nm NbN thin films. I will summarize our previous findings and introduce the next step to incorporate low-pass LC filters into our current cavity design. We measured the transmission through the filters to evaluate the attenuation of different filter designs. Implementing the LC filters on the QD-cQED chip will suppress microwave leakage through the dc bias lines, resulting in a significant increase in the cavity quality factor.

[1] Mi et al., APL 110, 043502 (2017)

[2] Harvey-Collard et al., PRApplied 14, 034025 (2020)   

Long-distance entangling gates in three-qubit quantum dot spin systems mediated by microwave photons

Attaining quantum dot (QD)-based processors with large number of qubits remains as a major experimental challenge. Recently, long-distance entangling gates between two electronic spins in double QDs mediated by microwave resonators have been developed. While this serves as an important initial step, scaling the systems to qubit numbers larger than two is crucial. We focus on three-qubit—resonator system, a two-electron triple QD coupled to a single-electron double QD via the resonator. We derive an effective Hamiltonian for this system and build protocols for high-fidelity entangling gates. This study paves the way for modular quantum computing using QD arrays with manageable number of qubits and resonators as quantum information busses.

This work is supported by U.S. Army Research Office (Grant No. W911NF-17-0287)

    

Strong coupling between a microwave photon and a singlet-triplet qubit

Spin qubits in semiconuctors are promising contenders for realizing scalable quantum computers because of their small footprint, long coherence times and fast gate operations. However, entangling gates between spin qubits are short range, limiting the scale-up towards larger quantum processors.

In circuit quantum-electrodynamics (QED), on the other hand, superconducting qubits are routinely interconnected with each other exploiting resonators as quantum buses. Implementing circuit QED techniques in the context of spin qubits is challenging and recent advances rely on micromagnets complicating scale-up.

Here, we present a different approach based on intrinsic spin-orbit interaction that is naturally present in zincblende InAs nanowires. Intrinsic spin-orbit interaction leviates the limitations introduced by micromagnets. We utilize a zincblende InAs nanowire in which a double quantum dot (DQD) is defined by epitaxially-grown crystal-phase barriers. The DQD is integrated in a circuit QED architecture featuring a magnetic field-resilient and high quality NbTiN resonator. The resonator is characterized by a large kinetic inductance giving rise to a large impedance of 2 kΩ enhancing the photon-qubit interaction. We investigate the hybrid DQD-resonator system and demonstrate clear indications of a coherent coupling between an electron singlet-triplet qubit and a resonator mode in the single photon limit.   

Spin qubits in photon-coupled microwave cavites

Electron spin qubits in microwave cavities represent a promising foundation for developing quantum computing hardware. Electron spin states have high coherence times compared to gate interaction time scales, and photon coupling allows for long-distance interaction between qubits. The strong spin-photon coupling regime can be realized via the dipole interaction, as Petta et al. [1] demonstrated by placing an electron in a double quantum dot (DQD) with a magnetic field gradient inside a microwave cavity. These studies later included two DQDs inside the cavity to demonstrate long-range spin-spin interactions [2]. Input/output theory describes the system's behavior when driven by an external field and determine the internal qubits states from the transmission amplitude of the output field [3]. Our studies showed that additional qubits inside the cavity render lower transmission amplitudes. As an alternative setup, we analyze results from a model of a double DQD qubit system consisting of two cavities, each containing one qubit, coupled via a photonic waveguide that allows for single photon exchange. In analogy with previous works, we utilize input/output theory to obtain transmission amplitudes and discuss the various regimes determined by tuning different parameters.

    

Fast and high-fidelity dispersive readout of a spin qubit via squeezing

Within the framework of input-output theory, we analyze the dispersive readout of a single spin in a semiconductor double quantum dot coupled to a microwave resonator. We demonstrate fast and high-fidelity readout of semiconductor spin qubits by using squeezed coherent states and nonlinear resonators. We find that for fixed dispersive coupling strength $chi_s$ and leakage rate $kappa$, the presence of squeezing can enhance the signal-to-noise ratio as well as the fidelity of the qubit-state readout, whereas the introduction of nonlinearity into the resonator (e.g., via a SQUID) can substantially speed up the optimal readout time. With current technology ($kappaapprox 2pi imes 3.0:mbox{MHz}$, $chi_sapprox 0.15kappa$), using a squeezed coherent state with $50$ photons and a squeezing parameter $rapprox 3.5$, a readout fidelity $Fapprox 90\%$ is achievable within a readout time $tapprox 200:mbox{ns}$, which is one order of magnitude faster than the optimal readout time ($approx 2:mu$s) without squeezing. Under the same condition, $Fapprox 95\%$ is achievable within a readout time $tapprox 100:mbox{ns}$ with a squeezing parameter $rapprox 6$ and a nonlinear strength $lambdaapprox -0.7kappa$.   

Interplay of Pauli Blockade with Electron-Photon Coupling in Quantum Dots

Both quantum transport measurements in the Pauli blockade regime and microwave cavity transmission measurements are important tools for spin-qubit readout and characterization. In our work [1] we theoretically investigate how a double quantum dot in a transport setup interacts with a coupled microwave resonator while the current through the DQD is rectified by Pauli blockade. We show that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms without additional components such as charge or current sensors for each dot. In the case double quantum dot realized in silicon, we show how the  valley quasi-degeneracy can impose limitations on this scheme. We also demonstrate that a large number of unknown double quantum dot parameters including (but not limited to) the valley splitting can be estimated from the resonator response simultaneous to a transport experiment, providing more detailed knowledge about the microscopic environment of the dots. Furthermore, we describe and quantify a back-action of the resonator photons on the steady state leakage current.

[1] F. Ginzel and G. Burkard, arxiv:2210.02982 (2022)   

Longitudinal coupling to hole spin qubits demonstrated in a silicon fin field-effect transistor

Quantum computers promise exponential speed-up for certain problems. Silicon quantum dot holes spin qubits are prime candidates for scalable quantum computing owing to their small footprint and compatibility with current semiconductor foundry fabrication techniques. The devices used here are silicon fin field-effect transistors (FinFETs) [1] which allow for spin qubit operation above 4K [2].

 

In this work, we investigate the longitudinal coupling of spin qubits to a MW electric field, i.e. an interaction of the form $propto sigma_z V_{MW} cos(omega t)$. This type of interaction has been proposed for efficient spin-resonator coupling for spin readout or long-range two-qubit gates [3,4], due to its many advantages, such as no resonator back-action or temperature resilience. However, since a longitudinally coupled MW field does not induce Rabi oscillations, it is not straightforward to extract the coupling strength. Here, we use a new technique: in a multi-tone experiment the longitudinal coupling renormalizes the Rabi oscillations induced by a transversally coupled electric field. Surprisingly, this effect becomes stronger when detuning the longitudinal driving field from the qubit Larmor frequency. Using the right parameters, the Rabi oscillations originating from the transversal drive can be switched off by the longitudinal driving field. In this condition we can quantify the coupling strength of the spin qubit to a longitudinal field and observe higher harmonics of the Rabi oscillations.

 

[1] Geyer et al., Appl. Phys. Lett. 118, 104004 (2021)

[2] Camenzind et al., Nat Electron 5, 178 (2022)

[3] Bosco et al., Phys. Rev. Lett. 129, 066801 (2022)

[4] Bøttcher et al., Nat Commun 13, 4773 (2022)   

Two-tone electrical drive of spin qubits

Longitudinal coupling of spin qubits to resonators has recently been demonstrated [1]. Theoretically, it had already been proposed as a resource to implement fast two-qubit gates in Si and Ge hole quantum dots [2]. Motivated by recent experiments on Si spin qubits in fin field-effect transistors [3] demonstrating spin qubit operations up to 4 K [4], here we theoretically investigate bimodal electrical microwave driving (transverse and longitudinal) of single spin qubits. The interplay of these drives at differing frequencies gives rise to a wealth of interesting physical phenomena. For instance, the longitudinal modulation induces a gap in the Floquet spectrum of the system, thus making the qubits more robust. We also discuss our findings in light of recent data [5]. Our theoretical description is general and could be applied to both electron and hole quantum dot qubits.

    

Longitudinal coupling used for resonator readout of quantum dot qubits

Superconducting resonators coupled to quantum dot qubits are expected to form key components in scalable quantum computing architectures [1]. Longitudinal coupling mechanisms in these systems can enable quantum-nondemolition readout even when the qubit and resonator frequencies are far apart [2,3]. This type of coupling has only recently been measured in quantum dot qubit devices [4], and its full utility remains undemonstrated. Here, we show resonator readout of a quantum dot hybrid qubit using dynamic longitudinal coupling, which is turned on by applying an ac modulation to the qubit. Good visibility is achieved at qubit-cavity detuning over 10 GHz. This allows measurement of qubit energy splittings, which are confirmed using reservoir tunneling spectroscopy. We assess the readout signal-to-noise ratio and discuss how to maximize its value for qubit operation by tuning the longitudinal coupling strength. Tunability and frequency flexibility are appealing features of dynamic longitudinal coupling, and our work demonstrates its potential as a powerful new technique for semiconductor qubit readout.

[1] N. Holman et al. npj Quantum Inf 7, 137 (2021).

[2] A. J. Kerman. New J Phys 15, 123011 (2013).

[3] R. Ruskov and C. Tahan. Phys Rev B 99, 245306 (2019).

[4] C. G. L. Bøttcher et al. Nat Commun 13, 4773 (2022).   

Remote entanglement by measurement of spin qubits via longitudinal (curvature) couplings to a superconducting resonator

Remote entanglement of spin qubits is an important resource for quantum communications, and quantum simulations. Based on our previous proposals [1,2] we study the feasibility of remote entanglement of spin qubits via joint continuous measurement by a superconducting resonator using longitudinal (curvature) couplings. As examples, we consider (i) double quantum dot (DQD) Singlet-Triplet qubits at the charge degeneracy point and (ii) DQD charge qubits with magnetic field gradient, both relevant to current experiments. The effects of charge dephasing and T1 (Purcell) relaxation as well as effects of measurement asymmetry and local qubit rotations on the entanglement fidelity are considered.

 

[1] R. Ruskov, A.N. Korotkov, Phys. Rev. B 67, 241305(R) (2003); R. Ruskov, A.N. Korotkov, and A. Mizel, Phys. Rev. B 73, 085317 (2006)

[2] R. Ruskov and C. Tahan, Phys. Rev. B 99, 245306 (2019); arXiv: 1704.05876

    

Electric-dipole spin resonance of a flopping mode acceptor-dot hybrid

Strong spin-orbit coupling for holes in silicon gives rise to location and field orientation dependant g-factors. SOC is further enhanced for so-called flopping mode qubits where a single hole is electrically driven between two quantum dots with different g-factors, which converts the electrical drive into an effective magnetic drive in the reference frame of the hole allowing for efficient electric dipole spin resonance (EDSR) to be driven.

In this work, we confine a single hole between a boron atom and a multi-hole quantum dot in a single-gate p-type nanowire transistor. A superconducting off-chip microwave resonator coupled to the gate allows for both readout and EDSR drive. We perform magneto- and two-tone spectroscopy and find the signature of EDSR driven by both photons in the superconducting resonator and the MW tone. We find the EDSR signatures to be strongly field-angle dependant. Our work paves the way for the implementation of an all-electrical qubit in a single industry-standard transistor.