Electron Spin Qubits Research Articles

Coherent control of electron spin qubits in silicon using a global field

Silicon spin qubits promise to leverage the extraordinary progress in silicon nanoelectronic device fabrication over the past half century to deliver large-scale quantum processors. Despite the scalability advantage of using silicon technology, realising a quantum computer with the millions of qubits required to run some of the most demanding quantum algorithms poses several outstanding challenges, including how to control many qubits simultaneously. Recently, compact 3D microwave dielectric resonators were proposed as a way to deliver the magnetic fields for spin qubit control across an entire quantum chip using only a single microwave source. Although spin resonance of individual electrons in the globally applied microwave field was demonstrated, the spins were controlled incoherently. Here we report coherent Rabi oscillations of single electron spin qubits in a planar SiMOS quantum dot device using a global magnetic field generated off-chip. The observation of coherent qubit control driven by a dielectric resonator establishes a credible pathway to achieving large-scale control in a spin-based quantum computer.

RF simulation platform of qubit control using FDSOI technology for quantum computing

In this paper, we report on simulations of an Electron Spin Resonance (ESR) RF control line for semiconductor electron spin qubits. The simulation includes both the ESR line characteristics (geometry and configuration, stack and material properties) and the electromagnetic (EM) environment at the vicinity of the qubits such as gates and interconnect network. With the accurate assessment of the magnetic and electric field distribution, we found that the EM environment of the qubits contributes significantly to the ESR line efficiency for spin control characterized by the magnetic over electric field ratio generated at the qubit location.

Beating the Thermal Limit of Qubit Initialization with a Bayesian Maxwell’s Demon

Fault-tolerant quantum computing requires initializing the quantum register in a well-defined fiducial state. In solid-state systems, this is typically achieved through thermalization to a cold reservoir, such that the initialization fidelity is fundamentally limited by temperature. Here, we present a method of preparing a fiducial quantum state with a confidence beyond the thermal limit. It is based on real time monitoring of the qubit through a negative-result measurement -- the equivalent of a `Maxwell's demon' that triggers the experiment only upon the appearance of a qubit in the lowest-energy state. We experimentally apply it to initialize an electron spin qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%, corresponding to a 20$\times$ reduction in initialization error compared to the unmonitored system. A fidelity approaching 99.9% could be achieved with realistic improvements in the bandwidth of the amplifier chain or by slowing down the rate of electron tunneling from the reservoir. We use a nuclear spin ancilla, measured in quantum nondemolition mode, to prove the value of the electron initialization fidelity far beyond the intrinsic fidelity of the electron readout. However, the method itself does not require an ancilla for its execution, saving the need for additional resources. The quantitative analysis of the initialization fidelity reveals that a simple picture of spin-dependent electron tunneling does not correctly describe the data. Our digital `Maxwell's demon' can be applied to a wide range of quantum systems, with minimal demands on control and detection hardware.

Modelling Conformational Flexibility in a Spectrally Addressable Molecular Multi‐Qubit Model System

AbstractDipolar coupled multi‐spin systems have the potential to be used as molecular qubits. Herein we report the synthesis of a molecular multi‐qubit model system with three individually addressable, weakly interacting, spin centres of differing g‐values. We use pulsed Electron Paramagnetic Resonance (EPR) techniques to characterise and separately address the individual electron spin qubits; CuII, Cr7Ni ring and a nitroxide, to determine the strength of the inter‐qubit dipolar interaction. Orientation selective Relaxation‐Induced Dipolar Modulation Enhancement (os‐RIDME) detecting across the CuII spectrum revealed a strongly correlated CuII‐Cr7Ni ring relationship; detecting on the nitroxide resonance measured both the nitroxide and CuII or nitroxide and Cr7Ni ring correlations, with switchability of the interaction based on differing relaxation dynamics, indicating a handle for implementing EPR‐based quantum information processing (QIP) algorithms.

Modelling Conformational Flexibility in a Spectrally Addressable Molecular Multi-Qubit Model System.

Dipolar coupled multi-spin systems have the potential to be used as molecular qubits. Herein we report the synthesis of a molecular multi-qubit model system with three individually addressable, weakly interacting, spin centres of differing g-values. We use pulsed Electron Paramagnetic Resonance (EPR) techniques to characterise and separately address the individual electron spin qubits; CuII , Cr7 Ni ring and a nitroxide, to determine the strength of the inter-qubit dipolar interaction. Orientation selective Relaxation-Induced Dipolar Modulation Enhancement (os-RIDME) detecting across the CuII spectrum revealed a strongly correlated CuII -Cr7 Ni ring relationship; detecting on the nitroxide resonance measured both the nitroxide and CuII or nitroxide and Cr7 Ni ring correlations, with switchability of the interaction based on differing relaxation dynamics, indicating a handle for implementing EPR-based quantum information processing (QIP) algorithms.

Quantum-Ready Germanium and Silicon

The semiconductor industry knows how to make and integrate billions of excellent transistors. What materials do we need to integrate excellent qubits at large scale for the quantum information age of tomorrow? What are the properties that we search in these materials to make them quantum-ready? I will focus on isotopically-engineered, strained silicon-germanium heterostructures enabling high-performance hole spin-qubits in germanium and electron spin qubits in silicon. In particular, I will make a case for the germanium quantum information route [1]. Germanium is emerging as a versatile material to realize devices capable of encoding, processing and transmitting quantum information. I will examine the materials science progress underpinning germanium-based planar heterostructures, review our most significant experimental results demonstrating key building blocks for quantum technology, and identify the most promising avenues toward scalable quantum information processing in germanium-based systems.[1] G. Scappucci et al, The germanium quantum information route, Nat Rev Mater (2020). https://doi.org/10.1038/s41578-020-00262-z Figure 1

Viewing SiGe Heterostructure for Qubits with Dislocation Theory

SiGe/Si/SiGe heterostructure serves as one of the ideal semiconductor material system to build large scale electron spin qubits[1]. To further push the scalability and extend the coherence times of qubits built on SiGe/Si/SiGe heterostructures, there are several factors to improve, one of that is the lattice homogeneity of strained Si. One source of lattice homogeneity break down are dislocations. Due to the difficulties of high quality SiGe bulk crystal growth [2-3], relaxed SiGe is commonly grown on Si substrates by epitaxy. Viewing the SiGe/Si/SiGe heterostructure on native Si substrate, dislocations half loops form unavoidably because of the misfit between SiGe and the Si substrate. These dislocation half loops consist of threading segments extending through the whole heterostructure (figure 1 (a) and (c)) [4]. Due to the stress caused by the strained Si quantum well layer, the threading dislocations can be driven to glide, resulting in additional misfit segments in the lower interface of strained Si layer when the critical thickness is exceeded (figure 1 (b)) [5]. The extension of these misfit segments is blocked when they meet other perpendicular dislocations (figure 1 (d)) [6]. These misfit dislocations destroy strain uniformity and cause tilt inside the Si layer, resulting in a distortion of the valley splitting and ultimately, reducing the coherence time of qubits [7-8].In this work, we present the observation of dislocations in SiGe/Si/SiGe heterostructures for qubit application by plan-view TEM (Figure 1 (right)). Here, the experimental observations agree with dislocation theory that threading dislocations (some are marked by (b)) will glide and elongate to have misfit segments (some are marked by (c)) in the interface when two requirements are fulfilled: misfit exists between epitaxial layer and substrate; critical thickness is exceeded. When the misfit dislocations meet perpendicular misfit dislocation line, they are blocked since the thickness is not enough to glide over it [6]. This is the case in figure 1 right marked by (d). Due to the misfit segment generation and blocking effects, the misfit dislocation spacing is proportional to the threading dislocation density both theoretically and experimentally. These misfit dislocations bring local strain field around them [9], which disturb the desired homogeneous strain field by misfit. Therefore, misfit dislocation generation needs to be suppressed if one wants to achieve homogeneous strain in Si thin layer in large scale.According to Matthews-Blakeslee theory, one can avoid the formation of misfit dislocations in the Si interface by controlling the strained layer within the critical thickness. The critical thickness of Si on Si0.7Ge0.3 is calculated as 8.5 nm. The Electron channeling contrast images of Si with difference thickness 10 nm and 5 nm grown on high threading dislocation relaxed Si0.7Ge0.3 buffer at 700°C by reduced pressure chemical vapor deposition in Figure 2 are collaborating with theory: obviously misfit dislocation appear in 10 nm Si on relaxed Si0.7Ge0.3 (Figure 2 (left)) and no misfit dislocation are presented in 5 nm Si on Si0.7Ge0.3 (Figure 2 (right)).Our results show that dislocation generation and movement needs to be taken into consideration to further develop SiGe heterostructure based qubits.

Viewing SiGe Heterostructure for Qubits with Dislocation Theory

Strained isotopically enriched 28Si strained layers in SiGe/Si/SiGe heterostrustructures is an excellent material platform for electron spin qubits. In this work, we report the fabrication of 28SiGe/28Si/28SiGe heterostructures for qubit devices by a hybrid MBE/CVD growth, where the thick relaxed SiGe buffer is realized by a reduced-pressure CVD and the 28SiGe/28Si/28SiGe stack is grown by an MBE. Here, we achieve a fully strained 28Si layer in such heterostructure with a 29Si concentration as low as 200 ppm within the MBE grown layers. It was possible to conclude that 29Si primarily originates from the residual natural Si vapour in the MBE chamber. Furthermore, we also present our studies about the growth temperature effect on the misfit dislocation formation in this heterostructure. It was possible to show that at a low MBE growth temperature, such as 350°C, the misfit dislocation formation is significantly suppressed.

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.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates.

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Harnessing many-body spin environment for long coherence storage and high-fidelity single-shot qubit readout

There is a growing interest in hybrid solid-state quantum systems where nuclear spins, interfaced to the electron spin qubit, are used as quantum memory or qubit register. These approaches require long nuclear spin coherence, which until now seemed impossible owing to the disruptive effect of the electron spin. Here we study InGaAs semiconductor quantum dots, demonstrating millisecond-long collective nuclear spin coherence even under inhomogeneous coupling to the electron central spin. We show that the underlying decoherence mechanism is spectral diffusion induced by a fluctuating electron spin. These results provide new understanding of the many-body coherence in central spin systems, required for development of electron-nuclear spin qubits. As a demonstration, we implement a conditional gate that encodes electron spin state onto collective nuclear spin coherence, and use it for a single-shot readout of the electron spin qubit with >99% fidelity.

Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays

We determine the interqubit crosstalk- and charge-noise-induced decoherence time ${T}_{2}^{*}$ for a system of $L$ exchange-coupled electronic spin qubits in arrays of size $L=3$--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that ${T}_{2}^{*}$ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring ${T}_{2}^{*}$. A key finding is that ${T}_{2}^{*}$ decreases with increasing $L$. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.

Anisotropy with respect to the applied magnetic field of spin qubit decoherence times

Electron spin qubits are a promising platform for quantum computation. Environmental noise impedes coherent operations by limiting the qubit relaxation (T1) and dephasing (Tϕ) times. There are multiple sources of such noise, which makes it important to devise experimental techniques that can detect the spatial locations of these sources and determine the type of source. In this paper, we propose that anisotropy in T1 and Tϕ with respect to the direction of the applied magnetic field can reveal much about these aspects of the noise. We investigate the anisotropy patterns of charge noise, evanescent-wave Johnson noise, and hyperfine noise in hypothetical devices. It is necessary to have a rather well-characterized sample to get the maximum benefit from this technique. The general anisotropy patterns are elucidated. We calculate the expected anisotropy for a particular model of a Si/SiGe quantum dot device.

Low Power, Fast and Broadband ESR Quantum Control Using a Stripline Resonator

Using a home-built Ku band ESR spectrometer equipped with an arbitrary waveform generator and a stripline resonator, we implement two types of pulses that would benefit quantum computers: BB1 composite pulse and a microwave frequency comb. Broadband type 1 (BB1) composite pulse is commonly used to combat systematic errors but previous experiments were carried out only on extremely narrow linewidth samples. Using a sample with a linewidth of 9.35 MHz, we demonstrate that BB1 composite pulse is still effective against pulse length errors at a Rabi frequency of 38.46 MHz. The fast control is realized with low microwave power which is required for initialization of electron spin qubits at 0.6 T. We also digitally design and implement a microwave frequency comb to excite multiple spin packets of a different sample. Using this pulse, we demonstrate coherent and well resolved excitations spanning over the entire spectrum of the sample (ranging from -20 to 20 MHz). In anticipation of scaling up to a system with large number of qubits, this approach provides an efficient technique to selectively and simultaneously control multiple qubits defined in the frequency-domain.

Adiabatic dynamical-decoupling-based control of nuclear spin registers

The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins around NV centers in diamond. We obtain a closed-form expression from Landau-Zener theory and show that it reliably describes the dynamics. By identifying robust Floquet states, we show that the technique enables polarization, one-shot flips, and state storage for nuclear spins. These results introduce a control paradigm that combines dynamical decoupling with adiabatic evolution.

Circuit-Based Compact Model of Electron Spin Qubit

Today, an electron spin qubit on silicon appears to be a very promising physical platform for the fabrication of future quantum microprocessors. Thousands of these qubits should be packed together into one single silicon die in order to break the quantum supremacy barrier. Microelectronics engineers are currently leveraging on the current CMOS technology to design the manipulation and read-out electronics as cryogenic integrated circuits. Several of these circuits are RFICs, as VCO, LNA, and mixers. Therefore, the availability of a qubit CAD model plays a central role in the proper design of these cryogenic RFICs. The present paper reports on a circuit-based compact model of an electron spin qubit for CAD applications. The proposed model is described and tested, and the limitations faced are highlighted and discussed.

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.

A silicon singlet–triplet qubit driven by spin-valley coupling

Spin–orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a singlet–triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiments to probe the charge noise power spectrum in a silicon metal-oxide-semiconductor double quantum dot. In addition, we assess qubit frequency drift over longer timescales to capture low-frequency noise. We present the charge noise power spectral density up to 3 MHz, which exhibits a 1/fα dependence consistent with α ~ 0.7, over 9 orders of magnitude in noise frequency.

Precision tomography of a three-qubit donor quantum processor in silicon.

Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

Fast universal quantum gate above the fault-tolerance threshold in silicon.

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction1. One of the most promising error correction codes is the surface code2, which requires universal gate fidelities exceeding an error correction threshold of 99 per cent3. Among the many qubit platforms, only superconducting circuits4, trapped ions5 and nitrogen-vacancy centres in diamond6 have delivered this requirement. Electron spin qubits in silicon7-15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation16. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers.