Excitation and coherent control of spin qudit modes in silicon carbide at room temperature

Quantum error correction of qudits beyond break-even

Hilbert space dimension is a key resource for quantum information processing1,2. Not only is a large overall Hilbert space an essential requirement for quantum error correction, but a large local Hilbert space can also be advantageous for realizing gates and algorithms more efficiently3-7. As a result, there has been considerable experimental effort in recent years to develop quantum computing platforms using qudits (d-dimensional quantum systems with d > 2) as the fundamental unit of quantum information8-19. Just as with qubits, quantum error correction of these qudits will be necessary in the long run, but so far, error correction of logical qudits has not been demonstrated experimentally. Here we report the experimental realization of an error-corrected logical qutrit (d = 3) and ququart (d = 4), which was achieved with the Gottesman-Kitaev-Preskill bosonic code20. Using a reinforcement learning agent21,22, we optimized the Gottesman-Kitaev-Preskill qutrit (ququart) as a ternary (quaternary) quantum memory and achieved beyond break-even error correction with a gain of 1.82 ± 0.03 (1.87 ± 0.03). This work represents a novel way of leveraging the large Hilbert space of a harmonic oscillator to realize hardware-efficient quantum error correction.

Exploring High-Spin Color Centers in Wide Band Gap Semiconductors SiC: A Comprehensive Magnetic Resonance Investigation (EPR and ENDOR Analysis)

High-spin defects (color centers) in wide-gap semiconductors are considered as a basis for the implementation of quantum technologies due to the unique combination of their spin, optical, charge, and coherent properties. A silicon carbide (SiC) crystal can act as a matrix for a wide variety of optically active vacancy-type defects, which manifest themselves as single-photon sources or spin qubits. Among the defects, the nitrogen-vacancy centers (NV) are of particular importance. This paper is devoted to the application of the photoinduced electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques at a high-frequency range (94 GHz) to obtain unique information about the nature and properties of NV defects in SiC crystal of the hexagonal 4H and 6H polytypes. Selective excitation by microwave and radio frequency pulses makes it possible to determine the microscopic structure of the color center, the zero-field splitting constant (D = 1.2-1.3 GHz), the phase coherence time (T2), and the values of hyperfine (≈1.1 MHz) and quadrupole (Cq ≈ 2.45 MHz) interactions and to define the isotropic (a = -1.2 MHz) and anisotropic (b = 10-20 kHz) contributions of the electron-nuclear interaction. The obtained data are essential for the implementation of the NV defects in SiC as quantum registers, enabling the optical initialization of the electron spin to establish spin-photon interfaces. Moreover, the combination of optical, microwave, and radio frequency resonant effects on spin centers within a SiC crystal shows the potential for employing pulse EPR and ENDOR sequences to implement protocols for quantum computing algorithms and gates.

Enhancing the the electrical readout of the spin-dependent recombination current in SiC JFETs for EDMR based magnetometry using a tandem (de-)modulation technique

Electrically detected magnetic resonance (EDMR) is a promising method to readout spins in miniaturized devices utilized as quantum magnetometers. However, the sensitivity has remained challenging. In this study, we present a tandem (de-)modulation technique based on a combination of magnetic field and radio frequency modulation. By enabling higher demodulation frequencies to avoid 1/f-noise, enhancing self-calibration capabilities, and eliminating background signals by 3 orders of magnitude, this technique represents a significant advancement in the field of EDMR-based sensors. This novel approach paves the way for EDMR being the ideal candidate for ultra-sensitive magnetometry at ambient conditions without any optical components, which brings it one step closer to a chip-based quantum sensor for future applications.

Quantum systems in silicon carbide for sensing applications

This paper summarizes recent studies identifying key qubit systems in silicon carbide (SiC) for quantum sensing of magnetic, electric fields, and temperature at the nano and microscale. The properties of colour centres in SiC, that can be used for quantum sensing, are reviewed with a focus on paramagnetic colour centres and their spin Hamiltonians describing Zeeman splitting, Stark effect, and hyperfine interactions. These properties are then mapped onto various methods for their initialization, control, and read-out. We then summarised methods used for a spin and charge state control in various colour centres in SiC. These properties and methods are then described in the context of quantum sensing applications in magnetometry, thermometry, and electrometry. Current state-of-the art sensitivities are compiled and approaches to enhance the sensitivity are proposed. The large variety of methods for control and read-out, combined with the ability to scale this material in integrated photonics chips operating in harsh environments, places SiC at the forefront of future quantum sensing technology based on semiconductors.

Stabilization of spin states of an open system: bichromatic driving of resonance transitions in NV ensembles in diamond

We apply a laser and two nearly degenerate microwave fields upon an ensemble of nitrogen-vacancy centers in diamond and observe magnetic resonance structures with two-component, composite shapes of nested Lorentzians with different widths. One component of them undergoes regular power-broadening, whereas the linewidth of the other one becomes power-independent and undergoes field-induced stabilization. We show that the observed width stabilization is a general phenomenon that results from competition between coherent driving and non-conservation of populations that occur in open systems. The phenomenon is interpreted in terms of specific combinations of state populations that play the role of bright and dark states.

Robust Quantum State Tomography Method for Quantum Sensing

Reliable and efficient reconstruction of pure quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Specifically, the purity of such reconstructed quantum systems is crucial in surpassing the classical shot-noise limit and achieving the Heisenberg limit, regarding the achievable precision in quantum sensing. However, the noisy reconstruction of such resourceful sensing probes limits the quantum advantage in precise quantum sensing. For this, we formulate a pure quantum state reconstruction method through eigenvalue decomposition. We show that the proposed method is robust against the depolarizing noise; it remains unaffected under high strength white noise and achieves quantum state reconstruction accuracy similar to the noiseless case.

Excited State Exchange Control of Photoinduced Electron Spin Polarization in Electronic Ground States

Ground-state electron spin polarization (ESP) is generated in radical elaborated (bpy)Pt(CAT-NN) and (bpy)Pt(CAT-p-Me₂PhMe₂-NN) (bpy = 5,5'-di-tert-butyl-2,2'-bipyridine, CAT = 3-tert-butylcatecholate, p-Ph = para-phenylene, NN = nitronylnitroxide). Photoexcitation produces an exchange-coupled, three-spin, charge-separated doublet ²S₁ (S = chromophore excited spin singlet configuration) excited state that rapidly decays to a ²T₁ (T = chromophore excited spin triplet configuration) excited state. The SQ-bridge-NN bond torsions affect the magnitude of the excited state exchange interaction (J_SQ-NN), which determines the ²T₁-⁴T₁ energy gap. Ground state ESP is dependent on the magnitude of J_SQ-NN, and we postulate that this results from differences in ²T₁ and ⁴T₁ state mixing. Mechanisms that lead to the rapid transfer of the excited state ESP to the ground state are discussed. Although subnanosecond ²T₁ state lifetimes are measured optically in solution, the ground state ESP decays very slowly at 20 K and is observable for more than a millisecond.

Long-lived spin-polarized intermolecular exciplex states in thermally activated delayed fluorescence-based organic light-emitting diodes

Spin-spin interactions in organic light-emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) are pivotal because radiative recombination is largely determined by triplet-to-singlet conversion, also called reverse intersystem crossing (RISC). To explore the underlying process, we apply a spin-resonance spectral hole-burning technique to probe electroluminescence. We find that the triplet exciplex states in OLEDs are highly spin-polarized and show that these states can be decoupled from the heterogeneous nuclear environment as a source of spin dephasing and can even be coherently manipulated on a spin-spin relaxation time scale T₂* of 30 ns. Crucially, we obtain the characteristic triplet exciplex spin-lattice relaxation time T₁ in the range of 50 μs, which far exceeds the RISC time. We conclude that slow spin relaxation rather than RISC is an efficiency-limiting step for intermolecular donor:acceptor systems. Finding TADF emitters with faster spin relaxation will benefit this type of TADF OLEDs.

