Semiconductor Spin Research Articles

Simple framework for systematic high-fidelity gate operations

Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, where is the difference in qubit frequencies.

A 2D quantum dot array in planar 28Si/SiGe

Semiconductor spin qubits have gained increasing attention as a possible platform to host a fault-tolerant quantum computer. First demonstrations of spin qubit arrays have been shown in a wide variety of semiconductor materials. The highest performance for spin qubit logic has been realized in silicon, but scaling silicon quantum dot arrays in two dimensions has proven to be challenging. By taking advantage of high-quality heterostructures and carefully designed gate patterns, we are able to form a tunnel coupled 2 × 2 quantum dot array in a 28Si/SiGe heterostructure. We are able to load a single electron in all four quantum dots, thus reaching the (1,1,1,1) charge state. Furthermore, we characterize and control the tunnel coupling between all pairs of dots by measuring polarization lines over a wide range of barrier gate voltages. Tunnel couplings can be tuned from about 30 μeV up to approximately 400 μeV. These experiments provide insightful information on how to design 2D quantum dot arrays and constitute a first step toward the operation of spin qubits in 28Si/SiGe quantum dots in two dimensions.

Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

Piezoelectric Nanocavity Interface for Strong Coupling between a Superconducting Circuit, Phonon, and Spin

We introduce a hybrid tripartite quantum system for strong coupling between a semiconductor spin, a mechanical phonon, and a microwave excitation of a superconducting circuit. Consisting of a piezoelectric resonator with an integrated diamond strain concentrator, this system achieves microwave-acoustic and spin-acoustic coupling rates of approximately megahertz or greater, allowing simultaneous ultrahigh cooperativities (approximately ${10}^{3}$ and approximately ${10}^{2}$, respectively). From finite-element modeling and master-equation simulations, we estimate superconducting-circuit-to-spin quantum state transfer fidelities exceeding 0.95 on the basis of separately demonstrated device parameters. We anticipate that this device will enable hybrid quantum architectures that leverage the advantages of both superconducting circuits and solid-state spins for information processing, memory, and networking.

High-rate entanglement between a semiconductor spin and indistinguishable photons

High-rate entanglement between a semiconductor spin and indistinguishable photons

Layer-dependent optically induced spin polarization in InSe

Optical control of spin in semiconductors has been pioneered using nanostructures of III-V and II-VI semiconductors, but the emergence of two-dimensional van der Waals materials offers an alternative low-dimensional platform for spintronic phenomena. Indium selenide (InSe), a group-III monochalcogenide van der Waals material, has shown promise for opto-electronics due to its high electron mobility, tunable direct bandgap, and quantum transport. There are predictions of spin-dependent optical selection rules suggesting potential for all-optical excitation and control of spin in a two-dimensional layered material. Despite these predictions, layer-dependent optical spin phenomena in InSe have yet to be explored. Here, we present measurements of layer-dependent optical spin dynamics in few-layer and bulk InSe. Polarized photoluminescence reveals layer-dependent optical orientation of spin, thereby demonstrating the optical selection rules in few-layer InSe. Spin dynamics are also studied in many-layer InSe using time-resolved Kerr rotation spectroscopy. By applying out-of-plane and in-plane static magnetic fields for polarized emission measurements and Kerr measurements, respectively, the $g$-factor for InSe was extracted. Further investigations are done by calculating precession values using a $\textbf{k} \cdot \textbf{p}$ model, which is supported by \textit{ab-initio} density functional theory. Comparison of predicted precession rates with experimental measurements highlights the importance of excitonic effects in InSe for understanding spin dynamics. Optical orientation of spin is an important prerequisite for opto-spintronic phenomena and devices, and these first demonstrations of layer-dependent optical excitation of spins in InSe lay the foundation for combining layer-dependent spin properties with advantageous electronic properties found in this material.

Optimal Control of a Cavity-Mediated iSWAP Gate between Silicon Spin Qubits

Semiconductor spin qubits may be coupled through a superconducting cavity to generate an entangling two-qubit gate. However, the fidelity of such an operation will be reduced by a variety of error mechanisms such as charge and magnetic noise, phonons, cavity loss, transitions to nonqubit states, and, for electrons in silicon, excitation into other valley eigenstates. Here, we model the effects of these error sources and the valley degree of freedom on the performance of a cavity-mediated two-qubit $\mathrm{i}$swap gate. For valley splittings inadequately large relative to the interdot tunnel coupling within each qubit, we find that valley excitation may be a limiter to the fidelity of this two-qubit gate. In addition, we show trade-offs between gating times and exposure to various error sources, identifying optimal operating regimes and device improvements that would have the greatest impact on the fidelity of the cavity-mediated spin $\mathrm{i}$swap gate. Importantly, we find that, while the impact of charge noise and phonon relaxation favor operation in the regime where the qubits are most spinlike to reduce sensitivity to these sources of noise, the combination of hyperfine noise and valley physics shifts the optimal regime to chargelike qubits with stronger effective spin-photon coupling so that gate times can be made as short as possible. In this regime, the primary limitation is the need to avoid Landau-Zener transitions as the gate is implemented.

