Fermionic quantum computation with Cooper pair splitters

Kostas Vilkelis1*, 2, Antonio Manesco2†, Juan Daniel Torres Luna1, Sebastian
Miles1, Michael Wimmer1, Anton Akhmerov2

1 Qutech, Delft University of Technology, Delft 2600 GA, The Netherlands

2 Kavli Institute of Nanoscience, Delft University of Technology, Delft 2600
GA, The Netherlands

*<EMAIL_ADDRESS><EMAIL_ADDRESS>
## Abstract

We propose a practical implementation of a universal quantum computer that
uses lo- cal fermionic modes (LFM) rather than qubits. Our design consists of
quantum dots tunnel coupled by a hybrid superconducting island together with a
tunable capacitive coupling between the dots. We show that coherent control of
Cooper pair splitting, elastic cotunneling, and Coulomb interactions allows us
to implement the universal set of quantum gates defined by Bravyi and Kitaev
[1]. Finally, we discuss possible limitations of the device and list necessary
experimental efforts to overcome them.

###### Contents

  1. 1 Introduction
  2. 2 Design
  3. 3 Effective Hamiltonian
    1. 3.1 Tunnel coupling
    2. 3.2 Capacitive coupling
  4. 4 Fermionic quantum gates
    1. 4.1 Unitary gate operations
    2. 4.2 Finite Zeeman splitting in the middle dot
    3. 4.3 Gate performance
  5. 5 Future directions
  6. 6 Summary
  7. A Schieffer-Wolff transformation
  8. B Convenience of the anti-parallel spin configuration
    1. B.1 Orthogonality with symmetric spin precession
    2. B.2 Stability and number of operations

##  1 Introduction

#### Simulation of fermionic systems with qubits is inefficient.

Over the years, qubits emerged as the de facto basis for quantum computation
with a plethora of host platforms: superconducting circuits [2, 3], trapped
ions [4, 5] and quantum dots [6], to name a few. Recent works used qubit-based
quantum computers to simulate fermionic systems [7, 8, 9]. However, the
mapping from qubits to local fermionic modes (LFMs) is inefficient because it
introduces additional overhead to the calculations [10, 11]. For example, a
map from $n$ qubits to fermions requires $O(n)$ additional operations through
the Jordan-Wigner transformation [12] and $O(\log{n})$ through the Bravyi-
Kitaev transformation [1].

#### Local fermionic modes are better for all problems.

An alternative to avoid the overhead in the qubit to LFM map is to use a
quantum computer that already operates with local fermionic modes [1].
Moreover, the advantage of local fermionic modes is not limited to the
simulation of fermionic systems. A set of $2n$ local fermionic modes maps
directly to $n$ parity-preserving qubits, which corresponds to $n-1$ qubits.
Therefore, the map from local fermionic modes to qubits only requires a
constant number of operations regardless of the system size and is, therefore,
more efficient than the reverse [1]. Recently, Ref. [13, 14] showed that local
fermionic modes offer advantages in quantum optimization problems of finding
the ground state energy of fermionic Hamiltonians.

#### We propose an experimental implementation of universal LFMs based on
recent advances in Cooper pair splitters

Motivated by this advantage of local fermionic modes over qubits, we propose
an experimental implementation of a quantum computer with local fermionic
modes. Our device is inspired by recently reported Cooper pair splitters [15,
16, 17, 18, 19, 20], and our design includes an additional tunable capacitance
to control Coulomb interactions. We show that the device implements the
necessary universal set of gates proposed by Bravyi and Kitaev [1]. We also
discuss the limitations of the device.

##  2 Design

#### Quantum computation with LFMs requires a universal set of gates

Figure 1:  The unit cell of a fermionic quantum computer. Two singly-occupied
spin-(anti)polarized quantum dots host the local fermionic modes $L$ and $R$.
Two tunnel barriers enable normal $t$ and spin-dependent $t_{SO}$ tunnelings
between the two dots. A middle superconducting island mediates superconducting
correlations between the two local fermionic modes. An external mutual
capacitor $C_{m}$ allows Coulomb interactions between the sites.

Bravyi and Kitaev [1] showed that fermionic quantum computation is equivalent
to parity-preserving qubit operations. As a consequence, given a set of
fermionic creation ($c^{\dagger}_{i}$) and annihilation operators ($c_{i}$),
it follows that

$\left\\{\begin{array}[]{c}\mathcal{U}_{1}(\alpha)=\exp\left(i\alpha
c^{\dagger}_{i}c_{i}\right)~{},\quad\mathcal{U}_{2}(\beta)=\exp\left[i\beta\left(c^{\dagger}_{i}c_{j}+c^{\dagger}_{j}c_{i}\right)\right]~{},\\\\[8.0pt]
\mathcal{U}_{3}(\gamma)=\exp\left[i\gamma\left(c^{\dagger}_{i}c^{\dagger}_{j}+c_{j}c_{i}\right)\right]~{},\quad\mathcal{U}_{4}(\delta)=\exp\left(i\delta
c^{\dagger}_{i}c_{i}c^{\dagger}_{j}c_{j}\right)\end{array}\right\\}$ (1)

with $\alpha=\beta=\gamma=\pi/4$, and $\delta=\pi$, is a universal set of gate
operators. The case of two LFMs is similar to two uncoupled qubits: each
operation within a given fermion parity sector is a rotation within
$\mathrm{SU}(2)$. In the odd fermion parity sector, the operations
$\mathcal{U}_{1}(\alpha)$ and $\mathcal{U}_{2}(\beta)$ are rotations around
perpendicular axes in the Bloch sphere. Likewise $\mathcal{U}_{3}(\gamma)$ and
$\mathcal{U}_{1}(\delta)$ are perpendicular rotations within the even fermion
parity sector. In the presence of an extra ancilla LFM, applying
$\mathcal{U}_{4}$ entangles the even and odd subspaces of the two
computational LFMs.

#### Gates processes have a simple physical interpretation within the spin-
polarized quantum dots platform

We thus propose a device where excitations occupy single-orbital sites,
numbered by the subindex $i$ and $j$. A practical platform for such a proposal
is an array of spin-polarized quantum dots, as the scheme shown in Fig. 1.
Within this platform, the unitary operations in Eq. 1 are a time-evolution of
the following processes:

  1. 1.

$c^{\dagger}_{i}c_{i}$ onsite energy shift of the fermionic state at site $i$;

  2. 2.

$c^{\dagger}_{i}c_{j}$ hopping of a fermion between sites $i$ and $j$;

  3. 3.

$c^{\dagger}_{i}c^{\dagger}_{j}$ superconducting pairing between fermions at
sites $i$ and $j$;

  4. 4.

$c^{\dagger}_{i}c_{i}c^{\dagger}_{j}c_{j}$ Coulomb interaction between
fermions at sites $i$ and $j$.

#### Plunger and tunnel gates control the onsite and hopping processes in
quantum dots

We control the onsite energies $\mu_{i}$ with plunger gates. Similarly, a
tunnel gate between neighboring pairs of quantum dots controls hopping
strength $t$ between them. Manipulation with plunger and tunnel gates is a
well-established technique in charge [21, 22] and spin [6] qubits.

#### We generate pairing between two quantum dots by using a Cooper pair
splitter

To implement the superconducting coupling between the spin-polarized dots, we
utilize the design of a triplet Copper pair splitter [16, 17, 18, 19, 20]. We
include an auxiliary quantum dot in proximity to an s-wave superconductor
mediating crossed Andreev reflection (CAR) and elastic cotunelling (ECT)
between the two quantum dots that encode the LFMs. Thus, the ECT rate $\Gamma$
sets the hopping strength between the two dots, whereas the CAR rate $\Lambda$
sets the effective superconducting pairing. Because the dots are spin-
polarised, the superconducting pairing must be of spin-triplet, enabled by
spin-orbit hopping in the hosting material. We quantify the spin-orbit
coupling in the hosting material by the spin precession angle between the dots
$\theta_{i}=2\pi d/l_{so}$, where $d$ is the interdot distance and $l_{so}$ is
the spin-orbit length. The spin-orbit coupling in InSb wires leads to a spin-
precession length $l_{\textrm{so}}\approx$100\text{\,}\mathrm{nm}$$ [23, 24]
resulting on non-negligible $\theta_{i}$ within the order of dot-to-dot
distance.

#### Capacitive coupling between two quantum dots defines the interaction
between LFMs

Finally, we achieve Coulomb interaction between a pair of dots through
capacitive coupling $C_{m}$. Our design requires a variable capacitive
coupling to implement the $\mathcal{U}_{4}$ gate. Several recent works
demonstrate variable capacitive coupling in various platforms: gate-tunable
two-dimensional electron gas [25], varactor diodes [26], and external double
quantum dots [27].

#### The three-site device defines the unit cell of the LFM quantum computer

We show the unit cell of a fermionic quantum computer with two LFMs in Fig. 1.
The basic building block consists of three tunnel-coupled quantum dots in a
material with large spin-orbit coupling. The middle dot is proximitized by an
$s$-wave superconductor with an induced gap $\Delta$ that mediates CAR and ECT
between the outer dots. The spin-polarised outer dots ($L,R$) encode the LFMs,
whereas the middle one is an auxiliary component. Finally, a tunable capacitor
couples the outer dots. We generalize the device to an arbitrary number of
LFMs by repeating the unit cell in a chain. To read out the fermionic state,
we propose to measure the occupation in each quantum dot through charge
sensing [28].

##  3 Effective Hamiltonian

###  3.1 Tunnel coupling

#### We consider the limit of spin-polarised quantum dots.

In the absence of capacitive and tunnel coupling, the approximate Hamiltonian
for the two spin-polarised dots is

$H_{d}=\sum_{i=L,R}\mu_{i}c^{\dagger}_{i\sigma_{i}}c_{i\sigma_{i}}~{},$ (2)

where $c_{i\sigma}$ is the electron anihilation operator at site $i$ and spin
$\sigma$, and $\mu_{i}$ is the corresponding chemical potential. The
Hamiltonian in Eq. (2) is valid if the charging energy and Zeeman splitting on
each dot are larger than all other energy scales in the problem. Recent
experiments on similar devices measure charging energy of
$2\text{\,}\mathrm{meV}$ and Zeeman splitting of
$400\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ at $200\text{\,}\mathrm{mT}$ [16,
17, 19, 20]. Both charging energy and Zeeman splitting are larger than the
usual induced superconducting gap inside the quantum dot
$\Delta\sim$100\text{\,}\mathrm{\SIUnitSymbolMicro eV}$$ [20, 29, 30],
justifying the approximation in Eq. (2).

#### The middle quantum dot is proximitized by a superconductor.

The proximity of the middle dot to the superconductor suppresses its
$g$-factor [31]. Thus, differently from the outer dots, we consider a finite
Zeeman energy $B$. The Hamiltonian of the middle dot is

$\displaystyle
H_{\text{ABS}}=\sum_{\sigma,\sigma^{\prime}}\left[\mu_{M}(\sigma_{0})_{\sigma\sigma^{\prime}}+B(\sigma_{z})_{\sigma\sigma^{\prime}}\right]c_{M\sigma}^{\dagger}c_{M\sigma^{\prime}}+\Delta
c^{\dagger}_{M\uparrow}c^{\dagger}_{M\downarrow}+\text{h.c.}$ (3)

where $c_{M\sigma}^{\dagger}$ is the creation operator of electron on the
middle dot with spin $\sigma$, $\Delta$ is the induced superconducting gap,
and $\sigma_{l}$ are the Pauli matrices ($l=\\{0,x,y,z\\}$) acting on the spin
subspace.

#### The dots are connected by normal and spin-orbit hoppings.

Both spin-polarised dots in Eq. (2) connect to the middle dot by symmetric
tunnel barriers with strength $t$. The barrier $t$ controls both normal and
spin-orbit tunneling processes:

$H_{t}=t\sum_{i=L,R}\cos\theta_{i}c_{i\sigma_{i}}^{\dagger}c_{M\sigma}+it\sum_{i=L,R}\sum_{\sigma^{\prime}}(\sigma_{y})_{\sigma_{i}\sigma^{\prime}}\sin\theta_{i}c_{i\sigma_{i}}^{\dagger}{c_{M\sigma^{\prime}}}+\text{h.c.}~{},$
(4)

where $\theta_{i}$ is the spin precession angle from dot $i$ to the middle
island. Thus, the total Hamiltonian is

$H=H_{d}+H_{\text{ABS}}+H_{t}~{}.$ (5)

#### We treat doubly-occupied states in the middle quantum dot perturbatively.

We obtain the effective low-energy Hamiltonian in the weak-coupling limit,
$t\ll\Delta$, through a Schrieffer-Wolf (the derivation is in Appendix A) [32,
33]:

$\tilde{H}=\sum_{i}\epsilon_{i}^{\sigma_{i}\sigma_{j}}c_{i\sigma_{i}}^{\dagger}c_{i\sigma_{i}}+\sum_{i,j}\Gamma_{\sigma_{i}\sigma_{j}}c^{\dagger}_{i\sigma_{i}}c_{j\sigma_{j}}+\Lambda_{\sigma_{i}\sigma_{j}}c^{\dagger}_{i\sigma_{i}}c^{\dagger}_{j\sigma_{j}}+\text{h.c.}~{},$
(6)

where $\epsilon_{i}^{\sigma_{i}\sigma_{j}}$ is the renormalised onsite energy
of dot $i$, $\Gamma_{\sigma_{i}\sigma_{j}}$ is the ECT rate and
$\Lambda_{\sigma_{i}\sigma_{j}}$ is the CAR rate. While $t\neq 0$, we do not
vary the chemical potential of the outer dots, $\mu_{L}=\mu_{R}=0$. For
simplicity, we also assume no Zeeman splitting within the middle dot $B=0$ and
that the spin precession angles are symmetric $\theta_{L}=\theta_{R}=\theta$
(see Appendix A for more general form). In such case, the effective parameters
for the anti-parallel spin configuration are:

$\displaystyle\Lambda_{\uparrow\downarrow}=\kappa\Delta\cos(2\theta)~{},\quad\Gamma_{\uparrow\downarrow}=-i\kappa\mu_{M}\sin{\left(2\theta\right)}~{},$
(7)

and for the parallel channel:

$\displaystyle\Lambda_{\uparrow\uparrow}=-i\kappa\Delta\sin{\left(2\theta\right)}~{},\quad\Gamma_{\uparrow\uparrow}=-\kappa\mu_{M}\cos{\left(2\theta\right)}~{},$
(8)

where

$\kappa=t^{2}/(\Delta^{2}+\mu_{M}^{2}-B^{2})~{}.$ (9)

Both onsite corrections terms are equal:

$\epsilon_{L}^{\sigma_{i}\sigma_{j}}=\epsilon_{R}^{\sigma_{i}\sigma_{j}}=\kappa\mu_{M}.$
(10)

We observe that the magnitude of $\Lambda_{\sigma_{i}\sigma_{j}}$ is maximum
at $\mu_{M}=0$ and drops with increasing chemical potential $\mu_{M}$. On the
other hand, $\Gamma_{\sigma_{i}\sigma_{j}}$ has maxima at finite $\mu_{M}$.
The magnitude of both processes depends on the spin-precession angle $\theta$
and spin configuration of the outer dots as shown in Fig. 2 (a) and (b). To
ensure that operation times for $\mathcal{U}_{2}$ and $\mathcal{U}_{3}$ are
similar, the convenient regime is where
$\max\Gamma_{\sigma_{i}\sigma_{j}}\sim\max\Lambda_{\sigma_{i}\sigma_{j}}$.

Figure 2: Absolute value of $\Lambda$ (blue) and $\Gamma$ (orange) as a
function of $\mu_{M}$ for different values of $B$ for the anti-parallel
configuration (a) and the parallel configuration (b). System parameters are
$t=0.15$, $\theta_{L}=0.7$ and $\theta_{R}=0.3$.

###  3.2 Capacitive coupling

#### The tunable capacitor mediates the Coulomb interaction between the dots.

The electrostatic energy between the two dots is [34]:

$\displaystyle
H_{C}=\sum_{i=L,R}\upsilon_{i}c_{i\sigma_{i}}^{\dagger}c_{i\sigma_{i}}+U_{m}c_{L\sigma_{L}}^{\dagger}c_{L\sigma_{L}}c_{R\sigma_{R}}^{\dagger}c_{R\sigma_{R}}~{},$
(11)

where $U_{m}=C_{m}e^{2}/\tilde{C}$ is the mutual interaction between the two
dots,

$\upsilon_{L/R}=\frac{C_{R/L}(2n_{g,L/R}+1)+C_{m}n_{g,R/L}}{2\tilde{C}}$ (12)

is the renormalization to the onsite energy, $\tilde{C}=C_{L}C_{R}-C_{m}^{2}$,
$C_{L}$ and $C_{R}$ are the capacitances of the left and right dots, $C_{m}$
is the mutual capacitance, and $n_{g,i}$ is the charge offset in the site $i$.
Notice that we consider singly-occupied dots in (11). This approximation is
valid when $U_{m}\ll\Delta\ll e^{2}C_{L/R}/\tilde{C}$ because the charging
energy renormalization due to the mutual capacitance is negligible in this
regime. The last term in (11) gives the Coulomb interaction between the dots
required to implement $\mathcal{U}_{4}$.

##  4 Fermionic quantum gates

###  4.1 Unitary gate operations

#### We switch the system parameters on and off to implement operations.

To achieve the fermionic quantum operations defined in Eq. (1), we need to
engineer specific time-dependent profiles for the tunable system parameters.
In this case, we control the following system parameters through Eqs. (11) and
(6): left and right plunger gates ($\mu_{L},\mu_{R}$), middle plunger gate
($\mu_{M}$), tunnel gates ($t$, we treat the two tunnel gates together), and
mutual capacitance ($C_{m}$). For simplicity, we only consider square pulses
in time

$\displaystyle H(\tau)=H_{P}(S)[\Theta(\tau)-\Theta(\tau-\tau_{P})]$ (13)

where $\Theta(\tau)$ is the Heaviside step function, $\tau$ is time and
$\tau_{P}$ is the duration of the pulse. We define the pulse Hamiltonian
$H_{P}(S)$ as a constant total Hamiltonian where
$S=\left\\{t,\mu_{M},...\right\\}$ are non-zero system parameters in the
pulse. For example, $H_{P}(\\{t\\})$ is a constant Hamiltonian with all system
parameters zero except the tunnel coupling $t$. We set the idle (reference)
Hamiltonian to one where all gates are zero, $t=\mu_{L}=\mu_{R}=\mu_{M}=U=0$.
Thus, the time-evolution operator simplifies to

$\displaystyle\mathcal{U}(\tau_{2},\tau_{1})=\exp\left[-\frac{i}{\hbar}\int_{\tau_{1}}^{\tau_{2}}d\tau^{\prime}~{}H(\tau^{\prime})\right]=\exp\left[-\frac{i}{\hbar}H_{P}(S)\tau_{P}\right]~{}.$
(14)

where $\tau_{2},\tau_{1}$ are the initial and final times, and $\tau_{P}$ is
the duration of the pulse. In practice, the transition between the idle
Hamiltonian and $H_{P}$ in Eq. (13) is not instantaneous but ramps up smoothly
over a time $\tau_{R}$ to minimize non-adiabatic transitions.

#### We design a minimal pulse sequence scheme that implements the universal
LFM operations at $B=0$

We engineer the unitary operations as an ordered sequence of pulses defined in
Eq. (14). For simplicity, we assume no Zeeman splitting in the middle dot,
$B=0$, and leave the discussion of the more general case to section 4.2. In
this case, the minimal pulse sequence scheme which implements the gates in Eq.
(1) is:

  1. 1.

onsite operation:

$\mathcal{U}_{1}=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L},\mu_{R}\\}\right)\tau_{P}\right]~{};$
(15)

  2. 2.

hopping operation:

$\displaystyle\begin{aligned}
\mathcal{U}_{2}&=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L}=\mu,\mu_{R}=\mu\\}\right)\tau_{P}^{(4)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t\\}\right)\tau_{P}^{(3)}\right]\\\
&\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L}=\mu,\mu_{R}=\mu\\}\right)\tau_{P}^{(2)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t,\mu_{M}\\}\right)\tau_{P}^{(1)}\right]\end{aligned}$
(16)

  3. 3.

superconducting pairing operation:

$\mathcal{U}_{3}=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t\\}\right)\tau_{P}\right]~{};$
(17)

  4. 4.

Coulomb interaction operation:

$\mathcal{U}_{4}=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L},\mu_{R}\\}\right)\tau_{P}^{(2)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{U\\}\right)\tau_{P}^{(1)}\right]~{};$
(18)

where we indicate as $\tau_{P}^{(i)}$ the duration of the $i$-th pulse.

#### Some gates require a single pulse because there is no renormalization of
other parameters.

In the above scheme, the operations $\mathcal{U}_{1}$ and $\mathcal{U}_{3}$
require a single pulse. The gate $\mathcal{U}_{1}$ requires a single pulse
because the dots are uncoupled from one another and the plunger gates affect
the onsite energies without inducing any sort of coupling between the dots.
Similarly, $\mathcal{U}_{3}$ is also a single operation because the CAR rate
is maximum at $\mu_{M}=0$ whereas both ECT rate and onsite corrections are
zero according to Eqs. (7— 10). We show the time-dependent simulation of the
$\mathcal{U}_{3}$ gate in Fig. 3.

#### The pulses that lead to unwanted renormalizations require correction
gates.

On the other hand, the first pulse of Eq. (16) introduces finite onsite
corrections to the outer dots and CAR according to Eqs. (7— 10). Since the
onsite corrections are equal, only a global phase factor is accumulated within
the odd fermion parity sector. On the other hand, both onsite corrections and
CAR result in undesired rotations within the even fermion parity subspace. We
undo these operations with an Euler rotation using two orthogonal operations,
resulting in the three subsequent pulses in Eq. (16). Similarly, the Coulomb
operation in Eq. (18) also requires a correction puls with the plunger gates
because the mutual capacitance $C_{m}$ renormalizes the onsite energies in the
outer dots, as shown in Eq. (11).

###  4.2 Finite Zeeman splitting in the middle dot

#### Zeeman field makes the Hamiltonian asymmetric.

The presence of Zeeman splitting in the middle dot $B$ introduces (see
Appendix A) an asymmetric the onsite renormalisation
$\epsilon_{L}^{\sigma_{i}\sigma_{j}}\neq\epsilon_{R}^{\sigma_{i}\sigma_{j}}$
and a shift in the minima of $\Gamma_{\sigma_{i}\sigma_{j}}$ shifts away from
$\mu_{M}=0$, as shown in Fig. 2. These changes affect the prescriptions for
$\mathcal{U}_{2}$ and $\mathcal{U}_{3}$ since these operations require finite
$t$.

#### Applied operations becomes non-orthogonal to $\mathcal{U}_{1}$.

The asymmetric onsite corrections break the orthogonality between
$\mathcal{U}_{1}$ and the unitary operation prescribed in Eq. (16). It is
still possible to implement the $\mathcal{U}_{2}$ with two non-orthogonal
rotation axes in the odd fermion parity sector with additional operations to
compensate for the non-orthogonality [35].

#### Zeeman field and spin-orbit asymmetry induce a finite ECT while applying
a CAR operation.

The operation in Eq. (17) also introduces finite
$\Gamma_{\sigma_{i}\sigma_{j}}$ in the odd parity sector. We show in Appendix
B that anti-parallel spin configuration with symmetric spin-orbit precession
$\theta_{L}=\theta_{R}$ removes the shifting $\Lambda$ minima away from
$\mu_{M}=0$ and restores the orthogonality of the operations within the even
parity sector.

###  4.3 Gate performance

Figure 3: Time-dependent simulation of pairing gate $\mathcal{U}_{3}$ acting
on an initial vacuum state with different pulse rise time $\tau_{R}$ profiles.
The vacuum population is $\left|\psi_{00}\right|^{2}$ whereas the double
occupation population (with middle dot unoccupied) is
$\left|\psi_{11}\right|^{2}$. Longer pulses (a) result in a smoother transient
population profile (b) and less leakage into the middle ABS state (c). The
configuration is the spin-antiparallel with finite Zeeman field within the
middle dot $B/\Delta=0.2$ and symmetric spin-orbit precession
$\theta_{L}=\theta_{R}=\pi/8$

#### Short pulse rise times induce transitions outside LFM dots

Switching on the pulse in Eq. (13) happens over a finite rise time $\tau_{R}$.
Short rise times $\tau_{R}$ induce transitions from the LFM dots into the
middle ABS at energy $\sim\Delta$ which limits the performance of the gates.
To avoid such transitions, the pulse times need to be
$\tau_{R}\gg\hbar/\Delta$. In Fig. 2 we show the time-dependent simulation of
the gate $\mathcal{U}_{3}$ with different rise times. We find that rise times
$\tau_{R}>2\hbar/\Delta$ ensures negligible transitions into the ABS. In a
system of $\Delta=$100\text{\,}\mathrm{\SIUnitSymbolMicro eV}$$ that
corresponds to rise times of $\tau_{R}>$13\text{\,}\mathrm{ps}$$.

#### Residual capacitance decoheres the device

Current tunable capacitors [25, 26] vary over a limited range. The upper limit
for the ratio between the maximum and minimum capacitance
$r=C_{\textrm{off}}/C_{\textrm{on}}$ is $r\approx 40$ [25, 26]. Thus, there is
a non-negligible residual capacitance between the dots when the
$\mathcal{U}_{4}$ gate is off. This residual capacitance acts as an unwanted
source of phase and limits the performance of the device. Because such error
is coherent, we argue it is possible to offset it after each or a few
operations with a compensating $\mathcal{U}_{4}$ pulse. However, since
$[\mathcal{U}_{3},\mathcal{U}_{4}]\neq 0$, the $\mathcal{U}_{3}$ operation
would require similar compensation pulses to Eq. (16) to offset the effect of
the residual capacitor.

##  5 Future directions

#### Charge noise is likely the key limiting factor of the device.

Although the device we proposed has the ingredients to implement universal
fermionic gates, further work is required to mitigate the main sources of
errors. Because of its similarities to a quantum dot charge qubit, we expect
the limiting decoherence mechanism to be the same - charge noise [36]. Typical
coherence times are on the order of a few nanoseconds [36, 21, 37, 38]. In
comparison, Dvir et al. [20] reports CAR/ECT strengths of
$\hbar/\Gamma_{\textrm{CAR/ECT}}\approx$10\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$ from which we estimate the gate pulse of our proposed device to be
$\approx$50\text{\,}\mathrm{ps}$$. On the other hand, if the outer dots in the
device shown in Fig. 1 are also proximitized by a superconductor, the local
fermionic modes would be encoded by Andreev quasiparticles. Because Andreev
states are linear combinations of electron and hole-like excitations, it is
possible to design a device that operates with neutral fermions. A similar
idea was recently proposed to avoid charge noise in fermion-parity qubits
[39]. Finally, minimization of the main sources of errors allows
implementation of error-correction codes for fermionic systems [40].

#### Control of induced superconductive gap would simplify the hopping
operation

In the current device, superconducting pairing persists under all possible
parameters. Because of that, the hopping operation in Eq. (16) requires a
complicated procedure in order to remove the effects of the induced
superconducting gap. To simplify the hopping operation, we suggest using a
device that allows control of the amount of induced superconducting pairing
into the middle dot. For example, a tunnel barrier between the middle dot and
the superconducting lead would mediate the induced superconducting pairing.
Alternatively, connecting the middle dot to two superconducting leads and
controlling the phase difference between them would also allow to control the
induced superconducting pairing.

#### Our device has limited geometry.

Our proposed device consists of a chain of single-orbital fermionic sites. The
device layout is a limiting factor, as it only allows nearest-neighbor
hoppings, superconducting pairing, and electrostatic interactions. The layout
limitations are detrimental to effective scalability. Thus, future works could
for example generalize the model to, for example, two-dimensional lattices.

#### Our device is a ready-to-use static simulator of one-dimensional
Hamiltonians with nn interactions.

We showed that the proposed device is a building block of a fermionic quantum
computer. However, we must also emphasize that the high control of the system
parameters allows to use the same device as a quantum simulator. For example,
a chain-like device with the unit cell shown in Fig. 1 at finite $\Gamma$ and
$U$ can be directly mapped to the Heisenberg model. Thus, together with
superconducting correlations, these devices would be an extension of other
quantum dot platforms [41].

#### Another way to get the interdot Coulomb interaction is with a floating
superconducting island.

We mentioned in Sec. 4 that all tunable capacitors proposed present a residual
mutual capacitance $C_{\mathrm{off}}$. The external capacitor is necessary
because direct mutual capacitance is suppressed by the charge screening in the
superconducting island. On the other hand, a floating superconducting island
offers a direct interdot capacitance [42]. In a device with a switch between a
floating and grounded superconductor, there would be direct control of the
mutual capacitance. Moreover, the large charge screening due to the grounded
superconducting island sets $C_{\mathrm{off}}\approx 0$, removing the need to
fix offset phases due to the residual capacitance.

##  6 Summary

We showed that Copper pair-splitting devices with tunable capacitors make up a
building block of a fermionic quantum computer. We derived the low-energy
Hamiltonian and showed that it contains all the necessary processes to build a
universal set of gate operations. Moreover, we showed how to use
experimentally controllable parameters to implement the gate operations. We
find that the presence of Zeeman splitting in the superconducting island
complicates the implementation of gates and necessitates additional steps.
Based on the low-energy theory, we also studied optimal regimes for the device
operation. While our design was mostly inspired by recent experiments, we also
discussed how to avoid foreseeable limitations such as (i) the use of neutral
fermions to suppress charge noise; (ii) a floating superconducting island to
simplify the layout; (iii) control of the superconducting gap to simplify gate
operations.

## Acknowledgements

The authors acknowledge the inputs of: Isidora Araya Day on perturbation
theory calculations; Mert Bozkurt and Chun-Xiao Liu on the device conception
and development of an effective model; Christian Prosko, Valla Fatemi, David
van Driel, Francesco Zatelli, and Greg Mazur on the experimental feasibility.

### Data Availability

All code used in the manuscript is available on Zenodo [32].

### Author contributions

A.A and M.W. formulated the initial project idea and advised on various
technical aspects. K.V. and A.M. supervised the project. K.V., A.M. and J.T.
developed the effective model and the device design. K.V., A.M., J.T, and S.M.
constructed the gate operations. K.V. performed the time-dependent
calculations. All authors contributed to the final version of the manuscript.

### Funding information

The project received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation program grant
agreement No. 828948 (AndQC). The work acknowledges NWO HOT-NANO grant
(OCENW.GROOT.2019.004) and VIDI Grant (016.Vidi.189.180) for the research
funding.

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##  Appendix A Schieffer-Wolff transformation

#### We rewrite the middle dot Hamiltonian in Andreev basis.

To obtain the effective Hamiltonian from Eq. (6), we perform a Schieffer-Wolff
transformation. We, first, diagonalize the Hamiltonian of the middle dot in
Eq. (3):

$H_{\text{ABS}}=(\epsilon_{\text{ABS}}+B)\gamma_{\uparrow}^{\dagger}\gamma_{\uparrow}+(\epsilon_{\text{ABS}}-B)\gamma_{\downarrow}^{\dagger}\gamma_{\downarrow}~{},$
(19)

where $\epsilon_{\text{ABS}}=\sqrt{\Delta^{2}+\mu_{M}^{2}}$, $\gamma_{\sigma}$
are the annihillation operators of Andreev quasiparticles

$\displaystyle\gamma_{\uparrow}^{\dagger}=uc^{\dagger}_{M\uparrow}+vc_{M\downarrow}~{},\quad\gamma_{\downarrow}^{\dagger}=uc^{\dagger}_{M\downarrow}-vc_{M\uparrow}~{},$
(20)

and $u$ and $v$ are the coherence factors.

#### Unnocupied states in the middle dot form our low-energy manifold.

We now define the occupation basis for the many-body states as
$|n_{L},n_{M},n_{R}\rangle$, where $n_{i}$ corresponds to the occupation
number at the site $i$. Notice that for the middle dot, we define the number
operator as $\hat{n}_{M\sigma}=\gamma_{M\sigma}^{\dagger}\gamma_{M\sigma}$,
whereas in the outer dots
$\hat{n}_{i\sigma_{i}}=c_{i\sigma_{i}}^{\dagger}c_{i\sigma_{i}}$. Because we
consider $\mu_{L/R},B\ll\Delta$, in the absence of hopping between the dots,

$\langle n_{L},0,n_{R}|H|n_{L},0,n_{R}\rangle\ll\langle
n_{L},n_{M},n_{R}|H|n_{L},n_{M},n_{R}\rangle~{},$ (21)

for $n_{L/R}\in\\{0,1\\}$, and $n_{M}>0$. Thus, the states with zero
occupation in the middle dot form our low-energy manifold.

#### When the hopping is small, we can treat it as a perturbation.

Occupied states in the middle dot are separated by an energy $\sim\Delta$ from
the low-energy manifold. In the weak coupling limit $t\ll\Delta$, the high-
energy subspace only contributes to the low-energy dynamics through virtual
processes. Therefore, we use a Schieffer-Wolff transformation to obtain the
effective Hamiltonian in the low-energy subspace in Eq. (6). Whenever
$\mu_{L}=\mu_{R}=0$, the terms in Eq. (6) for the anti-parallel spin
configuration are:

$\displaystyle\epsilon_{R}^{\uparrow\downarrow}$
$\displaystyle=\kappa\left(-2B\sin^{2}{\left(\theta_{R}\right)}+B+\mu_{M}\right),\quad\epsilon_{L}^{\uparrow\downarrow}=\kappa\left(-2B\cos^{2}{\left(\theta_{L}\right)}+B+\mu_{M}\right),$
(22)
$\displaystyle\Lambda_{\uparrow\downarrow}=\kappa\Delta\cos(\theta_{L}+\theta_{R})~{},\quad\Gamma_{\uparrow\downarrow}=-i\kappa\left[\mu_{M}\cos{\left(\theta_{L}+\theta_{R}\right)}-B\sin\left(\theta_{L}-\theta_{R}\right)\right]~{},$
(23)

and for the parallel configuration:

