††thanks: These authors contributed equally to this work;††thanks: These
authors contributed equally to this work;

# A hole spin qubit in a fin field-effect transistor above 4 kelvin

Leon C. Camenzind  Simon Geyer  Department of Physics, University of Basel,
Klingelbergstrasse 82, CH-4056 Basel, Switzerland  Andreas Fuhrer  IBM
Research-Zürich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland  Richard J.
Warburton  Dominik M. Zumbühl  e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>Department of Physics, University of Basel,
Klingelbergstrasse 82, CH-4056 Basel, Switzerland  Andreas V. Kuhlmann
e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>Department of
Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel,
Switzerland  IBM Research-Zürich, Säumerstrasse 4, CH-8803 Rüschlikon,
Switzerland

###### Abstract

The greatest challenge in quantum computing is achieving scalability.
Classical computing previously faced a scalability issue, solved with silicon
chips hosting billions of fin field-effect transistors (FinFETs). These FinFET
devices are small enough for quantum applications: at low temperatures, an
electron or hole trapped under the gate serves as a spin qubit. Such an
approach potentially allows the quantum hardware and its classical control
electronics to be integrated on the same chip. However, this requires qubit
operation at temperatures above 1 K, where the cooling overcomes heat
dissipation. Here, we show that silicon FinFETs can host spin qubits operating
above 4 K. We achieve fast electrical control of hole spins with driving
frequencies up to 150 MHz, single-qubit gate fidelities at the fault-tolerance
threshold, and a Rabi oscillation quality factor greater than 87. Our devices
feature both industry compatibility and quality, and are fabricated in a
flexible and agile way that should accelerate further development.

Quantum dot (QD) spin qubits [1] in silicon have potential applications in
large-scale quantum computation [2], due to their long coherence times [3] and
high quality factors [4, 5, 6], as well as the fact that complementary metal-
oxide-semiconductor (CMOS) manufacturing processes [7, 8, 9] can be used to
create dense arrays of interconnected spin qubits [10, 11]. Inspired by
conventional integrated circuits, on-chip integration of the classical control
electronics with the qubit array has been suggested as a way to overcome the
challenges in wiring up large numbers of multi-terminal QD devices [12].
However, since the electronics produce heat, the amount of control
functionality that can be implemented depends on the available cooling power.
Therefore, it is beneficial to be able to operate qubits at temperatures
greater than 1 K, where cooling power is orders of magnitude higher than at mK
temperatures [13, 14]. For example, Intel’s cryogenic control chip, which is
known as Horse Ridge, works at 3 K [15].

Spin qubits come in two distinct forms: electron [3, 16, 4, 5, 13, 14] and
hole [7, 17, 18, 19, 20]. With electrons, an artificial spin-orbit interaction
(SOI) can be engineered by equipping the qubit with a micromagnet [16, 4, 5].
Conversely, hole spins experience a strong intrinsic SOI [21]. All-electrical
spin control is achieved via electric-dipole spin resonance (EDSR) [22, 23,
24, 25, 26], where an applied oscillating electric field induces spin
rotations. Compared to electrons, holes can reduce device complexity, which
benefits scalability, because no additional device components are required to
generate a SOI. Furthermore, with holes in silicon nanowires or FinFETs [27,
28, 29], the SOI can be exceptionally strong and fully tunable, creating a
switchable coupling strength and a way to mitigate the effects of charge noise
[21, 30, 20]. Moreover, hole spins are better protected against nuclear spin
noise due to their weak hyperfine interaction [31].

Recently, electron spin qubits operating up to 1.5 K have been demonstrated
[13, 14]. In this article, we report hole spin qubits working at 1.5 to 5 K:
that is, in a temperature range where the thermal energy is much larger than
the qubit level splitting and cryogenic control electronics can be operated
[15]. The hole spin qubits are integrated in silicon FinFET devices that are
created using standard CMOS fabrication techniques, including self-aligned
gates and chemically-selective plasma etches instead of lift-off processes [8,
9]. In addition, a high degree of process flexibility and a short turnaround
are achieved by using electron-beam instead of advanced optical lithography
[32]. The fin provides a one-dimensional confinement for the holes, enabling
fast and electrically tunable effective spin-1/2 qubits [21, 30, 20]. We
demonstrate EDSR-based spin control with Rabi frequencies up to
$150\,\mathrm{MHz}$ and voltage-tunable qubit frequencies, a feature employed
to implement z-rotations as fast as $45\,\mathrm{MHz}$. We also show spin
rotations around the $x$\- and $y$-axis of the Bloch sphere with a single-
qubit gate fidelity of $98.9\,\mathrm{\%}$ at 1.5 K. A high robustness against
temperature allows for qubit operation above the boiling point of liquid 4He,
albeit with a reduced dephasing time $T_{2}^{*}$ compared to
$1.5\,\mathrm{K}$, which is consistent with an observed whitening of the
spectral noise density on increasing temperature.

Figure 1: Spin-orbit qubits in a FinFET. a, False-colour SEM image of an
unfinished device showing the two lead gates L1, L2 (yellow) as well as the
inter-dot barrier gate B (blue, ${\sim}\,35\,\mathrm{nm}$). An in-plane
external magnetic field $B_{\mathrm{ext}}$ is applied perpendicular to the fin
(red). b, Cross-sectional TEM image along the black dashed line shown in a
after integration of the QDs’ plunger gates P1, P2 (turquoise,
${\sim}\,15\,\mathrm{nm}$). In addition to a DC voltage, fast pulses and
microwaves can be applied to P1. Current flow is observed from source to drain
via the fin-shaped channel. c, Measurement of a spin-blocked pair of bias
triangles. The blue square and pink triangle mark the qubit
initialisation/readout and manipulation point, respectively. d, Schematic
illustration of the spin manipulation cycle with corresponding pulse scheme.
e, Rabi oscillation with $f_{\mathrm{Rabi}}=22\,\mathrm{MHz}$ measured on Q1
at $B_{\mathrm{ext}}=123\,\mathrm{\mathrm{mT}}$,
$f_{\mathrm{MW}}=3.311\,\mathrm{GHz}$, $A_{\mathrm{MW}}=1.1\,\mathrm{mV}$ and
$\mathrm{T}=1.5\,\mathrm{K}$. The data has been corrected by removing a small
constant offset, and is fitted (solid curve) to $I(t_{\mathrm{b}})=A\sin(2\pi
f_{\mathrm{Rabi}}t_{\mathrm{b}}+\theta)+B$ with $A$, $B$, $f_{\mathrm{Rabi}}$
and $\theta$ as fit parameters. f, Measurement of the current as a function of
$f_{\mathrm{MW}}$ and $B_{\mathrm{ext}}$. Along the red (blue) line the spin
resonance condition is met for Q1 (Q2). For each frequency the average current
has been subtracted. g, Electrical tunability of the qubit frequency with the
depth of the Coulomb pulse. Solid lines represent linear fits to the data. h,
Detuned Rabi oscillations showing a typical chevron pattern, measured at
$f_{\mathrm{MW}}=3.311\,\mathrm{GHz}$ and $A_{\mathrm{MW}}=1.4\,\mathrm{mV}$.
Dependence of $f_{\mathrm{Rabi}}$ on $A_{\mathrm{MW}}$ j and
$B_{\mathrm{ext}}$ i. Solid lines are linear fits to the data with zero
offset.

A scanning electron microscope (SEM) tilted side-view and a transmission
electron microscope (TEM) cross-sectional view of a co-fabricated device are
shown in Figs. 1a,b. Since these FinFETs are fabricated using CMOS processes,
they feature a highly uniform gate profile [32] and ultra-small gate lengths
[9], resulting in an estimated effective dot size of $\sim$ 7 nm
(Supplementary Section 6). By negatively biasing the gate electrodes, an
accumulation-mode hole double quantum dot (DQD), hosting two individual
spin-1/2 qubits, is formed [9]. Here, a pseudospin of $\pm 1/2$ is assigned to
the two lowest energy hole states, which for 1D-like hole systems can have
large contributions of both heavy-hole and light-hole basis states [21, 30].
We measure the direct current $I_{\mathrm{DC}}$ through the DQD, which when
combined with spin-to-charge conversion through Pauli spin blockade (PSB) [33,
34] provides qubit readout functionality (for further details on the device
and measurement setup see Methods). For the device investigated, PSB is
observed for the $(1,1)\rightarrow(0,2)/(2,0)$ charge state transitions and no
additional transitions are observed when further depleting the QDs. Here
$(m,n)$ denotes the effective hole occupancy of the left/right QD, while the
true hole occupancy is $(m+m_{0},n+n_{0})$ with possible additional holes
$m_{0},n_{0}$.

In the PSB regime hole tunnelling is forbidden by spin conservation if the two
spins, one per QD, occupy a spin-polarized triplet state
($\ket{(1,1)\mathrm{T}_{+}}$ or $\ket{(1,1)\mathrm{T}_{-}}$) and are thus
aligned parallel. The unpolarized triplet $\ket{(1,1)\mathrm{T}_{0}}$ is not
blockaded as it mixes with the singlet $\ket{(1,1)\mathrm{S}}$, which itself
is coupled to the singlet $\ket{(0,2)\mathrm{S}}$ such that hole transport
occurs [35]. Spin blockade can be lifted by flipping the direction of one hole
spin using EDSR [23, 24, 7, 17, 20], which is performed by applying square
voltage pulses and microwave (MW) bursts to gate P1 (Fig. 1b). The
measurements consist of three stages (Figs. 1c,d): first, the two holes spins
are initialised in a polarised spin state through PSB. Then, the system is
pulsed into Coulomb blockade, where the MW signal is applied. Finally, in the
readout stage a current is detected if the spins are antiparallel, such that
one hole can tunnel to the neighbouring QD and exit to the nearby reservoir.
This cycle is repeated many times for a measurable current, such that the
duration of the manipulation stage is limited to a few microseconds
(Supplementary Section 1).

For high-temperature operation of spin qubits [13, 14], spin-to-charge
conversion via PSB rather than energy-selective tunnelling [36] is favourable,
since the single-dot singlet-triplet splitting [9] is typically much larger
than the Zeeman energy. Thus, the measurements can be performed at higher
temperature and smaller external magnetic field, resulting in lower and
technically less demanding qubit frequencies.

EDSR takes place under the condition that the MW frequency $f_{\mathrm{MW}}$
equals the Larmor frequency $f_{L}=|g^{*}|\,\mu_{B}\,|B_{\mathrm{ext}}|/h$,
where $g^{*}$ denotes the effective hole Landé $g^{*}$-factor along the
magnetic field $B_{\mathrm{ext}}$ direction, $\mu_{B}$ Bohr’s magneton and $h$
Planck’s constant. In Fig. 1f the resonance appears as a V-shape that maps out
$f_{L}$ in the $f_{\mathrm{MW}}$-$B_{\mathrm{ext}}$ plane. The single-hole
spin resonance conditions differ slightly for the two qubits (Q1, Q2), making
them individually addressable. From the slope of the current lines, we extract
absolute values for the $g^{*}$-factor of $1.94\pm 0.05$ and $2.35\pm 0.05$,
respectively. These two different values indicate a sensitivity to the local
electric fields, which also provides an additional control knob for the
$g^{*}$-factor, and thus the qubit frequency [3, 5, 26, 18, 20]. This is
confirmed by Fig. 1g, where the $f_{L}$-dependence on the square pulse
amplitude $A_{\mathrm{p}}$ is shown.

When the MW drive is on resonance, the DQD current reveals Rabi oscillations
as a function of the burst duration $t_{\mathrm{b}}$. An example of a
$22\,\mathrm{MHz}$ Rabi oscillation, whose decay time is too long to be
observed within 87 $\pi$ rotations, corresponding to the longest applicable
$t_{\mathrm{b}}$, is given in Fig. 1d. For a detuned $f_{\mathrm{MW}}$ the
qubit rotates around a tilted axis on the Bloch sphere, resulting in faster
rotations of reduced contrast as demonstrated by the chevron pattern seen in
Fig. 1h. The Rabi frequency $f_{\mathrm{Rabi}}$ increases linearly not only
with the MW amplitude $A_{\mathrm{MW}}$ (Fig. 1i), but also $B_{\mathrm{ext}}$
(Fig. 1j) as expected for SOI-mediated spin rotations [22, 23, 20, 25, 26].
For these measurements, $A_{\mathrm{MW}}$ is calibrated using the photon-
assisted-tunnelling response (Supplementary Section 3) [23]. The maximum
$f_{\mathrm{Rabi}}$ observed is $147\,\mathrm{MHz}$ (Supplementary Section 5),
which corresponds to a spin-flip time of just ${\sim}\,3.4\,\mathrm{ns}$.
Under the assumption that EDSR occurs due to a periodic displacement of the
wave function as a whole, the $g^{*}$-factor is not modulated [26] and
$f_{\mathrm{Rabi}}$ depends on the spin-orbit length $l_{\mathrm{SO}}$ [23].
We can therefore state an estimate for $l_{\mathrm{SO}}$ in the range of $20$
to $60\,\mathrm{nm}$ (Supplementary Section 7), that is, similar values to the
one reported before [9] and in very good agreement with theory predictions
[21].