Asymmetric magnetic proximity interactions in MoSe2/CrBr3 van der Waals heterostructures.

Magnetic proximity interactions between atomically thin semiconductors and two-dimensional magnets provide a means to manipulate spin and valley degrees of freedom in non-magnetic monolayers, without using applied magnetic fields1-3. In such van der Waals heterostructures, magnetic proximity interactions originate in the nanometre-scale coupling between spin-dependent electronic wavefunctions in the two materials, and typically their overall effect is regarded as an effective magnetic field acting on the semiconductor monolayer4-8. Here we demonstrate that magnetic proximity interactions in van der Waals heterostructures can in fact be markedly asymmetric. Valley-resolved reflection spectroscopy of MoSe2/CrBr3 van der Waals structures reveals strikingly different energy shifts in the K and K' valleys of the MoSe2 due to ferromagnetism in the CrBr3 layer. Density functional calculations indicate that valley-asymmetric magnetic proximity interactions depend sensitively on the spin-dependent hybridization of overlapping bands and as such are likely a general feature of hybrid van der Waals structures. These studies suggest routes to control specific spin and valley states in monolayer semiconductors9,10.

Probing details of spin-orbit coupling through Pauli spin blockade

Spin-orbit interaction (SOI) plays a fundamental role in many low-dimensional semiconductor and hybrid quantum devices. In the rapidly evolving field of semiconductor spin qubits, SOI is an essential ingredient that can allow for ultrafast qubit control. The exact manifestation of SOI in a given device is, however, often both hard to predict theoretically and probe experimentally. Here, we develop a detailed theoretical connection between the leakage current through a double quantum dot in Pauli spin blockade and the underlying SOI in the system. We present a general analytic expression for the leakage current, which allows to connect experimentally observable features to both the magnitude and orientation of an effective spin-orbit field acting on the moving carriers. Motivated by the large recent interest in hole-based quantum devices, we further zoom in on the case of Pauli blockade of hole spins, assuming a strong transverse confinement potential. In this limit we also find an analytic expression for the current at low external magnetic field, that includes the effect of hyperfine coupling of the hole spins to randomly fluctuating nuclear spin baths. This result can be used to extract information about both hyperfine and spin-orbit coupling parameters for hole spins in devices with a significant fraction of nonzero nuclear spins.

Non-adiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition.

In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Electrically driven spin resonance with bichromatic driving

Electrically driven spin resonance (EDSR) is an established tool for controlling semiconductor spin qubits. Here, we theoretically study a frequency-mixing variant of EDSR, where two driving tones with different drive frequencies are applied, and the resonance condition connects the spin Larmor frequency with the sum of the two drive frequencies. Focusing on flopping-mode operation, we calculate the parameter dependence of the Rabi frequency and the Bloch-Siegert shift. A shared-control spin qubit architecture could benefit from this bichromatic EDSR scheme, as it enables simultaneous single-qubit gates.

A single hole spin with enhanced coherence in natural silicon

Semiconductor spin qubits based on spin–orbit states are responsive to electric field excitations, allowing for practical, fast and potentially scalable qubit control. Spin electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin–orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 μs, exceeding by an order of magnitude existing values reported for hole spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin–orbit coupling in isotopically purified silicon. Our finding enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.

Review of performance metrics of spin qubits in gated semiconducting nanostructures

This Technical Review collects values of selected performance characteristics of semiconductor spin qubits defined in electrically controlled nanostructures. The characteristics are envisioned to serve as a community source for the values of figures of merit with agreed-on definitions allowing the comparison of different spin qubit platforms. We include characteristics on the qubit coherence, speed, fidelity, and the qubit-size of multiqubit devices. The focus is on collecting and curating the values of these characteristics as reported in the literature, rather than on their motivation or significance.

Electron spin coherence on a solid neon surface

A single electron floating on the surface of a condensed noble-gas liquid or solid can act as a spin qubit with ultralong coherence time, thanks to the extraordinary purity of such systems. Previous studies suggest that the electron spin coherence time on a superfluid helium (He) surface can exceed 100 s. In this paper, we present theoretical studies of the electron spin coherence on a solid neon (Ne) surface, motivated by our recent experimental realization of single-electron charge qubit on solid Ne. The major spin decoherence mechanisms investigated include the fluctuating Ne diamagnetic susceptibility due to thermal phonons, the fluctuating thermal current in normal metal electrodes, and the quasi-statically fluctuating nuclear spins of the 21Ne ensemble. We find that at a typical experimental temperature about 10 mK in a fully superconducting device, the electron spin decoherence is dominated by the third mechanism via electron–nuclear spin–spin interaction. For natural Ne with 2700 ppm abundance of 21Ne, the estimated inhomogeneous dephasing time is around 0.16 ms, already better than most semiconductor quantum-dot spin qubits. For commercially available, isotopically purified Ne with 1 ppm of 21Ne, can be 0.43 s. Under the application of Hahn echoes, the coherence time T 2 can be improved to 30 ms for natural Ne and 81 s for purified Ne. Therefore, the single-electron spin qubits on solid Ne can serve as promising new spin qubits.