Acoustically induced coherent spin trapping

Spin centers are promising qubits for quantum technologies. Here, we show that the acoustic manipulation of spin qubits in their electronic excited state provides an approach for coherent spin control inaccessible so far. We demonstrate a giant interaction between the strain field of a surface acoustic wave (SAW) and the excited-state spin of silicon vacancies in silicon carbide, which is about two orders of magnitude stronger than in the ground state. The simultaneous spin driving in the ground and excited states with the same SAW leads to the trapping of the spin along a direction given by the frequency detuning from the corresponding spin resonances. The coherence of the spin-trapped states becomes only limited by relaxation processes intrinsic to the ground state. The coherent acoustic manipulation of spins in the ground and excited state provides new opportunities for efficient on-chip quantum information protocols and coherent sensing.

Chromophore-radical excited state antiferromagnetic exchange controls the sign of photoinduced ground state spin polarization

A change in the sign of the ground-state electron spin polarization (ESP) is reported in complexes where an organic radical (nitronylnitroxide, NN) is covalently attached to a donor-acceptor chromophore via two different meta-phenylene bridges in (bpy)Pt(CAT-m-Ph-NN) (mPh-Pt) and (bpy)Pt(CAT-6-Me-m-Ph-NN) (6-Me-mPh-Pt) (bpy = 5,5'-di-tert-butyl-2,2'-bipyridine, CAT = 3-tert-butylcatecholate, m-Ph = meta-phenylene). These molecules represent a new class of chromophores that can be photoexcited with visible light to produce an initial exchange-coupled, 3-spin (bpy˙-, CAT+˙ = semiquinone (SQ), and NN), charge-separated doublet 2S1 (S = chromophore excited spin singlet configuration) excited state. Following excitation, the 2S1 state rapidly decays to the ground state by magnetic exchange-mediated enhanced internal conversion via the 2T1 (T = chromophore excited spin triplet configuration) state. This process generates emissive ground state ESP in 6-Me-mPh-Pt while for mPh-Pt the ESP is absorptive. It is proposed that the emissive polarization in 6-Me-mPh-Pt results from zero-field splitting induced transitions between the chromophoric 2T1 and 4T1 states, whereas predominant spin-orbit induced transitions between 2T1 and low-energy NN-based states give rise to the absorptive polarization observed for mPh-Pt. The difference in the sign of the ESP for these molecules is consistent with a smaller excited state 2T1 - 4T1 gap for 6-Me-mPh-Pt that derives from steric interactions with the 6-methyl group. These steric interactions reduce the excited state pairwise SQ-NN exchange coupling compared to that in mPh-Pt.

Spin defects in hBN as promising temperature, pressure and magnetic field quantum sensors

Spin defects in solid-state materials are strong candidate systems for quantum information technology and sensing applications. Here we explore in details the recently discovered negatively charged boron vacancies (VB-) in hexagonal boron nitride (hBN) and demonstrate their use as atomic scale sensors for temperature, magnetic fields and externally applied pressure. These applications are possible due to the high-spin triplet ground state and bright spin-dependent photoluminescence of the VB-. Specifically, we find that the frequency shift in optically detected magnetic resonance measurements is not only sensitive to static magnetic fields, but also to temperature and pressure changes which we relate to crystal lattice parameters. We show that spin-rich hBN films are potentially applicable as intrinsic sensors in heterostructures made of functionalized 2D materials.

Metal Ion Control of Photoinduced Electron Spin Polarization in Electronic Ground States

Both the sign and intensity of photoinduced electron spin polarization (ESP) in the electronic ground state doublet (²S₀/D₀) of chromophore-radical complexes can be controlled by changing the nature of the metal ion. The complexes consist of an organic radical (nitronyl nitroxide, NN) covalently attached to a donor-acceptor chromophore via a m-phenylene bridge, (bpy)M(CAT-m-Ph-NN) (1) (bpy = 4,4'-di-tert-butyl-2,2'-bipyridine, M = Pd^II (1-Pd) or Pt^II (1-Pt), CAT = 3-tert-butylcatecholate, m-Ph = meta-phenylene). In both complexes, photoexcitation with visible light produces an initial exchange-coupled, three-spin (bpy^•-, CAT^•+ = semiquinone (SQ), and NN^•), charge-separated doublet ²S₁ (S = chromophore excited spin singlet configuration) excited state that rapidly decays to the ground state via a ²T₁ (T = chromophore excited spin triplet configuration) state. This process is not expected to be spin selective, and only very weak emissive ESP is found for 1-Pd. In contrast, strong absorptive ESP is generated in 1-Pt. It is postulated that zero-field-splitting-induced transitions between the chromophoric ²T₁ and ⁴T₁ states (1-Pd and 1-Pt) and spin-orbit-induced transitions between ²T₁ and NN-based quartet states (1-Pt) account for the differences in polarization.

Room temperature coherent manipulation of single-spin qubits in silicon carbide with a high readout contrast

Spin defects in silicon carbide (SiC) with mature wafer-scale fabrication and micro/nano-processing technologies have recently drawn considerable attention. Although room-temperature single-spin manipulation of colour centres in SiC has been demonstrated, the typically detected contrast is less than 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\%$\end{document}, and the photon count rate is also low. Here, we present the coherent manipulation of single divacancy spins in 4H-SiC with a high readout contrast (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$-30\%$\end{document}) and a high photon count rate (150 kilo counts per second) under ambient conditions, which are competitive with the nitrogen-vacancy centres in diamond. Coupling between a single defect spin and a nearby nuclear spin is also observed. We further provide a theoretical explanation for the high readout contrast by analysing the defect levels and decay paths. Since the high readout contrast is of utmost importance in many applications of quantum technologies, this work might open a new territory for SiC-based quantum devices with many advanced properties of the host material.

Creation of Negatively Charged Boron Vacancies in Hexagonal Boron Nitride Crystal by Electron Irradiation and Mechanism of Inhomogeneous Broadening of Boron Vacancy-Related Spin Resonance Lines

Optically addressable high-spin states (S ≥ 1) of defects in semiconductors are the basis for the development of solid-state quantum technologies. Recently, one such defect has been found in hexagonal boron nitride (hBN) and identified as a negatively charged boron vacancy (VB−). To explore and utilize the properties of this defect, one needs to design a robust way for its creation in an hBN crystal. We investigate the possibility of creating VB− centers in an hBN single crystal by means of irradiation with a high-energy (E = 2 MeV) electron flux. Optical excitation of the irradiated sample induces fluorescence in the near-infrared range together with the electron spin resonance (ESR) spectrum of the triplet centers with a zero-field splitting value of D = 3.6 GHz, manifesting an optically induced population inversion of the ground state spin sublevels. These observations are the signatures of the VB− centers and demonstrate that electron irradiation can be reliably used to create these centers in hBN. Exploration of the VB− spin resonance line shape allowed us to establish the source of the line broadening, which occurs due to the slight deviation in orientation of the two-dimensional B-N atomic plains being exactly parallel relative to each other. The results of the analysis of the broadening mechanism can be used for the crystalline quality control of the 2D materials, using the VB− spin embedded in the hBN as a probe.

Room temperature coherent control of spin defects in hexagonal boron nitride

Optically active spin defects are promising candidates for solid-state quantum information and sensing applications. To use these defects in quantum applications coherent manipulation of their spin state is required. Here, we realize coherent control of ensembles of boron vacancy centers in hexagonal boron nitride (hBN). Specifically, by applying pulsed spin resonance protocols, we measure a spin-lattice relaxation time of 18 microseconds and a spin coherence time of 2 microseconds at room temperature. The spin-lattice relaxation time increases by three orders of magnitude at cryogenic temperature. By applying a method to decouple the spin state from its inhomogeneous nuclear environment the optically detected magnetic resonance linewidth is substantially reduced to several tens of kilohertz. Our results are important for the employment of van der Waals materials for quantum technologies, specifically in the context of high resolution quantum sensing of two-dimensional heterostructures, nanoscale devices, and emerging atomically thin magnets.

Robust and Efficient High-Dimensional Quantum State Tomography

The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterizing the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical, efficient, and robust technique of measuring higher-dimensional quantum states. The achieved fidelities are over 99.9% for qutrits (d=3) and ququints (d=5), and 99.1% for quvigints (d=20)-the highest values ever realized for qudit pure states. We also show excellent performance for mixed states, achieving average fidelities of 96.5% for qutrits. We demonstrate robustness against experimental sources of noise, both statistical and environmental. The technique is applicable to any higher-dimensional system, from a collection of qubits through to individual qudits, and any physical realization, be it photonic, superconducting, ionic, or spin.

Dynamic Polarization of Electron Spins Interacting with Nuclei in Semiconductor Nanostructures

We suggest a new spin orientation mechanism for localized electrons: dynamic electron spin polarization provided by nuclear spin fluctuations. The detrimental effect of nuclear spin fluctuations can be harnessed and employed to provide angular momentum for the electrons via the hyperfine interaction in a weak magnetic field. For this, the sample is illuminated by an unpolarized light, which directly polarizes neither the electrons nor the nuclei. We predict that, for the electrons bound in localized excitons, 100% spin polarization can be reached in longitudinal magnetic fields of a few millitesla. The proof of principle experiment is performed on momentum-indirect excitons in (In,Al)As/AlAs quantum dots, where in a magnetic field of 17 mT the electron spin polarization of 30% is measured.

Anisotropic Spin-Acoustic Resonance in Silicon Carbide at Room Temperature

We report on acoustically driven spin resonances in atomic-scale centers in silicon carbide at room temperature. Specifically, we use a surface acoustic wave cavity to selectively address spin transitions with magnetic quantum number differences of ±1 and ±2 in the absence of external microwave electromagnetic fields. These spin-acoustic resonances reveal a nontrivial dependence on the static magnetic field orientation, which is attributed to the intrinsic symmetry of the acoustic fields combined with the peculiar properties of a half-integer spin system. We develop a microscopic model of the spin-acoustic interaction, which describes our experimental data without fitting parameters. Furthermore, we predict that traveling surface waves lead to a chiral spin-acoustic resonance that changes upon magnetic field inversion. These results establish silicon carbide as a highly promising hybrid platform for on-chip spin-optomechanical quantum control enabling engineered interactions at room temperature.

Coherent Manipulation with Resonant Excitation and Single Emitter Creation of Nitrogen Vacancy Centers in 4H Silicon Carbide

Silicon carbide (SiC) has become a key player in the realization of scalable quantum technologies due to its ability to host optically addressable spin qubits and wafer-size samples. Here, we have demonstrated optically detected magnetic resonance (ODMR) with resonant excitation and clearly identified the ground state energy levels of the NV centers in 4H-SiC. Coherent manipulation of NV centers in SiC has been achieved with Rabi and Ramsey oscillations. Finally, we show the successful generation and characterization of single nitrogen vacancy (NV) center in SiC employing ion implantation. Our results highligh the key role of NV centers in SiC as a potential candidate for quantum information processing.

Uncomputability and complexity of quantum control

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e., there is no algorithm that can decide whether dynamics of an arbitrary quantum system can be manipulated by accessible external interactions (coherent or dissipative) such that a chosen target reaches a desired value. This conclusion holds even for the relaxed requirement of the target only approximately attaining the desired value. These findings do not preclude an algorithmic solvability for a particular class of quantum control problems. Moreover, any quantum control problem can be made algorithmically solvable if the set of accessible interactions (i.e., controls) is rich enough. To arrive at these results, we develop a technique based on establishing the equivalence between quantum control problems and Diophantine equations, which are polynomial equations with integer coefficients and integer unknowns. In addition to proving uncomputability, this technique allows to construct quantum control problems belonging to different complexity classes. In particular, an example of the control problem involving a two-mode coherent field is shown to be NP-hard, contradicting a widely held believe that two-body problems are easy.