A key parameter for the qubit controllability is the quality factor defined as
$\mathrm{Q}=2f_{\mathrm{Rabi}}T_{2}^{\mathrm{Rabi}}$, where
$T_{2}^{\mathrm{Rabi}}$ is the decay time of the Rabi oscillations. For the
data presented in Fig. 1e no decay is observed within ${\sim}\,2\,\mathrm{\mu
s}$, that is, $\mathrm{Q}\gg 87$. In terms of quality factors, our hole spin
qubits therefore outperform their hot electron counterparts [13, 14].

Figure 2: Hot qubit coherence. a, Ramsey-fringe experiment performed at
$4.2\,\mathrm{K}$. $B_{\mathrm{ext}}$ is fixed at $267\,\mathrm{\mathrm{mT}}$.
The pulse sequence, which consists of two 15 ns-long $\frac{\pi}{2}$-bursts
separated by the waiting time $\tau$, is illustrated in the bottom right
inset. $\phi$ denotes the phase of the second pulse with respect to the first
one, here $\phi=0$. Decay of Ramsey fringes at $1.5\,\mathrm{K}$ b and
$3\,\mathrm{K}$ c. The data were taken on resonance with a $\tau$-dependent
phase $\phi(\tau)$, which adds an artificial oscillation [50]. Solid curves
show fits to $A+B\sin(\omega\tau+\theta)\exp[-(\tau/T_{2}^{*})^{\beta+1}]$
with temperature dependent $\beta$. d, Temperature dependence of the spin
dephasing time revealing a power-law decay
$T_{2}^{*}\propto\mathrm{T}^{-\eta}$, where $\eta=0.46\pm 0.02$ for Q1 and
$\eta=0.81\pm 0.06$ for Q2, respectively.

Next, we evaluate the spin coherence by performing a Ramsey experiment. Here,
two $\frac{\pi}{2}$-pulses separated by a delay time $\tau$ during which the
qubit can freely evolve and dephase are applied. When $f_{\mathrm{MW}}$ is
detuned from the qubit resonance, the current through the device shows
coherent oscillations known as Ramsey fringes. The data of Fig. 2a is measured
at a temperature of $\mathrm{T}=4.2\,\mathrm{K}$, which corresponds to the
boiling point of liquid 4He, and which can be achieved in a technically non-
demanding way by immersing the sample in a liquid 4He bath or at the second
stage of a dry pulse-tube refrigerator. The dephasing time $T_{2}^{*}$ is
determined by fitting the envelope of the fringe decay to
$\exp(-(\tau/T_{2}^{*})^{\beta(\mathrm{T})+1})$, where $\beta$ depends on
temperature as discussed later. Despite the fact that our qubit readout is
protected against temperature by the large orbital energies, which exceed the
thermal energy available at $4.2\,\mathrm{K}$ by an order of magnitude, a
degradation of the signal contrast on increasing temperature is observed (Fig.
2b,c). The reasons for this are not yet fully understood, however we speculate
that this is due to spin-flip cotunneling (Supplementary Section 8). The
T-dependence of $T_{2}^{*}$ in the range of 1.5 to $5\,\mathrm{K}$ is
presented for both qubits in Fig. 2d. While Q1 can be manipulated faster than
Q2, it lags behind in coherence. The spin dephasing time drops with increasing
temperature, described by a power-law decay $\propto\mathrm{T}^{-\eta}$ with
$\eta=0.5$ (0.8) for Q1 (Q2), a rather weak temperature dependence similar to
previous reports [14, 13]. The obtained values for $T_{2}^{*}$ are consistent
with the EDSR spectral width (Supplementary Section 9), and a spin relaxation
time ${T_{1}}\,{>}\,10\,\mathrm{\mu s}$ was found at 4.2 K (Supplementary
Section 12). In the following the focus is on the more coherent Q2.

Spin rotations around at least two different axes are required to reach any
point on the Bloch sphere. In Fig. 3a we demonstrate two-axis qubit control at
both $1.5\,\mathrm{K}$ and $4.2\,\mathrm{K}$ by employing a Hahn-type echo
sequence. A modulation of the relative phase $\phi$ of the second
$\frac{\pi}{2}$-pulse yields a set of Ramsey fringes that are phase-shifted by
$\pi$ for a $\pi_{x}$ and $\pi_{y}$ echo pulse, which is applied to extend the
coherence. The performance of the hole spin rotations is characterised using
randomised benchmarking [37, 38] (see Fig. 3b and Methods). At
$1.5\,\mathrm{K}$, a single-qubit gate fidelity of $F_{\mathrm{s}}=98.9\pm
0.2\,\mathrm{\%}$ is obtained, which is at the fault-tolerance level [2, 3]
and very similar to the values recently reported for hot electron spin qubits
[14, 13]. The fidelity is reduced to $F_{\mathrm{s}}=98.6\pm 1.6\,\mathrm{\%}$
($97.9\pm 1.1\,\mathrm{\%}$) at $3\,\mathrm{K}$ ($4.2\,\mathrm{K}$), revealing
a similar scaling with temperature as $T_{2}^{*}$. We thus expect to be able
to enhance the gate fidelities further by improving the qubit coherence, and
by optimisation of the gate pulses [39].

Figure 3: X, Y and Z qubit gates. a, Demonstration of two-axis qubit control
by applying a Hahn-type echo sequence, where the relative phase $\phi$ of the
second $\frac{\pi}{2}$-pulse is varied. The measurements at $1.5\,\mathrm{K}$
(circles) and $4.2\,\mathrm{K}$ (diamonds) are phase-shifted by $\pi$ due to
the two orthogonal echo pulses, as shown in the right panel. b, Standard
randomised benchmarking at $1.5\,\mathrm{K}$ (circles), $3\,\mathrm{K}$
(squares) and $4.2\,\mathrm{K}$ (diamonds) is performed by applying a varying
number of Clifford gates $m$ and preparing either a $\ket{\uparrow}$ or
$\ket{\downarrow}$ final state. The normalised difference of currents is
fitted to a single exponential decay to extract the single-qubit gate
fidelities $F_{\mathrm{s}}$ (see Methods for further details). The shaded
regions show the one-sigma error range of the fit parameters. The maximum $m$
decreases with increasing temperature due to a reduced readout contrast. c,
Schematic representation of the pulse scheme used to demonstrate qubit
rotations around the $z$-axis of the Bloch sphere. In a modified Hahn echo
sequence a square pulse of amplitude $A_{\mathrm{Z}}$ and duration
$t_{\mathrm{Z}}$ is applied to shift the qubit precession frequency (see Fig.
1 g). The resulting phase-shift-induced oscillations are shown in d for
different $A_{\mathrm{Z}}$. Solid curves represent fits to a sinusoidal
function, where the oscillation frequency is given by the induced qubit
frequency shift. Traces are offset by an increment of 0.3 for clarity. e, The
speed of the $z$-rotations increases linearly with $A_{\mathrm{Z}}$. The solid
line represents a linear fit to the data, yielding a frequency-shift of 8.9
MHz/meV. The data presented in this figure was taken for Q2 at
$f_{\mathrm{MW}}=8.812\,\mathrm{GHz}$.

Besides rotations around the $x$\- and $y$-axis of the Bloch sphere,
$z$-rotations can be realised by exploiting the electrical tunability of the
qubit frequency (Fig. 1g). For this purpose a square pulse of amplitude
$A_{\mathrm{Z}}$ and duration $t_{\mathrm{Z}}$ is added to a Hahn echo
sequence (Fig. 3c) in order to rapidly detune the spin precession frequency,
which leads to a phase pick up around the $z$-axis of the Bloch sphere [5]. As
a consequence, the DQD current oscillates as a function of $t_{\mathrm{Z}}$
(Fig. 3d) at a frequency that increases linearly with $A_{\mathrm{Z}}$ up to
${\sim}\,45\,\mathrm{MHz}$ (Fig. 3e).

Figure 4: Dynamical decoupling and noise spectroscopy. a, The spin coherence
time can be enhanced by decoupling the qubit from low-frequency noise using a
CPMG pulse sequence (see bottom-right schematic). A power-law dependence of
the coherence time on the number of refocusing pulses $n_{\pi}$ is confirmed
by fitting (solid lines) the data to
$T_{2}^{\mathrm{CPMG}}=T_{2}^{0}(n_{\pi})^{\frac{\beta}{1+\beta}}$, where
$\beta$ represents the scaling exponent of a power-law noise spectrum,
$S(f)\propto f^{-\beta}$. b, Time trace of the qubit frequency obtained from
repeated Ramsey measurements. The shaded region indicates the frequency
uncertainty due to readout noise. c, Temperature dependence of the noise
exponent $\beta$ extracted from either CPMG or Ramsey measurements. The data
presented in this figure was taken for Q2 at
$f_{\mathrm{MW}}=8.812\,\mathrm{GHz}$.

Finally, in order to gain insight into the sources of decoherence we perform
noise spectroscopy by employing Carr-Purcell-Meiboom-Gill (CPMG) pulse
sequences [40], where a series of $n_{\pi}$ $\pi_{y}$-pulses is applied as a
spectral filter for the environmental noise [41, 42, 5]. For a power-law noise
spectrum $S(f)\propto f^{-\beta}$, the CPMG coherence time
$T_{2}^{\mathrm{\,CPMG}}$ is expected to scale as
$T_{2}^{\mathrm{\,CPMG}}\propto(n_{\pi})^{\frac{\beta}{1+\beta}}$ [42]. This
dependency is confirmed by Fig. 4a, and a $\beta$ of $0.88\pm 0.11$ ($0.26\pm
0.03$) is determined for $1.5\,\mathrm{K}$ ($3\,\mathrm{K}$), revealing a
whitening of the noise on increasing the temperature and thus a reduced noise-
decoupling efficiency. For $n_{\pi}=32$, the maximum $n_{\pi}$ achievable with
our transport-based readout scheme, the hole spin coherence time is extended
to $5.4\,\mathrm{\mu s}$ at $1.5\,\mathrm{K}$, which corresponds to an
increase by a factor of 27 compared to the unprotected qubit. While our CPMG
measurements are sensitive to the noise at frequencies of
$f{\sim}\,{10^{5}}\,{-}\,10^{7}\,\mathrm{Hz}$, we independently probe $S(f)$
at $f{\sim}\,{10^{-3}}\,{-}\,10^{-1}\,\mathrm{Hz}$ by tracking the Larmor
frequency fluctuations through repeated Ramsey experiments [5] (Fig. 4b). The
temperature dependence of $\beta$ demonstrates a noise whitening in both
frequency ranges, and the good agreement of the $\beta$-values for the two
frequency windows suggests a similar coloured noise spectrum over a wide range
of frequencies. From the scaling of $\beta$ with T we cannot uniquely identify
the underlying noise sources, such as charge or nuclear spin fluctuations
[43]. We note, however, that the longest $T_{2}^{*}$ measured is
${\sim}\,440\,\mathrm{ns}$ (Supplementary Section 10), which does not only
exceed the dephasing times reported so far for hole spins in silicon at mK
temperatures [44], but is also close to the estimated limit of
${\sim}\,500\,\mathrm{ns}$ set by the hole spin hyperfine interaction
(Supplementary Section 11). This sub-$\mu$s limit is a consequence of the hole
spins interacting with a relatively small number of nuclear spins $N_{s}\sim
310$, which increases the Overhauser field fluctuations that scale with
$1/\sqrt{N_{s}}$ [45], and also represents a lower bound due the anisotropy of
the hole hyperfine interaction [31].

We have reported hole spin qubits in silicon FinFETs that operate above
$4\,\mathrm{K}$. The strong SOI allows for spin rotations as fast as
$147\,\mathrm{MHz}$ and the weak hyperfine coupling ensures $T_{2}^{*}$ up to
$440\,\mathrm{ns}$. In addition to two-axis control, we implement fast
z-rotations by employing the electrical tunability of the $g^{*}$-factor. At
$1.5\,\mathrm{K}$, we achieve fault-tolerant single-qubit gate fidelities.
These results have been achieved using an industry-compatible FinFET device
architecture, which is also well suited to implementing larger arrays of
interacting qubits, such as a linear chain of exchange-coupled QD spins.
Connectivity beyond nearest neighbours can be realised by coupling to a
superconducting microwave resonator [46] or coherent spin shuttling [47].

In the quest for a higher qubit quality factor, hyperfine-induced dephasing
can be prevented by engineering a nearly nuclear-spin-free environment [3].
While a stronger SOI results in shorter gate times, it also increases the
susceptibility to charge noise. For hole spins in silicon FinFETs, however, an
unusually strong and at the same time electrically tunable SOI, allowing for
on demand switching between qubit idling and manipulation modes, has been
predicted [21, 20, 30]. Furthermore, fast single-shot readout of hole spins is
required for accurate qubit measurements. At few-kelvin temperatures this can
be realised using a DQD charge sensor that exploits tunneling between two
quantised states [48]. This technique is more resilient against temperature
than a single sensor QD, and high-fidelity single-shot readout up to 8 K at a
bandwidth greater than 100 kHz was demonstrated. In addition, a read time
resolution $<$ 1 $\mu$s, i.e. fast compared to our hole spin lifetime, was
demonstrated using radio frequency reflectometry of a silicon DQD [49]. These
readout techniques can be combined with the advance reported here, a hole spin
qubit in a FinFET at temperatures of 4 K and above.

Methods
Device fabrication. The fin structures are defined along [110] direction on a
near-intrinsic, natural silicon substrate (${\rho>10\,\mathrm{k\Omega cm}}$,
(100) surface) by means of electron-beam lithography (EBL) and dry etching
[8]. The gate oxide is formed by thermal oxidation of the silicon, yielding a
${\simeq}\,7\,\mathrm{nm}$-thick silicon dioxide (SiO2) layer, which is
covered by ${\simeq}\,20\,\mathrm{nm}$ of titanium nitride (TiN) grown by
atomic layer deposition (ALD). The first layer of gates containing L1, L2 and
B is patterned using EBL and dry etching. Subsequently, the gate stack
(${\simeq}\,4.5\,\mathrm{nm}$ SiOx, ${\simeq}\,20\,\mathrm{nm}$ TiN) of the
second gate layer hosting P1 and P2 is grown by ALD. The plunger gates are
implemented by means of a self-aligned process [9], where the gaps between the
gates of the first gate layer (highlighted in turquoise in Fig. 1a) act as a
template for the plungers gates. The gate lengths of the device measured are
$l_{\mathrm{B}}\,{\sim}\,35\,\mathrm{nm}$ and
$l_{\mathrm{P}}\,{\sim}\,15\,\mathrm{nm}$. Source and drain contacts are
p-type and made of platinum silicide (PtSi), which is formed by sputtering a
${\simeq}\,15\,\mathrm{nm}$-thick Pt layer on a beforehand cleaned silicon
surface, followed by a silicidation anneal at $450\,\mathrm{{}^{\circ}C}$ for
$10\,\mathrm{\mathrm{min}}$ in an argon ambient. Finally, the devices are
encapsulated in a ${\simeq}\,100\,\mathrm{nm}$-thick SiO2 layer that is grown
by plasma-enhanced chemical vapour deposition and are accessed via tungsten
interconnects.

Experimental setup. All measurements are performed using a variable
temperature insert that can be operated at $1.5-50\,\mathrm{K}$. MW and DC
signals can be applied simultaneously to gate P1 (see Fig. 1b) via a bias-tee
on the sample board. DC voltages are supplied by a low-noise voltage source
(BasPI SP927) and the source-drain current is measured with a current-to-
voltage amplifier at gain $10^{9}$ (BasPI SP983c). A square voltage pulse used
to drive the device between Coulomb blockade (qubit manipulation stage) and
Pauli spin blockade (qubit initialisation and readout stage) is provided by an
arbitrary waveform generator (Tektronix AWG5204), which also controls the I
and Q inputs of a vector signal generator (Keysight E8267D) to generate phase-
controlled square-shaped MW bursts. The latter ones and the square pulse are
combined using a wideband power combiner (Mini-Circuits ZC2PD-5R263-S+). The
qubit readout current is distinguished from the background by chopping the MW
signal at a frequency of $89.2\,\mathrm{\mathrm{Hz}}$ and demodulating the
current at this frequency with a lock-in amplifier (Signal Recovery 7265). For
further details see Supplementary Section 1.

Clifford benchmarking protocol. Randomised benchmarking is performed by
applying a randomised sequence of a varying number of Clifford gates $m$
before the spin state is rotated such that the final state ideally becomes
either the $\ket{\uparrow}$ or $\ket{\downarrow}$ state. Each of the 24 gates
in the Clifford group is constructed from the set
$\\{\mathrm{I},\pm\mathrm{X},\pm\mathrm{Y},\pm\mathrm{X}/2,\pm\mathrm{Y}/2\\}$
[38]. Assuming that the qubit initial state is $\ket{\downarrow}$, a current
flow is only observed when spin blockade is lifted for a final
$\ket{\uparrow}$ state. Thus, the difference in current between sequences
designed to output either a $\ket{\uparrow}$ or $\ket{\downarrow}$ state,
$\Delta\mathrm{I}=\mathrm{I}^{\ket{\uparrow}}-\mathrm{I}^{\ket{\downarrow}}$,
is proportional to
$p_{\uparrow}^{\ket{\uparrow}}-p_{\uparrow}^{\ket{\downarrow}}$. For each $m$
we average over 10 randomised sequences and the average Clifford-gate fidelity
$F_{\mathrm{c}}$ is obtained from fitting the normalised current difference to
$(2F_{\mathrm{c}}-1)^{m}$. Since a Clifford gate consists of on average 1.875
gates, the average single-qubit gate fidelity $F_{\mathrm{s}}$ is derived by
$F_{\mathrm{s}}=1-(1-F_{\mathrm{c}})/1.875$.

Data availability
The data supporting the plots of this paper are available at the Zenodo
repository at https://doi.org/10.5281/zenodo.4579586.

Acknowledgements
We thank M. de Kruijf, C. Kloeffel, D. Loss, F. Froning and F. Braakman for
fruitful discussions. Moreover, we acknowledge support by the cleanroom
operation team, in particular by U. Drechsler, A. Olziersky and D. Davila
Pineda, at the IBM Binnig and Rohrer Nanotechnology Center, as well as
technical support at the University of Basel by S. Martin and M. Steinacher.
This work was partially supported by the Georg H. Endress Foundation, the NCCR
SPIN, the Swiss Nanoscience Institute (SNI), the Swiss NSF (grant nr. 179024),
and the EU H2020 European Microkelvin Platform EMP (grant nr. 824109). L.C.C.
acknowledges support by a Swiss NSF mobility fellowship (P2BSP2_200127).

Author contributions
A.V.K., L.C.C., S.G., A.F., R.J.W. and D.M.Z. conceived the project and
experiments. A.V.K. and S.G. fabricated the device. L.C.C. and D.M.Z. prepared
the cryogenic measurement setup. A.V.K. S.G., L.C.C. and D.M.Z. performed the
experiments. A.V.K, L.C.C., and S.G. analysed the data and wrote the
manuscript with input from all the authors.

Competing interests
The authors declare no competing interests.

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# Privacy-Preserving Record Linkage

Dinusha Vatsalan  School of Computing, Macquarie University, NSW 2109,
Australia  School of Science and Technology, Hellenic Open University, Patras,
Greece<EMAIL_ADDRESS>Dimitrios Karapiperis<EMAIL_ADDRESS>Vassilios S. Verykios<EMAIL_ADDRESS>
††journal: Encyclopedia of Big Data Technologies

Definition

Given several databases containing person-specific data held by different
organizations, Privacy-Preserving Record Linkage (PPRL) aims to identify and
link records that correspond to the same entity/individual across different
databases based on the matching of personal identifying attributes, such as
name and address, without revealing the actual values in these attributes due
to privacy concerns.

##  1 Synonyms

Private Data Matching, Private Record Linkage, Blind Data Linkage, Private
Data Integration

##  2 Overview

In the current era of Big Data personal data about people, such as customers,
patients, tax payers, and clients, are dispersed in multiple different sources
collected by different organizations. Several applications have begun to
leverage tremendous opportunities and insights provided by linked and
integrated data. Examples range from healthcare, businesses, social sciences,
to government services and national security. Linking data is also used as a
pre-processing step in many data mining and analytics projects in order to
clean, enrich, and understand data for quality results [6].

However, the growing concerns of privacy and confidentiality issues about
personal data pose serious constraints to share and exchange such data across
organizations for linking. Since a unique entity identifier is not available
in different data sources, linking of records from different databases needs
to rely on available personal identifying attributes, such as names, dates of
birth, and addresses. Known as quasi identifiers (QIDs), these values in
combination not only allow uniquely identifying individuals but also reveal
private and sensitive information about them [44].

Privacy-preserving record linkage (PPRL) aims to identify the same entities
from different databases by linking records based on encoded and/or encrypted
QIDs, such that no sensitive information of the entities is revealed to any
internal (parties involved in the process) and external (external adversaries
and eavesdroppers) parties. While a variety of techniques and methodologies
have been developed for PPRL over the past two decades, as surveyed in [44,
45], this research field is still open to several challenges, especially with
the Big Data revolution.

A typical PPRL process involves several steps, starting from pre-processing
databases, encoding or encrypting records using the privacy masking functions
[44], applying blocking or other forms of complexity reduction methods [6],
then matching records based on their QIDs using similarity functions [6], and
finally clustering or classifying matching records that correspond to the same
entity. Additional steps of evaluation of the linkage as well as manual review
of certain records are followed in non-PPRL applications. However, these two
steps require more research for PPRL as they generally require access to raw
data and ground truth which is not possible in a privacy-preserving context.

Despite several challenges, the output of PPRL could certainly bring in
enormous potential in the Big Data era for businesses, government agencies,
and research organizations. PPRL has been an active area of research in the
recent times and it is now being applied in real-world applications [5, 30].
In this chapter, we will describe some of the key research findings of PPRL
and example PPRL applications. We will also discuss directions for future
research in PPRL.

##  3 Key research findings

In this section, we present the key research findings in PPRL with regard to
the methodologies and technologies used, as characterized in Figure 1.

Figure 1: A taxonomy of methodologies and technologies used in PPRL.

###  3.1 Linkage model

Type of parties: Considering the number and type of parties involved, the
linkage model can be categorized as two-party or multi-party protocols with or
without one or several linkage units (LUs). Two database owners (DOs)/parties
involve in two-party protocols in order to identify the matching records in
their databases. This linkage model requires more sophisticated techniques to
ensure that the parties do not learn any sensitive information about each
other’s data. A LU is therefore commonly used in linkage models to
conduct/facilitate the linkage. A major drawback of LU-based protocols is that
they require a trusted LU in order to avoid possible collusion attacks, where
one of the DOs collude with the LU to learn about other DO’s data [44]. In
some models several (more than one) LUs are used, for example, one is
responsible for secret keys management, another one for facilitating the
complexity reduction step, while matching of records is conducted by a
different LU. Separating the tasks across several LUs reduces the amount of
information learned by a single party, however collusion could compromise the
privacy. In multi-party linkage the aim is to identify cluster of records from
multiple (more than two) databases that refer to the same entity. The linkage
process becomes complicated with the increase of number of databases.
Processing can be distributed among multiple parties to improve efficiency as
well as to improve privacy guarantees by reducing the amount of information
learned by a single party.

Linkage schema: The linkage schema dimension consists of feature selection,
schema matching, and schema optimization. Different types of QIDs have been
used for PPRL, with the most commonly used QIDs include name (string), address
(string or text), age (numeric), gender (categorical), and date of birth
(date). Schema matching identifies the common schema across different
databases [32]. The success of linkage depends on the parameter setting used
which needs to be tuned appropriately in order to optimize the linkage
results. Grid search and random search are two optimization methods, however
they tune parameters in an isolated way disregarding past evaluations of
parameter combinations [3]. Bayesian optimization can efficiently bring down
the time spent to get the optimal set of parameters [36] by taking into
account the information on the parameter combinations it has previously seen
thus far when choosing the parameter set to evaluate next.

###  3.2 Threat model

Adversary model: Different adversary models are assumed in PPRL methodologies
[44], which are categorized as honest-but-curious/semi-honest, malicious, and
advanced models. The semi-honest model is the most commonly used adversary
model in existing PPRL techniques [44], where the parties are assumed to
honestly follow the steps of the protocol while being curious to learn from
the information they received throughout the protocol. This model is not
realistic in real applications due to the weak assumption of privacy against
adversarial attacks. Malicious model, on the other hand, provides a strong
assumption of privacy such that the parties involved in the protocol may not
follow the steps of the protocol by deviating from the protocol, sending false
input, or behaving arbitrarily. However, more complex and advanced privacy
techniques are required to make the protocols resistant against such malicious
adversaries. Hybrid models, such as accountable computing and covert models,
lie in between the semi-honest model, which is not realistic, and the
malicious model, which requires computationally expensive techniques [44].

Attacks: Several attacks have been developed for PPRL techniques to
investigate the resistance of such techniques to those attacks. Frequency
attacks are most commonly used, where the frequency of encoded values are
mapped to the frequency of known unencoded values [41]. Collusion attacks are
possible in LU-based and multi-party models where subsets of parties collude
to learn another party’s data [41, 29]. More sophisticated attacks have been
developed against certain privacy techniques. For example, Bloom filters (as
described below) are susceptible to cryptanalysis attacks, which allow the
iterative mapping of bit patterns back to their original unencoded QID values
based on their frequency alignments depending upon the parameter setting used
[7, 23].

###  3.3 Evaluation model

Evaluation of the performance of PPRL consists of five main criteria:
Computation and communication costs determine the efficiency aspect that are
often measured either theoretically using the big-O notation [10] or
empirically using runtime, memory size, number of communication steps, number
and size of messages to be communicated, and number of comparisons required
[44]. Privacy guarantees are either formally proven or empirically measured
using metrics such as Information gain and disclosure risk metrics [41]
against privacy attacks. Correctness and fairness correspond to the linkage
quality aspect, where correctness is the accuracy of linkage results measured
using precision, recall, area under curve (AUC), and F1-measure [6], and
fairness is the accuracy of linkage results with regard to different subgroups
of individuals [46].

###  3.4 Technologies

Privacy technologies: We categorize the key privacy technologies as:

  1. 1.

Cryptography refers to secure multi-party computation techniques, such as
homomorphic encryptions, secret sharing, and secure vector operations [25].
These techniques are provably secure and highly accurate, however, they are
computationally expensive. An example PPRL technique based on cryptographic
techniques is the secure edit distance algorithm for matching two strings or
genome sequences [1], which is quadratic in the length of the strings.

  2. 2.

Embedding techniques allow data to be mapped into a multi-dimensional metric
space while preserving the distances between original data [32]. It is
difficult to determine the appropriate dimensionality for the metric space. A
recent work proposed a framework for embedding string and numerical data with
theoretical guarantees for rigorous specification of space dimensionality
[17].

  3. 3.

Differential privacy is a rigorous definition that provides guarantees of
indistinguishability of an individual regardless of the presence or absence of
the individual’s record in the data with high probability. It has been used in
PPRL to perturb data by adding noise such that every individual in the dataset
is indistinguishable [41, 44]. However, adding noise incurs utility loss and
volume increase. Output constrained differential privacy is a recently
introduced privacy model for PPRL that allows disclosing matching records
while being insensitive to the presence or absence of a single non-matching
record [14].

  4. 4.

Statistical linkage key (SLK) contains derived values from QIDs which is
generated using a combination of components of a set of QIDs. An example is
the SLK-581 consisting of the second and third letters of first name, the
second, third and fifth letters of surname, full date of birth, and sex, which
was developed by the Australian Institute of Health and Welfare to link
records from the Home and Community Care datasets [31]. A recent study has
shown that SLK-based techniques fall short in providing sufficient privacy
protection and sensitivity [31].

  5. 5.

Probabilistic methods are the most widely used techniques for practical PPRL
applications due to their efficiency and controllable privacy-utility trade-
off. These methods use probabilistic data structures for mapping/encoding data
such that the actual distances between original data are preserved depending
on the false positive probability of the mapping. A recent study has shown
that, if effectively used, probabilistic techniques can achieve high linkage
quality comparable to using unencoded records [30].

For example, Bloom filter encoding is one probabilistic method that has been
used in several PPRL solutions [12, 30, 33, 34, 38, 39]. A Bloom filter
$b_{i}$ is a bit array of length $l$ bits where all bits are initially set to
$0$. $k$ independent hash functions, $h_{j}$, with $1\leq j\leq k$, are used
to map each of the elements $s$ in a set $S$ into the Bloom filter by setting
the bit positions $h_{j}(s),1\leq j\leq k$ to $1$.

Figure 2: Bloom filter-based matching for string [33] (left) and numerical
[40] (right) data.

As shown in Figure 2, the set $S$ of $q$-grams (sub-strings of length $q$) for
string QIDs (left) or neighbouring values for numerical QIDs (right) can be
hash-mapped into Bloom filters [33, 40]. The resulting Bloom filters can be
matched using a similarity function, such as the Dice-coefficient [6] which is
calculated as: $Dice\\_sim(b_{1},\cdots,b_{p})=\frac{p\times
c}{\sum_{i=1}^{p}x_{i}}$, where $p$ is the number of Bloom filters compared,
$c$ is the number of common bit positions that are set to $1$ in all $p$ Bloom
filters, and $x_{i}$ is the number of bit positions set to $1$ in $b_{i}$,
$1\leq i\leq p$. The matching can either be done by a LU [12, 33] or
collaboratively by the DOs [38, 39].

Complexity reduction technologies: The bottleneck of the PPRL process is the
comparison of records across different databases using similarity functions,
which is equal to the product of the sizes of the databases. Computational
technologies have been used to improve the scalability of PPRL:

  1. 1.

Blocking is defined on selected attributes (blocking keys) and it partitions
the records in a database into several blocks or clusters based on the
blocking key values such that comparison can be restricted to the records of
the same block. A variety of blocking techniques has been developed [44].
Recent examples are randomized blocking methods based on Locality-Sensitive
Hashing, which provide theoretical guarantees for identifying similar record
pairs in the embedding space with high probability [12, 18].

  2. 2.

Meta-blocking is the process of restructuring a collection of generated blocks
to be compared in the next step such that unnecessary comparisons are pruned.
Block processing for PPRL only received much attention in the recent years
with the aim to improve the scalability in Big Data applications by employing
such techniques along with blocking techniques [16, 28].

  3. 3.

Filtering is an optimization technique for a particular similarity function to
eliminate pairs/sets of records that cannot meet the similarity threshold for
the selected similarity measure [34, 38].

  4. 4.

Parallel/distributed processing for PPRL has only seen limited attention so
far. Parallel linkage aims at improving the execution time proportionally to
the number of processors [9, 18]. This can be achieved by partitioning the set
of all record pairs to be compared, for example using blocking, and conducting
the comparison of the different partitions in parallel on different
processors.

  5. 5.

Advanced communication patterns can be used to reduce the exponential growth
of complexity for multi-party linkage. Such communication patterns include
sequential, ring by ring, tree-based, and hierarchical patterns. Some of these
patterns have been investigated for PPRL on multiple databases [42].

Linkage technologies: A variety of linkage methods and technologies has been
used.

  1. 1.

Similarity functions are required for fuzzy/approximate matching of QIDs in
order to account for data errors and variations in the QIDs used for linkage.
Different similarity functions have been used for different QID data types and
different encoding/masking functions. For example, Bloom filter encoding-based
PPRL requires token-based similarity functions, such as Jaccard, Hamming, or
Dice coefficient functions (as described above) [33, 12]. Similarly, embedding
techniques have used Euclidean or edit distance as similarity functions [32,
17].

  2. 2.

Matching techniques determine how the linkage of records needs to be
performed. It is a common practice to first de-duplicate records (internally
link) within a single database before linking with records from other
databases. This is known as one-to-one linking. If the databases are not de-
duplicated (i.e. they contain multiple records corresponding to the same real-
world entity), then many-to-many linking is required. Further, in multi-
database linking, subset matching is required in certain applications to
identify records that match across any subset of databases (for example,
patients visited at least three out of five hospitals) [43].

  3. 3.

Classification techniques, ranging from simple threshold-based, rule-based, to
probabilistic linkage and machine learning, have been used in the PPRL
literature [44]. The aim of these classifiers is to classify the record pairs
into ‘matches’ or ‘non-matches’ based on the similarity between their QIDs.
While machine learning-based classifiers can provide higher linkage quality,
they require training data with ground-truth labels (of ‘matches’ and ‘non-
matches’) for supervised techniques.

  4. 4.

Clustering is an unsupervised technique that aims to group matching records
corresponding to the same real-world entity into one cluster. A recent work
studies incremental clustering techniques for multi-party PPRL [43].

  5. 5.

Fairness-aware linkage is important to ensure fairness in linkage with respect
to vulnerable sub-groups of the population. Errors in the linkage will
propagate through to the subsequent data analysis. Fairness in the linkage
process enables fair upstream data analysis. Fairness-aware classification and
clustering algorithms have been developed in the literature [26], however,
mitigating fairness-bias specifically in PPRL has not yet been studied.

##  4 Examples of application

Linking data is increasingly being required in a number of application areas
[6]. When databases are linked within a single organization, then generally
privacy and confidentiality are not of great concern. However, linking data
from several organizations imposes legal and ethical constraints on using
personal data for the linkage, as described by the Australian Data-Matching
Program Act111https://www.legislation.gov.au/Details/C2016C00755, the EU
General Data Protection Regulation222https://gdpr.eu/, and the HIPAA Act in
the USA333http://www.hhs.gov/ocr/privacy/. PPRL is therefore required in
several real applications, as the following examples illustrate:

  1. 1.

Healthcare applications: Several healthcare applications ranging from health
surveillance, epidemiological studies, and clinical trials, to public health
research require PPRL as an efficient building block. For example, a study on
surgical treatment received by aboriginal and non-aboriginal people with lung
cancer linked data from hospitals and clinical registries with data from
central cancer registries and from the Australian Bureau of Statistics using
PPRL techniques [8]. Bloom filter-based PPRL was used to link data from
several cantonal and national registries in Switzerland to investigate long-
term consequences of childhood cancer [20]. In 2016, the Interdisciplinary
Committee of the International Rare Diseases Research Consortium launched a
task team to explore approaches to PPRL for linking several genomic and
clinical data sets [2].

  2. 2.

Government services and research: The traditionally used small-scale survey
studies have been replaced by linking databases to develop policies in a more
efficient and effective way [19]. The research program ‘Beyond 2011’
established by the Office for National Statistics in the UK, for example aimed
to study the options for production of population statistics for England and
Wales, by linking anonymous data [35]. Social scientists use PPRL in the field
of population informatics to study insights into our society [21].

  3. 3.

Business collaboration: Many businesses take advantage of linking data across
different organizations, such as suppliers, retailers, wholesalers, and
advertisers, for improving efficiency, targeted marketing, and reducing costs
of their supply chains. PPRL can be used for cross-organizational
collaborative decision making which involves a great deal of private
information that businesses are often reluctant to disclose [47].

  4. 4.

National security applications: PPRL techniques are being used by national
security agencies and crime investigators to identify individuals who have
committed fraud or crimes [27]. These applications integrate data from various
sources, such as law enforcement agencies, Internet service providers, the
police, tax agencies, government services, as well as financial institutions
to enable the accurate identification of crime and fraud, or of terrorism
suspects.

##  5 Future directions for research

In this section we describe the various open challenges and research
directions of PPRL for Big Data applications, as categorized in Figure 3.

###  5.1 Scalability

The _volume_ of data increases both due to the large size of databases and the
number of different databases. Challenges of linking large databases have been
addressed by using computational techniques to reduce the number of required
comparisons between records. However, these techniques do not solve the
scalability problem for Big Data completely. For example, even small blocks of
records resulting from a blocking technique can still lead to a large number
of comparisons between records with the increasing volume of data. Moreover,
only limited work has been done to address the challenges of linking multiple
databases.

Scalable blocking techniques are required that can generate blocks of suitable
sizes across multiple databases, as are advanced filtering techniques that
effectively prune potential non-matches even further. With multiple databases,
identifying subsets of records that match across only a subset of databases
(for example, patients in three out of five hospital databases) is even more
challenging due to the large number of combinations of subsets. Advanced
communication patterns, distributed computing, and adaptive comparison
techniques are required towards this direction for scalable PPRL applications.
These techniques are largely orthogonal so that they can be combined to
achieve maximal efficiency.

Figure 3: Challenges of PPRL for Big Data.

Another major aspect of Big Data is the _velocity_ , i.e. the dynamic nature
of data. Current techniques are only applicable in batch-mode on static and
well defined relational data. Required are approaches for dynamic data, real-
time integration, and data streams, for adaptive systems to link data as they
arrive at an organization, ideally in (near) real-time.

###  5.2 Linkage Quality

Big Data are often complex, noisy, and erroneous, which refer to the
_veracity_ and _variety_ aspects. The linkage can be affected by the quality
of data, especially in a privacy-preserving context where linkage is done on
the masked or encoded version of the data. Masking data reduces the quality of
data to account for privacy and hence the quality of data would have an
adverse effect on the whole PPRL process leading to low linkage quality. The
trade-off between quality and privacy needs to be handled carefully for
different privacy masking functions. The affect of poor data quality on the
linkage quality becomes worse with increasing number of databases. More
advanced classification techniques, such as collective [4] and graph-based
[15] techniques, need to be investigated to address the linkage quality
problem of PPRL.

Developing classifiers that are fair with respect to a protected/sensitive
feature [46], such as gender or race, is an important problem for
classification in general and specifically for record linkage. Fairness of a
classifier with regard to a certain protected feature determines how much the
classifier distorts from producing correct predictions with equal
probabilities for individuals across different protected groups/values. There
has been increased interest in this field due to the concerns that classifiers
may introduce significant bias towards certain minority or vulnerable group
with regard to the protected feature, such as race or gender, for example
against black people in fraud and crime detection systems [13, 24] or against
women in job recommendation systems [11]. However, fairness has not been
studied specifically for PPRL so far.

Assessing the linkage quality in a PPRL project is very challenging because it
is generally not possible to inspect linked records due to privacy concerns.
Knowing the quality of linkage is crucial in many Big Data applications such
as in the health or security domains. An initial work has been done on
interactive PPRL [22] where parts of sensitive values are iteratively revealed
for manual assessment in such a way that the privacy compromise is limited.
Implementing such approaches in real applications is an open challenge that
must be solved. Using heuristic measures to approximately evaluate the linkage
quality is another option that requires more research.

###  5.3 Privacy

Another open challenge in PPRL is how resistant the techniques are against
different adversarial attacks. Most work in PPRL assume the _semi-honest_
adversary model [25] and the trusted LU-based model. Furthermore, these works
assume that the parties do not collude with each other [44]. Only few PPRL
techniques consider the _malicious_ adversary model as it imposes a high
complexity [44]. More research is therefore required to develop novel security
models that lie between these two models and prevent against collusion risks
for PPRL.

Sophisticated attack methods [7, 23] have been recently developed that exploit
the information revealed during the PPRL protocols to iteratively gather
information about sensitive values. Therefore, existing PPRL techniques need
to be hardened to ensure they are not vulnerable to such attacks [33].
Evaluation of PPRL techniques is challenged due to the absence of benchmarks,
datasets, and frameworks. Different measurements have been used [12, 41, 44],
making the comparison of different PPRL techniques difficult. Synthetic
datasets generated with real data characteristics using data generators [37]
have been used as an alternative to benchmark datasets. This limits the
evaluation of PPRL techniques to assess their application in the real setting.

Further, there has not been much interaction between practitioners and
researchers of PPRL to allow better understanding of the whole data life cycle
and to evaluate the applicability of PPRL in real applications. A
comprehensive privacy strategy is essential including a closely aligned PPRL
and privacy-preserving data technologies for strategic Big Data applications.

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