A Cryo-CMOS Wideband Quadrature Receiver With Frequency Synthesizer for Scalable Multiplexed Readout of Silicon Spin Qubits

In this article, a cryo-CMOS receiver integrated with a frequency synthesizer for scalable multiplexed readout of qubits is presented, focusing on radio frequency (RF) reflectometry readout of silicon-based semiconductor spin qubits/quantum dots. The proposed spin qubit readout chip consists of a wideband low noise amplifier (LNA), a quadrature mixer, a complex filter, a pair of in-phase/quadrature (I/Q) intermediate frequency (IF) amplifier chains, and a type-II charge-pump phase-locked loop (PLL) with a programmable frequency divider providing local oscillator (LO) signals. Noise optimizations are applied to the LNA design and the quadrature active mixer design to obtain the required performance. A mode-switching complementary voltage-controlled oscillator (VCO) is proposed to achieve low-power and low-phase noise in a wide-frequency tuning range (46.5%). Circuit modifications and design considerations for robust cryogenic temperature operation are presented and discussed. Measurements show that the receiver provides an average gain of 65 dB, a minimum noise figure of 0.5 dB, an IF bandwidth of 0.1–1.5 GHz, and an image rejection ratio of 23 dB at 3.5 K with a power consumption of 108 mW. This cryo-CMOS receiver with frequency synthesizer for spin qubit readout is a first step toward fully-integrated qubit readout and control.

Long-lifetime spin excitations near domain walls in 1T-TaS2

SignificanceThere is an intense ongoing search for two-level quantum systems with long lifetimes for applications in quantum communication and computation. Much research has been focused on studying isolated spins in semiconductors or band insulators. Mott insulators provide an interesting alternative platform but have been far less explored. In this work we use a technique capable of resolving individual spins at atomic length scales, to measure the two-level switching of spin states in 1T-TaS2. We find quasi-1D chains of spin-1/2 electrons embedded in 1T-TaS2 which have exceptionally long lifetimes. The discovery of long-lived spin states in a tractable van der Waal material opens doors to using Mott systems in future quantum information applications.

Dissipation and gate timing errors in SWAP operations of qubits

We examine how dissipation and gate timing errors affect the fidelity of a sequence of SWAP gates on a chain of interacting qubits in comparison to noise in the interqubit interaction. Although interqubit interaction noise and gate timing errors are always present in any qubit platform, dissipation is a special case that can arise in multivalley semiconductor spin qubit systems, such as Si-based qubits, where dissipation may be used as a general model for valley leakage. In our Hamiltonian, each qubit is coupled via Heisenberg exchange to every other qubit in the chain, with the strength of the exchange interaction decreasing exponentially with distance between the qubits. Dissipation is modeled through the term $-i\gamma\mathbf{1}$ in the Hamiltonian, and $\gamma$ is chosen so as to be consistent with the experimentally observed intervalley tunneling in Si. We show that randomness in the dissipation parameter should have little to no effect on the SWAP gate fidelity in the currently fabricated Si circuits. We introduce quasistatic noise in the interqubit interaction and random gate timing error and average the fidelities over 10,000 realizations for each set of parameters. The fidelities are then plotted against $J_\text{SWAP}$, the strength of the exchange coupling corresponding to the SWAP gate. We find that dissipation decreases the fidelity of the SWAP operation -- though the effect is small compared to that of the known noise in the interqubit interaction -- and that gate timing error creates an effective optimal value of $J_\text{SWAP}$, beyond which infidelity begins to increase.

Entangling spin and charge degrees of freedom in semiconductor quantum dots

In this theoretical manuscript I propose a scheme for entangling a single electron semiconductor spin qubit with a single electron semiconductor charge qubit in a triangular triple quantum dot configuration. Two out of three quantum dots are used to define a single electron semiconductor charge qubit. Furthermore, the spin qubit is embedded in the Zeeman sub-levels of the third quantum dot. Combining single qubit gates with entangling CNOT gates allows one to construct a SWAP gate, and therefore to use the semiconductor spin qubit as a long-lived memory for the semiconductor charge qubit.

Variability of Electron and Hole Spin Qubits Due to Interface Roughness and Charge Traps

Semiconductor spin qubits may show significant device-to-device variability in the presence of spin-orbit coupling mechanisms. Interface roughness, charge traps, layout or process inhomogeneities indeed shape the real space wave functions, hence the spin properties. It is, therefore, important to understand how reproducible the qubits can be, in order to assess strategies to cope with variability, and to set constraints on the quality of materials and fabrication. Here we model the variability of single qubit properties (Larmor and Rabi frequencies) due to disorder at the Si/SiO$_2$ interface (roughness, charge traps) in metal-oxide-semiconductor devices. We consider both electron qubits (with synthetic spin-orbit coupling fields created by micro-magnets) and hole qubits (with intrinsic spin-orbit coupling). We show that charge traps are much more limiting than interface roughness, and can scatter Rabi frequencies over one order of magnitude. We discuss the implications for the design of spin qubits and for the choice of materials.

Quantum logic with spin qubits crossing the surface code threshold

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to correct errors faster than they occur1. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code2,3. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology4. Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm5. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices.