# Quantum Information Processing With Integrated Silicon Carbide Photonics

Sridhar Majety 111Corresponding author<EMAIL_ADDRESS>Department of
Electrical and Computer Engineering, University of California, Davis, CA
95616, USA  Pranta Saha  Department of Electrical and Computer Engineering,
University of California, Davis, CA 95616, USA  Victoria A. Norman  Department
of Electrical and Computer Engineering, University of California, Davis, CA
95616, USA  Department of Physics, University of California, Davis, CA 95616,
USA  Marina Radulaski  Department of Electrical and Computer Engineering,
University of California, Davis, CA 95616, USA

## Abstract

Color centers in wide band gap semiconductors are prominent candidates for
solid-state quantum technologies due to their attractive properties including
optical interfacing, long coherence times, spin-photon and spin-spin
entanglement, as well as the potential for scalability. Silicon carbide color
centers integrated into photonic devices span a wide range of applications in
quantum information processing, in a material platform with quantum-grade
wafer availability and advanced processing capabilities. Recent progress in
emitter generation and characterization, nanofabrication, device design, and
quantum optical studies have amplified the scientific interest in this
platform. We provide a conceptual and quantitative analysis of the role of
silicon carbide integrated photonics in three key application areas: quantum
networking, simulation, and computing.

##  1 Introduction

Quantum mechanical effects such as superposition and entanglement open the
doors to novel quantum information processing (QIP) technologies in
communication, computation, sensing, and metrology, that are hard or
impossible to build using conventional classical technologies. Among the
various implementations with superconducting qubits, trapped ions, and neutral
atoms, the solid-state systems with optically addressable spin states (quantum
dots, crystal defects) have shown the most promise in distributed QIP owing to
the ability to create entanglement between the spin degree of freedom and a
photon(s), serving as stationary and flying qubit(s), respectively [1]. Having
photons as couriers of quantum information is beneficial, as they are
unaffected by thermal noise and can travel long distances via fiber-optic
cable without interacting with each other. Flying qubits from separate systems
can be transported to a common location to perform entanglement swapping, thus
creating remote entanglement between systems without their direct interaction.
Moreover, solid-state platforms are scalable and offer a chip-scale
integration.

For the purposes of QIP, one of the primary requirements is the ability of a
single photon emitter (SPE) to generate indistinguishable photons that can be
mutually entangled. There have been notable strides using quantum dots for
this purpose [2, 3], however, the significant variability in the emission
wavelengths (with the quantum dot size, charge, and temperature) has been
challenging to overcome in a scalable fashion. On the other hand, the color
centers, which are point defects in wide bandgap semiconductors that behave
like quasi-atoms, have nearly identical and well reproducible properties.

Color center platforms have not yet realized their full QIP potential. Several
remarkable demonstrations have been made in this regard, such as spin-photon
entanglement [4], remote entanglement of solid-state spins separated by 1.3 km
[1], a multinode quantum network [5], implementation of fault-tolerant
operation of a logical qubit [6], memory-enhanced quantum communication [7],
and a quantum register that uses nine nuclear spins coupled to a single
electron spin, with quantum memory nearing one minute [8]. Most of these
demonstrations were made using the nitrogen-vacancy (NV) center in diamond,
which has defined the color center field that is now populated by a variety of
quantum emitters with complementary or advanced properties.

There are several challenges to overcome in order to scale the experimental
demonstrations to large-scale implementations and to harness the full
potential of quantum technologies. For applications in quantum networks,
further research is required to maximize the collection of emitted photons
into fibers, waveguides, and minimize the optical losses in the fiber-optic
cable and operational errors. The field of quantum computation can be further
boosted by developing quantum memories with long coherence times (few seconds
or higher), high-fidelity single-shot readouts of spin states, and high
fidelity quantum gates. Color centers emerging in diamond and silicon carbide
(SiC) are optically addressable with properties like long spin coherence
times, nearly identical emission wavelengths. These properties coupled with
methods like defect engineering, nanophotonic integration, and better error
correction protocols can overcome some of the existing challenges.

There have been multiple useful review articles on silicon carbide and color
center photonics [9, 10, 11, 12, 13, 14] which guide the reader through the
variety of emitter properties, devices, and techniques. In this perspective
paper, we fill the gap in understanding of the concepts of the next generation
of integrated optical quantum hardware. We believe our perspectives will
inform scientists working on tangential areas of semiconductor defects and
quantum information processing interested in the opportunities in integrated
SiC quantum photonics. We open by discussing quantum optical properties of SiC
color centers and suitability for quantum hardware, followed by a review of
their integration into photonic devices. We then outline three key
applications in quantum networking, simulation, and computing and discuss
their implementation prospects with integrated color center photonics in SiC.

##  2 QIP with color centers in SiC

In this section, we discuss methods for characterizing quantum optical
properties of SiC color centers, review the set of characterized emitters in
the field, and discuss how their properties are suitable for quantum
information processing.

###  2.1 Quantum optical properties of color centers

Color centers create a set of ground and excited states within the bandgap of
the host material and are often approximated as a two or a three level system.
The optical properties of color centers are inspected in a photoluminescence
or a photoluminescence excitation spectroscopy where the emitter is excited by
an above-band or a resonant laser, respectively. The emission spectrum has two
features: a sharp peak called the zero phonon line (ZPL) corresponding to a
fully optical (no-phonon) transition, and a broad phonon sideband (PSB)
involving transitions to the vibronic levels of the ground state. The ratio of
light emitted into the ZPL is called the Debye-Waller Factor (DWF).

Color centers are single photon emitters (SPEs) and as such suitable for
applications in quantum light generation, spin-photon entanglement, and
entanglement distribution. For these applications, it is desired to
characterize the emitter’s single-photon purity, which in ideal case yields a
low probability of multi-photon emission and a high emission rate (brightness)
[15]. An SPE is a non-classical light source with sub-Poissonian statistics
and anti-bunching behavior quantified by the zero-time second-order
autocorrelation function ($g^{(2)}(\tau=0))$, and higher order autocorrelation
functions $g^{(n)}({\tau_{i}})$ [16, 17]. The $g^{(2)}(\tau)$ function values
are measured by the coincidence counts in a Hanbury-Brown-Twiss (HBT)
interferometer. The HBT interferometer takes the signal from an optical mode
and, using a 50:50 beam splitter, separates it into two paths terminated by
single photon detectors with timed difference $\tau$ between detection events.
As such, HBT is a reduced version of the Hong-Ou-Mandel interferometer
(discussed in next paragraph) shown in Figure 1b, where only one emitter is
excited while the other one is left obsolete. If a color center is truly an
SPE (and there is no luminescing background), the detectors will never have an
immediate correlated detection event, yielding $g^{(2)}(\tau=0)=0$. In
practice, however, $g^{(2)}(\tau=0)<0.5$ is used as a confirmation of the
single-photon emission.

Figure 1: a) (top) Schematic of a Hong-Ou Mandel interference setup to measure
the indistinguishability of silicon vacancy in silicon carbide. (bottom) Plot
showing two-photon coincidence counts as a function of time delay between the
arrival of two photons at the superconducting nanowire single photon detectors
(SNSPDs). It can be seen that the coincidence counts at zero delay has
diminished, resulting in a visibility of 90% [18]. Reproduced with permission
from Morioka, et al., Nat Commun 11, 2516 (2020); licensed under a Creative
Commons Attribution (CC BY) license. b) Perspective figure showing a concept
of the on-chip realization of the HOM setup. Single color centers (E1, E2) are
positioned at the center of an asymmetric cavity, resonant with the ZPL of the
emitters. The emission into an asymmetric cavity preferentially propagates to
one side coupling into the waveguide. The HOM interference occurs in the
central region where the waveguide arms propagate in proximity mimicking a
beam-splitter. The coincidence counts are measured using SNSPDs (D1, D2) that
couple evanscently to the waveguide signal.

The coherent emission of color center light is possible through the ZPL, which
presumably emits indistinguishable photons with identical spectral and
temporal profiles. The Hong-Ou-Mandel (HOM) interferometer (Figure 1a) is used
to quantify this property with either subsequently emitted photons from the
same emitter, or photons emitted simultaneously from separate emitters. When
two indistinguishable photons are simultaneously incident on a 50:50 beam
splitter, they undergo bunching. This results in a dip in the coincidence
counts at the output detectors as shown in Figure 1a. The degree of
indistinguishability of the photons is quantified by the HOM visibility,
determined by the depth of the dip in the coincidence counts. In a recent
experiment with silicon vacancy [18], the measured visibility was $V=0.85$,
which compares well to $V=0.90(6)$ obtained in diamond for quantum networking
applications [1].

With advances in SiC material processing, an on-chip HOM interferometer, as
shown in Figure 1b, could be fabricated. The illustrated setup has three
different regions, the cavities with color centers, the waveguide beam
splitter, and the superconducting nanowire single photon detectors (SNSPDs).
First, the ZPL emission from each of the color centers (E1, E2) is enhanced in
the cavity and coupled into a waveguide [19]. Second, the waveguides are laid
out in close proximity to create coupling of optical modes. This region
performs the function of a beam splitter. Third, the photons in each waveguide
are detected using an SNSPD integrated on top of SiC [20, 21]. SNSPDs offer
advantages like high detection efficiency, low dark count rates, and low
jitter over a broad wavelength range [22, 23, 24]. When two indistinguishable
photons in each of the waveguides arrive simultaneously to the beam splitter
region, they undergo bunching and are to be detected only at one of the two
detectors (D1, D2).

The coherence of a quantum system is susceptible to dephasing due to the
thermal fluctuations in the environment, proximity to electron and nuclear
spins, and population relaxation. The rate of dephasing of the state of a
quantum system (spin) is determined by the coherence time, during which the
quantum system can be reliably manipulated and measured. Systems with long
coherence times would allow for the application of more quantum operations,
required to build large scale quantum systems with hundreds of qubits [25].
For typical spin-based two-qubit quantum gates which have a predicted gate
operation time of $\sim 500$ ns [26], to perform 100,000 gate operations on
the quantum state, needed for the implementation of quantum error correction
[27], a coherence time of the order of 50 ms is required. The effect of
dephasing mechanisms can be minimized using techniques like isotopic
purification and dynamical decoupling. Another option to extend coherence
times is using gate operations to transfer the electron spin onto a nuclear
spin memory [28, 8].

In addition to the long spin coherence that allows for complex manipulations,
the quantum gates should also reach high fidelities. Recent demonstrations in
divacancy centers [29] achieve 99.984% single-qubit gate fidelity, entangling
CNOT gate fidelity of 99% and entangled state generation fidelity of 81%. In a
recent silicon vacancy study [30], the projected values for the single-qubit X
gate and the Bell state preparation fidelities are 97% and 94% respectively.
For comparison, Bell state violation experiments in diamond used systems with
fidelities for Bell state preparation of 92% and X gate of 99.8%. The quantum
repeater proposals [31] target fidelity of 95% for Bell state creation. This
shows that silicon carbide divacancy and silicon vacancy centers are
approaching the performance suitable for quantum networks.

###  2.2 Color centers in SiC

In this section, we discuss the color centers in the most common polytypes of
SiC i.e., 3C-SiC (cubic lattice), 4H- and 6H-SiC (hexagonal lattice). SiC
hosts a variety of color centers like divacancy, silicon vacancy, nitrogen
vacancy, and transition metal defects (chromium, vanadium, molybdenum,
tungsten) with emission wavelengths in the near infrared region as shown in
Figure 2. Each defect in the lattice can exist in multiple orientations due to
the presence of inequivalent lattice sites: hexagonal-like (h) and cubic-like
(k). The defects in SiC exist naturally in as-grown material or can be in situ
doped during the crystal growth process. However, most of the studied color
centers are generated through implantation where projectiles (electrons,
protons, neutrons, ions) with sufficient energy are penetrated through the
material surface. The implantation is followed by annealing in vacuum or inert
atmosphere to activate the implants. This also helps repair the crystal
lattice damage caused during implantation, though not completely [32]. The
residual damage can create pathways for decoherence of the electron spin,
which is a disadvantage while building QIP hardware. This can partly be
overcome by using lighter projectiles like electrons, protons (over heavier
ions) on in situ doped substrates or using low energy ions to create shallow
defects followed by growth of an high-quality epitaxial layer [33, 34].

The neutral divacancy defect (VSiVC0) in SiC consists of a pair of neighboring
silicon and carbon vacancies. The different possible orientations for each of
the vacancies in 4H-SiC result in the photoluminescence of the divacancy to
have six sharp lines (PL1-PL6) in the wavelength range of 1100 nm (PL1, PL2 -
axial divacancies and PL3, PL4 - basal divacancies) [35]. Divacancy is a
spin-1 system (like diamond NV center), but has advantageous properties like
DWF of 5% [36], highly-spin dependent optical fine structure (high-fidelity
initialization and single shot readout) [37], and spin-coherence time of up to
5 seconds[38]. At the emission wavelengths of the divacancies, the fidelity of
quantum frequency conversion to a telecommunications band is higher than for
NV centers in diamond [39].

Figure 2: Emission wavelengths of color centers in 4H-SiC on the
electromagnetic spectrum.

The negatively charged silicon vacancy (VSi${}^{{}^{-}}$) in SiC is formed at
the site of a missing Si atom in the lattice and is a spin-3/2 defect. In
4H-SiC, VSi${}^{{}^{-}}$ has two inequivalent lattice sites (h, k), resulting
in emission spectrum consisting of two ZPLs i.e., V1 (861.6 nm) and V2 (916.5
nm) [40, 41]. Similarly in 6H-SiC, VSi${}^{{}^{-}}$ has three inequivalent
lattice sites (h, k1, k2) leading to an emission spectrum with three ZPLs
i.e., V1 (864.7 nm), V2 (886.3 nm) and V3 (907.1 nm) [40, 41]. The
h-VSi${}^{{}^{-}}$ (V1 center) in 4H-SiC which has 8% of emission into the ZPL
at 4K [42] and millisecond spin coherence times (under dynamical decoupling)
[43, 44] provides avenues for high-fidelity spin-photon entanglement [18] and
deterministic spin initialization [45, 46]. VSi${}^{{}^{-}}$ is well-suited
for photonic integration due to its single spin orientation along the c-axis
for all inequivalent lattice sites [40, 47], which is necessary for their
deterministic orientation in devices. Moreover, the optical transitions in
h-VSi${}^{{}^{-}}$ are decoupled from charge fluctuations [48] resulting in
low spectral diffusion in an emitter ensemble [49] and making it robust to
surface charge fluctuations in nanofabricated devices.

The negatively charged nitrogen vacancy (NCVSi${}^{{}^{-}}$) in SiC consists
of a substitutional nitrogen atom at a carbon site adjacent to a silicon
vacancy. The emission has multiple ZPLs corresponding to the inequivalent
lattice sites with emission wavelengths close to the telecommunications range,
making it suitable for low-loss fiber transmission [50, 51, 52, 53]. A recent
study has identified the emission wavelength of NV center in 3C-SiC at 1289 nm
[54] correcting the previously reported value of 1468 nm [52]. Coherent
control of NV spins at room temperature [55], robust photon purity, and
photostability of single NV centers at elevated temperatures [56] have been
demonstrated. The possibility of coupling electron spin of NV-center to the
nuclear spin of the substitutional nitrogen should be studied for quantum
memory applications.

Other promising but less explored color centers in SiC are transition metal
defects like chromium ion (Cr4+) [57, 58, 59], vanadium ion (V4+) [60, 61],
molybdenum ion (Mo5+) [62, 63, 64], tungsten ion (W5+) [65] and erbium ion
(Er3+) [66, 67]. Some of these impurities have high DWF (Cr4+ \- 73%, V4+ \-
22% (h), 39% (k)) suited for generating indistinguishable photons. Since the
transition metals are not among the naturally occurring impurities in SiC,
they are generated either by doping during the crystal growth or ion
implantation on the wafer.

###  2.3 Motivation for QIP implementations as a SiC platform

After the earliest demonstration of NV center in diamond as a quantum system
that can be individually initialized, manipulated and measured with high
fidelity at room temperature [68], this spin-1 emitter has been the candidate
for majority of the important demonstrations in the field of QIP. Despite
being the traditionally most widely studied color center, diamond NV has
several shortcomings including a low DWF of 3% [69, 70] that prevents
achieving high entanglement rates, unavailability of single-crystal diamond
wafers, emission wavelength far outside the telecommunication wavelength range
(637 nm), and large spectral shifts caused by fluctuations of charges in its
surrounding [71]. The spectral shifts are further pronounced by proximity to
surfaces [72], which makes this emitter challenging for efficient nanophotonic
integration. It is worth noting that quantum frequency conversion of NV center
emission to telecommunication wavelengths with preserved spin-photon
entanglement is possible [73]. Other color centers explored in diamond, group-
IV color centers: silicon vacancy [74, 75], germanium vacancy [76], tin
vacancy [77, 78] and lead vacancy [79] have higher DWF and better optical
stability, however, their emission wavelengths are far from the
telecommunication bands and they have not yet demonstrated long coherence
times except at mK temperatures [74, 76].

Silicon carbide hosts a variety of color centers [80, 10] with long spin
coherence times [81, 82, 83], excellent brightness [84] and manipulations of
nuclear spin [85, 86]. SiC offers benefits like large bandgap, high thermal
conductivity, and strong second-order nonlinearity. It also hosts color
centers at infra-red wavelengths and is available in several polytypes
(3C-SiC, 4H-SiC, 6H-SiC) offering flexibility in terms of material properties
and color center configurations. Due to its decades-long industry presence,
SiC is available as high-quality single crystal wafers, has mature
nanofabrication processes, and is CMOS process compatible. Most importantly,
SiC color centers have longer spin coherence times than the ones in the
naturally occurring diamond [83, 87] and on par with isotopically purified
diamond.

##  3 Integration with photonics

Color center properties are sensitive to its environment (neighboring crystal
defects, nuclear spins, surface related charges, and coupling to phonons)
which poses a challenge to their naturally available forms in achieving
theoretically calculated spin-optical properties. In this section, we will
look into different approaches to mitigate the influence of environment on the
color center properties through material engineering and integration with
nanophotonics, to achieve improved spin-optical characteristics (more
indistinguishable photons, efficient optical initialization of spin, longer
coherence times, on-chip integration and scalability) and better spin-photon
interfaces for applications in QIP.

###  3.1 Isotopic Purification

Naturally available SiC has 1.1% 13C and 4.7% 29Si atoms, both with a nuclear
spin of I = 1/2. The electron spin of the color centers and the nuclear spins
have an always-on hyperfine interaction. This interaction can be used to
transfer and store the electron spin state in a nuclear spin [88] (quantum
memory), which has a long coherence time, on the order of a few seconds,
necessary for QIP applications like error correction and entanglement
purification. But, the electron spin immersed in the nuclear spin bath
experiences decoherence due to fluctuating nuclear spins, that results in a
nuclear spin decoherence of the nearby nuclear spin. This issue can be
addressed using isotopic purification, which is the careful engineering of the
nuclear environment of the color centers. A detailed study of the optimal
nuclear spin concentration for maximum usable nuclear memories was done [29].
Isotopically purified SiC [89] was used to demonstrate millisecond electron
spin coherence times [83, 18, 29, 46], coupling to single nuclear spin with 1
kHz resolution [46], and high-fidelity electron spin control (99.984%) [29].

###  3.2 Passive and active photonic devices

To build a large quantum network with photon-based entanglement distribution,
an important criterion is the availability of network nodes with efficient
spin-photon interfaces. This can be achieved by efficiently collecting the
photons emitted by a color center in the bulk and by enhancing the proportion
of photons emitted into the ZPL. Passive devices couple light into an optical
mode to improve collection efficiencies and low-loss guiding of the photons.
Active devices improve the spontaneous emission rates of the color centers.

Color center emission in a high refractive index bulk is directed based on its
dipole orientation, and when a fraction of this emission reaches the bulk-air
interface, it undergoes total internal reflection, resulting in low collection
efficiencies of the emitted photons. The most implemented approach for
improving collection efficiencies is fabricating a solid immersion lens (SIL)
on top of the color center, this ensures that the color center emission has a
normal incidence at the bulk-air interface. SIL fabricated in SiC on top of a
silicon vacancy [81, 90] demonstrated collection enhancements up to 3.4 times.
Similar enhancements were achieved using scalable nanopillars with integrated
silicon vacancies [91, 92] and erbium color centers [67]. The collection
efficiencies can be further enhanced by deterministic emitter positioning
within these devices. Nanofabricated waveguides can be used for coupling color
center emission into well-defined modes, to be routed on a chip in a nearly
lossless way. High-coherence spin-optical properties of silicon vacancy
integrated into SiC waveguides was demonstrated recently [30]. The emission in
the waveguide mode can be coupled into a fiber for off-chip processing using
free space grating couplers [93] and tapered fiber couplers [94] that were
fabricated in diamond and yet to be developed for SiC.

Active devices like photonic crystal cavities (PCC) create light-matter
interaction by confining light to sub-wavelength volumes, resulting in an
increased density of states at the resonant wavelength of the cavity. When the
ZPL wavelength of the color center is resonant with the cavity, the
spontaneous emission rate of the color center is enhanced through Purcell
effect. The enhancement in radiative emission is given by Purcell factor (FP):

$F_{P}=\left[\frac{3}{4\pi^{2}}\bigg{(}\frac{\lambda}{n}\bigg{)}^{3}\bigg{(}\frac{Q}{V}\bigg{)}\right]\left[\left|\frac{E}{E_{\textnormal{max}}}\right|\cos(\phi)\right]\xi$

FP can be maximized by integrating a color center into a cavity with high
quality factor (Q) and low cavity mode volume (V). FP can be further boosted
by optimally positioning the emitter inside the cavity, which corresponds to
the spatial overlap ($\left|E/E_{\textnormal{max}}\right|\cos(\phi)$) term in
the equation. It should be noted from the equation above that the Q/V value
required to achieve the same FP value for different color centers depends on
the DWF of the color center ($\xi$). Several cavity geometries like 1D
nanobeam PCC [95, 36, 92], 2D PCC [96, 97, 98], microdisk resonator [99, 100],
triangular cross-section nanobeams [101] were fabricated in SiC, as shown in
Figure 3 (right). Silicon vacancy [92, 95], neutral divacancy [36], and Ky5
color centers [102, 103] coupled to SiC cavities demonstrated Purcell factors
of up to $F_{P}=120$.

Figure 3: The SEM images of silicon carbide photonic devices. Passive devices
(clockwise from top left): Triangular cross-section waveguide in 4H-SiC with
integrated silicon vacancies (Reproduced with permission from Nat. Mater. 21,
67–73 (2022). Copyright 2021, Springer Nature.), nanopillars in 4H-SiC with
silicon vacancies (Reproduced with permission from Nano Lett. 17(3), 1782–1786
(2017). Copyright 2017, American Chemical Society.), vertical coupler
fabricated in 4H-SiCOI to convert free-space Gaussian beam into fundamental
waveguide mode (Reproduced with permission from Optica 7, 1139-1142 (2020).);
Active Devices: Suspended nanobeam array fabricated in 4H-SiCOI and (below)
magnified image of individual nanobeam PCC with integrated silicon vacancies
(Reproduced with permission from Nat. Photonics 14, 330–334 (2020). Copyright
2019, Springer Nature.), nanobeam PCC in 4H-SiC with integrated neutral
divacancies (Reproduced with permission from Nano Lett. 20 (5), 3427–3434
(2020). Copyright 2020, American Chemical Society.), triangular cross-section
nanobeam PCC fabricated in 4H-SiC [101] (Reproduced from Appl. Phys. Lett.
113, 231106 (2018), with the permission of AIP Publishing.).

Purcell factor considers only the radiative emission resonant with the cavity,
which might not be the only path for the emitter to decay from the excited
state. Other pathways like non-radiative decay, emission into the phonon
sideband, and pure dephasing might exist. Cooperativity (C) is the ratio of
radiative emission rate through the cavity to the total decay rate of the
emitter in the absence of the cavity [104, 105]. Although the spontaneous
emission is enhanced through Purcell effect (FP $>$ 1), the emission through
the cavity can still be smaller compared to the overall emission - weak
coupling regime (C $<$ 1). To achieve deterministic atom-photon interactions,
the coupling between the cavity and emitter should be stronger than all the
other dephasing mechanisms - strong coupling regime (C $>$ 1) [106, 105].
Further, emitter ensembles in a cavity with collective coupling rates to the
cavity resonant mode comparable to the inhomogeneous broadening exhibit longer
storage times, apt for quantum memory applications [107].

Putting these concepts into the context of QIP, to reach 99% coherent emission
(through the ZPL) of a color center with DWF of 5% and fully optical
recombination (no non-radiative recombination channels), the emission would
need to be Purcell enhanced by a factor $F_{P}\sim 2,000$. To achieve this in
a representative nanocavity with a cubic wavelength mode volume
$V=(\lambda/n)^{3}$ would require a quality factor of $Q\sim 5\times 10^{5}$.
Assuming now that there is a non-radiative decay channel with three times the
rate of the radiative recombination, the nanocavity would need to achieve
$F_{P}\sim 8,000$ and $Q\sim 2\times 10^{6}$. Related calculations for color
centers in SiC are reported in Table 1. Q-factors up to $6.3\times 10^{5}$
[98] have already been achieved in SiC nanocavities without emitters. Thus,
there needs to be more research focus on color center integration into the SiC
nanocavities.

Defect | ZPL | DWF | $T_{2}$ | Fiber loss | Propagation length in fiber (km) | Target Q-factor for $V=(\lambda/n)^{3}$
---|---|---|---|---|---|---
| (nm) |  | (ms) | (dB/km) | before 1/e loss | during $T_{2}$ | radiative decay only | 3:1 non-rad.:rad. decay
NV${}^{{}^{-}}$(diamond) | 637 | 3% | 1.8 | 10 | 0.4 | 374 | $1.4\times 10^{6}$ | $5.8\times 10^{6}$
VSi${}^{{}^{-}}$(4H-SiC) | 861-917 | 6-9% | 20 | 1.5 | 2.9 | 4,160 | $(0.15-0.34)\times 10^{6}$ | $(0.6-1.4)\times 10^{6}$
VSiVC0(4H-SiC) | 1078-1132 | 5% | 5300 | 0.8 | 5.4 | $1.1\times 10^{6}$ | $0.5\times 10^{6}$ | $2.1\times 10^{6}$
NCVSi${}^{{}^{-}}$(4H-SiC) | 1176-1242 | 5% (3C) | 0.017 | 0.6 | 7.2 | 3.53 | $0.5\times 10^{6}$ | $2.1\times 10^{6}$

Table 1: Emission parameters for NV center in diamond, and silicon vacancy
(VSi${}^{{}^{-}}$), divacancy (VSiVC0), and nitrogen vacancy
(NCVSi${}^{{}^{-}}$) in 4H-SiC. $T_{2}$ is the electron spin-coherence time.
The highest measured electron spin-coherence times[108, 44, 38, 55] and
DWF[70, 42, 36, 54] are presented. The distance covered by the photon during
$T_{2}$ is calculated by assuming a constant speed of light in the fiber
(refractive index = 1.44) at all wavelengths. The target Q-factors to achieve
99% emission through the ZPL are calculated for a cavity with mode volume of
$(\lambda/n)^{3}$ for cases of purely radiative recombination and 3:1 non-
radiative to radiative decay ratio.

###  3.3 Nanofabrication Methods

To build scalable QIP technologies, photonic devices need to be fabricated in
a repeatable manner on chip-scale. Despite the mature nanofabrication
processes in SiC, the substrate is chemically inert and difficult to etch
through wet-etching methods. Dry etching methods [109, 110, 111] used to
fabricate photonic devices in SiC were not able to achieve simulated ultra-
high values of Q-factor due to fabrication errors (misalignment of features),
surface roughness (low Q-factor), and imperfect emitter positioning in the
cavity (poor coupling between cavity and emitter). Surface passivation using
epitaxial AlN was used to improve the photostability, charge state stability,
and enhance the emission of carbon anti-site vacancy in 4H-SiC [112].

Integration of color center photonics with other platforms starts with
heteroepitaxially grown high quality single crystal thin films on silicon and
silicon dioxide. The low temperature phase, 3C-SiC, which readily grows on
silicon substrates was used to fabricate photonic devices [113, 97, 114]. But,
these 3C-SiC thin films had high densities of crystal defects due to the
lattice mismatch with Si, resulting in large material absorption and
degradation in color center optical properties [103]. Smart-cut method used to
create SiC-on-insulator (SiCOI) [115] is not suitable for color center
photonics as the SiC layer suffered from implantation damages that are
irreparable through annealing at elevated temperatures. Recently, 4H-SiCOI was
produced by wafer bonding 4H-SiC on insulator (silicon dioxide) followed by
grinding and polishing the SiC to obtain high-quality thin films suitable for
fabricating high performing photonic devices and color center integration
[92]. While successful in generating high-quality individual devices, this
process faces challenges in achieving uniform film thickness through polishing
on a wafer-scale.

Underetching of photonic structures which creates optical isolation and
prevents mode leakage into the bulk was used to demonstrate PCC with high
Q-factor ($>10^{4}$). Dopant selective photoelectrochemical etch [116] was
used to fabricate 1D nanobeam PCC with Purcell enhancement up to 80 times [95,
36]. But, this method is limited due to the requirement of specific doping
profiles in SiC. Angled etching is another underetching method first
demonstrated in diamond [117] and later demonstrated in SiC [101, 30]. The
triangular cross-sections resulting from the angled etching in SiC was
achieved using Faraday cage method and can be done at wafer scale using ion
beam etching methods used in diamond [118].

Nanofabrication process variability results in deviation of the cavity’s
resonant wavelength designed to match the ZPL wavelength of the color center.
The cavity can be tuned into resonance by condensing gas on the devices [119,
120] and effectively reversed by heating the chip. For a much more precise and
fast tuning, the emitter can be tuned into resonance with the cavity using DC
Stark effect [121, 122, 123, 124] and strain fields [125, 126]. Both these
methods can be used to tune spatially separated emitters into mutual resonance
necessary for remote entanglement. Despite advanced fabrication processes and
high crystal quality, the emitters experience spectral diffusion (broadening
of optical linewidths) due to charge fluctuations in the local environment
caused by surface charges, and distribution of emitters which capture and
release charges. Strain generated during growth and nanofabrication of
photonic devices also contributes to the degradation of optical linewidths.
But this spectral diffusion/instability is an extrinsic property that can be
solved either by integrating charge depletion using advanced doping epitaxy or
by optimized optical excitation via time-dependent drive or optimized steady-
state illumination [14]. The charge state of the emitters were successfully
controlled through optical illumination [127] and integration of emitters into
Schottky barrier diodes [124]. Emitters integrated into the depletion region
of a p-i-n diode enabled deterministic control over the charge state of the
emitter [128, 121] and electrical readout of the spin state [129]. Optimal
emitter distribution can be achieved using more controllable defect generation
methods like focused ion beam [130], laser writing [131, 132], proton beam
writing [133], and ion implantation on patterned substrates [134].

###  3.4 External fields

Upon addressing the inhomogeneities in the color center environment through
isotopic purification and integration into electronic and photonic devices,
the single photon emission of a color center can be tuned by a direct
application of an external interaction such as electric field, magnetic field,
mechanical strain, and acoustic fields [25, 13]. The energy levels of the
color center are sensitive to the applied external field, causing a split or
shift of the ground and/or excited states (tuning). For QIP applications, the
tuning achieved by the application of electric or strain fields should be
larger than the inhomogeneous broadening ($\sim 10$ GHz for VSi${}^{{}^{-}}$
[30]), before the material experiences any dielectric or mechanical failure
[25].

The splitting and shifting of energy levels due to an electric and magnetic
field are called the Stark and Zeeman effect. Electric fields have been used
to tune the ZPL of silicon vacancy [124, 122] and divacancy [121, 123] in
4H-SiC by up to 60 GHz and 800 GHz, respectively. In another take, a magnetic
field applied along the c-axis of 4H-SiC was used to suppress the parasitic
spin mixing of silicon vacancy, to achieve controlled generation of
indistinguishable photons [18]. Strain that is applied externally or formed
intrinsically during crystal growth can result in tuning of the emission
wavelength of color centers. Moreover, the density-functional theory predicts
that silicon vacancy [42] and divacancy [135, 136] in SiC produce larger ZPL
shifts under strain fields than electric fields [124, 122, 121, 123]. Silicon
vacancy in 6H-SiC has been shown to exhibit strain-induced ZPL shifts up to 6
THz [137, 138]. In an engineered acoustic device, the coupling of spin to
strain was demonstrated for divacancy in SiC [139]. This shows that the
engineering toolbox has multiple methods to counter the inhomogeneous
broadening of color center emission at or beyond the required magnitudes.

##  4 Quantum Information Hardware Applications

In this section, we discuss methods of employing color centers for
applications in quantum networking, simulation, and computing.

###  4.1 Quantum Repeaters

In classical communication, the loss experienced by the signal (photons)
propagating in the fiber is compensated through its amplification at
intermediate points in the channel, thus enabling long-distance communication.
In the quantum domain, communication over long distances cannot be implemented
in such a fashion due to the consequences of the no-cloning theorem. In
addition to the fiber losses (which scale exponentially with distance between
entangled links), the photons in the quantum communication channel also
experience depolarization losses. A long range entanglement can be generated
using quantum repeater (QR) schemes which involve dividing the communication
channel into smaller segments connected by the QR stations, followed by
establishing entanglement between the ends of each of the segments. Then, the
desired long range entanglement is generated by performing entanglement
swapping of the entangled states of each segment.

The QR stations are designed to perform some (or all) of the following three
tasks: heralded entanglement generation (HEG) for correcting loss errors,
heralded entanglement purification (HEP) to correct for operation errors (from
measurements and gate operations), and entanglement swapping to extend the
entanglement. Entanglement (HEG) is generated between color centers in two
remote QR stations by first creating spin-photon entanglement locally,
followed by interference of the photons on a beam splitter to create spin-spin
entanglement [86, 29, 140], as shown in Figure 4. HEP using color centers
begins with swapping a low-fidelity electron spin-spin entanglement onto
nuclear spins (memory qubits), followed by another cycle of HEG (low-
fidelity), and finally local gate operations are performed on the electron and
nuclear spin in each QR station to generate a higher fidelity entanglement
link [141, 142].

The heralding involves two-way signaling between QR stations to verify the
success of entanglement/purification, which requires long-lived quantum
memories [143] and determines the achievable communication rates. Instead,
quantum error correction (QEC) can be used to overcome the loss and operation
errors deterministically, requiring one-way signaling. Depending on the
approach for overcoming losses, quantum repeaters can be classified into three
generations, each offering improved communication rates over implementations
without quantum repeaters, which follows an inverse exponential scaling with
the total distance between the ends of the network.

The first generation QRs overcomes loss and operation errors through HEG and
HEP respectively. The communication rate (1 Hz range) is limited by the two-
way signaling and would require quantum memories with milliseconds or higher
coherence times for longer distances (> 1000 km), even for optimized protocols
[144]. The second generation QRs, like the first one, overcomes loss through
HEG but uses QEC on encoded qubits[31, 145, 6] to rectify operation errors.
The communication rate (kHz range) depends on the time needed for two-way
signaling between adjacent QR stations and local gate operations, relaxing the
long coherence time requirement for memory qubits. The third generation QRs
uses QEC for overcoming both loss and operation errors [146, 147, 148]. Since
two-way signaling is not involved in this generation, the communication rates
depend on the local gate operation times, achieving rates (MHz) close to the
classical repeaters. However, this generation suffers from low tolerance to
matter-photon coupling losses ($\lesssim$ 10%) even with hundreds of qubits
per repeater station [148].

The successful implementation of the different QR generations depends on the
various parameters of the technological building blocks in their architecture.
This includes the fidelity and operation time of the gates performing local
operations, as well as the coupling efficiency (emission of photons from
matter qubits, coupling of photons into the fiber, coupling between photons
and matter qubits, detection efficiency). Cost function [148] analysis shows
that a) high gate error probability ($\gtrsim 1\%$) is more suited for the
first generation QRs, b) low/intermediate gate error probability ($\lesssim
1\%$), low coupling efficiency ($\lesssim 90\%$), and slow gate operation
($\gtrsim 1\mu$s) benefit the second generation QRs, and c) low gate error
probability ($\lesssim 1\%$), high coupling efficiency ($\gtrsim 90\%$), and
fast gate operation ($\lesssim 1\mu$s) favors the third generation QRs [149].

Color center systems in SiC used to demonstrate HEG [86, 29] are suitable for
implementation of the first and the second generation of QRs. Their potential
for long-distance emission propagation and the technological requirements for
highly indistinguishable photon generation are analyzed in Table 1. Spectral
inhomogeneity of disparate emitters can be improved by 1) minimizing spectral
diffusion through optical illumination [127] and integration of color centers
into Schottky [124], p-i-n [128, 121] diodes, and 2) Emission tuning through
the application of electric field [124, 122, 121, 123] and strain [42, 135,
136, 137, 138]. Isotopic purification and dynamical decoupling should be
employed to assure long spin-coherence times. Color centers with higher spin-
coherence times (seconds range) can be used to implement the first generation
QRs for longer distances ($\gtrsim 1000$ km). The emission rates can be
improved by efficient integration of color centers into nanophotonic devices
through Purcell effect. As discussed in the previous section, nanophotonic
integration can be further improved through triangular cross-section devices,
optimal positioning of color center in the cavity, and improved
nanofabrication to reduce scattering losses. Efficient nanophotonic
integration also boosts the spin-photon coupling efficiency necessary for
implementation of the third generation QRs. To complete the tool set, the HEP
obtained with NV center in diamond [141] is yet to be demonstrated using SiC
color centers.

Critical steps in the implementation of entanglement protocols like high-
fidelity spin state initialization and resonant readout [29, 37], single-shot
readout via spin-to-charge conversion [38], and high-fidelity nuclear spin
initialization [29, 150] were demonstrated using neutral divacancies in SiC.
Despite the low DWF of divacancy ($\sim$5%), single-shot readout measurements
can be pursued through Purcell enhancement in integrated cavities [36].
Silicon vacancy has a strong intersystem crossing which allows for high-
fidelity spin initialization [46], but also prevents high-fidelity readout
[151]. Here too, integration into a nanocavity with moderate Purcell factor of
less than 100, can result in photon counts sufficient to achieve quantum non-
demolition readout of the spin state [46]. Efficient quantum frequency
conversion of emission from divacancy and silicon vacancy to the
telecommunications band should be developed to extend the range of quantum
communication. Integration of SNSPDs onto photonic devices would boost the
success rates of the measurement protocols [20, 21]. Other potential color
centers that need to be studied closely are the ones with emission in
telecommunications band (NV-, V4+, Er3+) to minimize the fiber losses, and
those with large DWF (Cr4+, V4+) that offer high photon counts for single-shot
readout. It should be noted that the current state-of-the-art performance of
color centers in SiC (especially divacancy) are more promising than the NV
center in diamond for QIP applications. SiC photonic devices require lower
Q-factors for achieving high photon counts and their color center’s ZPL
photons propagate for much longer distances in fiber, as shown in Table 1.

The demanding requirements on the matter qubits for the implementation of
quantum repeaters presents an opportunity for an all-photonic quantum repeater
scheme implemented using single-photon sources, linear optical elements,
photon detectors, and optical switches [152]. Realization of the highly
entangled states known as graph states (Figure 6a) are needed to implement an
all-photonic measurement-based quantum repeaters [153, 154]. A photonic
cluster state can be generated by continuous optical pumping of a single
photon emitter to produce a chain of photons that are entangled with other
photons and the emitter [155]. Assuming millisecond spin coherence and
nanosecond optical lifetime, a back of the envelope calculation would predict
cluster states of the order of $10^{6}$ photons. However, to make this
estimate more realistic to experimental conditions, the effects of non-
radiative recombination and photon collection would need to be considered.
These reductions could be made up for by Purcell enhancement in nanocavities.
Approaches for generating large clusters of entangled photons for divacancy,
silicon vacancy, and NV center in SiC have been proposed [156]. To
deterministically generate cluster states that outperform matter qubit based
QRs, very high fidelity and fast entangling gates, and high photon generation
and collection rates will be required [157].

Figure 4: The entanglement schemes designed in the three generations of
quantum repeaters as a guide for SiC quantum information processing [5, 7, 1,
31, 145, 6, 146, 147, 148].

###  4.2 Quantum Simulation

The idea of quantum information systems as models for quantum materials
simulation has been around since the first quantum computing proposals. While
a quantum advantage in simulation has not yet been demonstrated, with
advancements in emitter integration into nanocavities, these nanophotonic
systems are progressing toward versatile cavity quantum electrodynamical
(CQED) platforms. Coupled cavity arrays with integrated emitters, as
illustrated in Figure 5, have been of special interest for all-photonic
quantum simulation. The modeling of such systems has shown their
representation potential for the dynamics of complex condensed matter phases
such as charge density waves, supersolidity, and the quantum phase transitions
between the superfluid and Mott insulator phases [158, 159]. CQED-based
quantum information frameworks primarily rely on the strong light and matter
interaction, where the photon loss rates from the cavity and emitter, $\kappa$
and $\gamma$ respectively, are less than twice the emitter-cavity coupling
strength, $g$, which is related to the DWF by

$g=\sqrt{\frac{3\pi c^{3}\xi}{2\tau\omega^{2}n^{2}V}}$

where $\tau$ is the lifetime of the emitter, $V$ is the cavity mode volume,
and $\xi$ is the DWF [160]. The strong coupling regime has been demonstrated
in systems like single atoms in Fabry-Pérot cavities, single quantum dots in
solid-state cavities, and in superconducting Josephson junction systems [161,
162, 163, 164], however, each of these systems has at least one fundamental
drawback. Atom-Fabry-Pérot systems can be difficult to scale up to the size
that more complex quantum information systems require. Quantum dots, as
mesoscopic objects, can have a relatively wide distribution of emission
wavelengths even when fabricated by the same process. Superconducting
Josephson junction systems operate at millimeter wavelengths which are not
compatible with distributed QIP.

While much progress has been made to make up for these various difficulties,
SiC color centers in nanophotonic cavities inherently address all these
issues. Firstly, color centers are scalable via integration into devices, as
detailed in Section 3. Secondly, the linewidths of zero-phonon lines of color
centers are generally much smaller than those of quantum dots. Finally, the
near-infrared emission wavelengths provide some flexibility in the fabrication
of scalable cavity arrays, since the features do not need to be as small as in
the case of diamond emitters. This is not to imply that bringing color center
systems into strong coupling CQED systems is devoid of challenges. The current
state-of-the-art in color center-based nanophotonics is stymied by the low DWF
and the presence of non-radiative recombination, which adds difficulty to
achieving strong light-matter interaction in such systems. With careful
nanodevice design, it is possible to modify $\xi$, $\tau$, and $V$ as
discussed in Section 3. However, there has also been significant work in
investigating multiple color centers acting as an ensemble, which scales the
light-matter interaction strength by $\sqrt{N}$, where $N$ is the number of
emitters in the ensemble, to achieve strong coupling and demonstrate
polaritonic physics [165, 166, 167, 168].

Figure 5: An illustration of an all-photonic quantum simulator that could be
implemented in a triangular SiC coupled cavity array with integrated color
centers [167, 168].

###  4.3 Measurement-Based Quantum Computing

One of the major goals of QIP is building a fully scalable quantum computer
that can execute arbitrary quantum algorithms and distribute complex
computations. With this motivation, the measurement-based quantum computer
(MQC) [169, 170], also known as the one-way quantum computer, was proposed as
an alternative to the more established circuit model. The universal resource
for MQC is a highly entangled state known as the cluster state (Figure 6a).
Any sequential quantum circuit can be imprinted on the cluster state with only
single qubit measurements. Standard procedure for cluster state generation is
divided into two steps: (i) prepare all qubits in the
$\ket{+}=(\ket{0}+\ket{1})/\sqrt{2}$ state (in the Pauli Z computational
basis), and (ii) implement Ising-type next-neighbor interaction by applying
the control-Z (entangling) gates between each pair of qubits. With each
computational step, the entanglement is consumed by the subsequent measurement
of qubits in a certain direction. Cluster state provides MQC with multiple
advantages over the circuit-based model including decomposing large
computational space into steps by re-utilizing the cluster [169],
concatenation of gate simulations [170], distributed [171, 172, 173], loss-
tolerant[174, 175], and fault-tolerant [176, 177] quantum computation. Apart
from MQC, the cluster state remains an efficient resource for quantum
repeaters, as discussed previously.

Due to long coherence times and ease of manipulation of photons, optical
quantum computing with cluster states [178] emerged from the combination of
linear optics quantum computation (popularly known as KLM scheme) [179] and
MQC [169]. Using photons to produce highly entangled graph states is
difficult, as photons naturally do not interact with each other. In earlier
times, photonic graph states were generated either by measurement-induced
entanglement [180] (with cavities and multiplexer [181]) or by spontaneous
parametric down conversion (SPDC) combined with the so called fusion gates
[182]. As their generation depended on probabilistic photodetection process,
photonic graph states have reached experimental size of only ten photons [183]
with this approach. Deterministic generation of 1D photonic cluster strings
was first realized by the Lindner-Rudolph protocol [184] from quantum dots
with specific level structure and selection rules. Although 1D graph state
suffices for quantum repeaters, the universal quantum computation requires a
2D graph state. This need was met in a proposal suggesting the use of
entangled photons from entangled quantum emitters [185]. Basing on this idea,
subsequent protocols [186, 187, 188, 189] have been developed for generating
arbitrarily large photonic graph states from solid-state emitters such as
trapped ions, quantum dots, and NV centers in diamond. The protocol for 2D
cluster state generation from NV centers in diamond [189] requires only
microwave pulses (for emitter manipulation), optical pumping (for photon
generation), and waveplate and polarization photon counters (for measurement)
to implement MQC, thus making it suitable for implementation with SiC color
center photonics.

Although the silicon carbide protocols have been studied only in terms of 1D
photonic cluster state generation [156], the field can benefit from the wide
pool of studies in diamond NV center with whom divacancies and NV centers in
SiC share similar electronic structure and selection rules. As a result,
protocol for 2D photonic cluster state generation from NV centers in diamond
[189] can be directly implemented in divacancies and NV centers in SiC. Figure
6 manifests a perspective on MQC with SiC color centers. First, a highly
entangled $n\times m$ cluster state is generated from entangled color centers
where $n$ is the number of color centers and $m$ is the number of pump cycles
(Figure 6a). In the inset, the energy level structures of divacancy and NV
center in SiC are shown. With zero magnetic field, the ground $\ket{\pm 1}$
and excited $\ket{E_{\pm}}$ states are degenerate but do not mix. Each ground
state couples to one excited state with spontaneous emission of light having
opposite circular polarization ($\sigma^{\pm}$) which generates spin-photon
entanglement, while the $\ket{0}$ acts as an auxiliary state. Individual color
centers can be entangled with each other via protocols involving electron and
nuclear spin entanglement [189]. After 2D cluster state generation, a quantum
logic network is implemented on the cluster state with single qubit
measurements (Figure 6b). A $\sigma_{x}$ measurement acts like a _wire_
between adjacent pairs of qubits, a $\sigma_{y}$ measurement removes the qubit
from linear cluster but links the neighboring qubits which simultaneously
makes it work like a _wire_ , and a $\sigma_{z}$ measurement removes the qubit
from the rest of the cluster state. Measurements in the cos($\phi)\sigma_{x}$
$\pm$ sin($\phi)\sigma_{y}$ basis are performed in order to realize arbitrary
rotations to compensate for the randomness in rotations due to Pauli
observables. However, in a more general sense, the measurement basis depends
on the preceding measurements, which imposes a temporal order for a particular
quantum logic implementation in a certain direction [169, 170].

To implement these MQC protocols in color centers, the main challenge is to
apply entangling gates to generate the 2D cluster state and do at least one
round of measurement before the spin decoheres. Assuming 30 $\mu$s time to
apply entangling gates with high fidelity ($\gtrsim 99\%$), as seen in diamond
NV center [187], this puts the lower limit on the required coherence time to
hundreds of microseconds. This timescale makes divacancy and silicon vacancy
in SiC currently the best suited candidates for SiC-based MQC, as they have
spin coherence times in the milliseconds-seconds range [83, 30] (see Table 1).
Experimental challenges such as spontaneous emission rate and inefficient
photon collection due to low ZPL emission, and photon loss during multi-
emitter entanglement also impede deterministic cluster state generation from
realization in color centers [156, 186, 187, 189]. These issues can be
resolved by coupling SiC color centers to a photonic crystal cavity that
extends into a single-mode waveguide attached to a detector (see Figure 1b),
fiber or an efficient grating coupler [95, 92, 167, 30]. Therefore, integrated
SiC photonics has the potential to be a rich toolbox for full-fledged
execution of MQC.

Figure 6: Color center implementation of all optical quantum computation with
cluster states. a) Generation of the photonic cluster state using repeated
emissions from entangled color centers. Inset figure shows the so called I-I
energy level structure for spin-photon entanglement creation, exhibited in
spin-$\frac{3}{2}$ and spin-1 emitters in SiC, such as silicon vacancy,
divacancy, and NV center [156]. b) Quantum logic network implemented on the
cluster state via single qubit measurements in different bases [169, 170].
Operating principles are detailed in the main text.

##  5 Summary

In this perspective paper, we have presented integrated silicon carbide
photonics as a powerful playground for quantum technology development.
Although SiC has benefits as a material platform for QIP applications like
CMOS compatible, wafer-scale nanofabrication processes, and availability of
color centers with emission in telecommunications wavelength, progress needs
to be made on the realm of entanglement generation in integrated color center
devices.

In an international and interdisciplinary scientific effort, this field is
moving to demonstrate unique capabilities in materials engineering, spin-
photon entanglement, and cavity-emitter interaction. The potential impact on
quantum networking, simulation, and computing has been drawing a larger
community to explore SiC color centers, and we hope this paper will serve as a
guiding material to connect concepts from related fields.

## Acknowledgements

This work is supported by the National Science Foundation (CAREER-2047564) and
the UC Davis Summer GSR Award for Engineering or Computer-related Applications
and Methods.

## Author Declarations

### Conflict of Interest

The authors have no conflicts to disclose.

### Data Availability

Data sharing is not applicable to this article as no new data were created or
analyzed in this study.

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