$\displaystyle\epsilon_{R}^{\uparrow\uparrow}$
$\displaystyle=\kappa\left(-2B\cos^{2}{\left(\theta_{R}\right)}+B+\mu_{M}\right),\quad\epsilon_{L}^{\uparrow\uparrow}=\kappa\left(-2B\cos^{2}{\left(\theta_{L}\right)}+B+\mu_{M}\right),$
(24)
$\displaystyle\Lambda_{\uparrow\uparrow}=-i\kappa\Delta\sin{\left(\theta_{L}+\theta_{R}\right)}~{},\quad\Gamma_{\uparrow\uparrow}=-\kappa\left[\mu_{M}\cos{\left(\theta_{L}+\theta_{R}\right)}-B\cos\left(\theta_{L}-\theta_{R}\right)\right]~{},$
(25)

where

$\kappa=t^{2}/(\Delta^{2}+\mu_{M}^{2}-B^{2})~{}.$ (26)

#### We write the expressions for the shifts of the minima of ECT.

At finite $B$, the chemical potential $\mu_{M}$ at which
$\Gamma_{\sigma_{i}\sigma_{j}}=0$ shifts to:

$\displaystyle\mu_{\text{shift}}^{\uparrow\downarrow}=\frac{B\sin{\left(\theta_{L}-\theta_{R}\right)}}{\sin{\left(\theta_{L}+\theta_{R}\right)}},\quad\mu_{\text{shift}}^{\uparrow\uparrow}=\frac{B\cos{\left(\theta_{L}-\theta_{R}\right)}}{\cos{\left(\theta_{L}+\theta_{R}\right)}}~{},$
(27)

for anti-parallel and parallel spin configurations.

##  Appendix B Convenience of the anti-parallel spin configuration

###  B.1 Orthogonality with symmetric spin precession

In Eq. (22) for the anti-parallel spin configuration we notice that when the
spin precession angles are equal $\theta_{L}=\theta_{R}=\theta$, the double
occupation onsite energy $\epsilon_{L}+\epsilon_{R}=0$ is zero at $\mu_{M}=0$
and the ETC minima shifts disappear as shown in Eq. (27). That restores the
orthogonality of operations within the even parity sector and thus we express
$\mathcal{U}_{3}({\gamma})$ operation as:

$\displaystyle\mathcal{U}_{3}({\gamma})=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L/R}\\}\right)\tau_{P}^{(2)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t\\}\right)\tau_{P}^{(1)}\right]~{},$
(28)

where we compensate a finite $\epsilon_{L}-\epsilon_{R}$ with an onsite pulse.
On the other hand, the hopping operation requires additional operations to
compensate for non-orthogonality [35]:

$\displaystyle\begin{aligned}
\mathcal{U}_{2}(\beta)&=\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L}=\mu,\mu_{R}=\mu\\}\right)\tau_{P}^{(N+4)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t\\}\right)\tau_{P}^{(N+3)}\right]\\\
&\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L}=\mu,\mu_{R}=\mu\\}\right)\tau_{P}^{(N+2)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L/R}\\}\right)\tau_{P}^{(N+1)}\right]\\\
&\times\prod_{j=1}^{N/2}\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{t,\mu_{M}\\}\right)\tau_{P}^{(2j)}\right]\times\exp\left[-\frac{i}{\hbar}H_{P}\left(\\{\mu_{L/R}\\}\right)\tau_{P}^{(2j-1)}\right]\end{aligned}$
(29)

where $N$ is the number of pulses required to correct for the non-
orthogonality within the odd parity sector.

###  B.2 Stability and number of operations

To quantify the degree of linear dependence of the operations, we define the
following metric

$\displaystyle\mathcal{L}_{o}=\sqrt{\frac{\left(\epsilon_{L}-\epsilon_{R}\right)^{2}}{\left(\epsilon_{L}-\epsilon_{R}\right)^{2}+\Gamma^{2}}},$
(30)
$\displaystyle\mathcal{L}_{e}=\sqrt{\frac{\left(\epsilon_{L}+\epsilon_{R}\right)^{2}}{\left(\epsilon_{L}+\epsilon_{R}\right)^{2}+\Lambda^{2}}}$
(31)

for $\mathcal{L}_{e}$ even $\mathcal{L}_{o}$ and odd fermion parity sectors.
If $\mathcal{L}_{e/o}=0$, the operations are orthogonal and the scheme
outlined in Section 4 is valid. On the other hand, if $\mathcal{L}_{e/o}=1$,
it is impossible to generate a universal set of operations. To understand how
robust the scheme in Eq. (28) is, we consider small deviations from the
perfect spin precession case: $\theta_{L}=\theta$ and
$\theta_{R}=\theta+\delta$. In this case, the metric $\mathcal{L}_{e/o}$
reads:

$\displaystyle\mathcal{L}_{o}=\left[1+\left(\frac{\mu_{M}}{B}\tan{2\theta}\right)^{2}\right]^{-1/2}+O(\delta)~{},$
(32)
$\displaystyle\mathcal{L}_{e}=\delta\left(\frac{B}{\Delta}\right)\tan{2\theta}+O(\delta^{2})~{}.$
(33)

Depending on the linear dependence $\mathcal{L}_{e/o}$ of the hopping and
pairing operations, we can estimate the maximal number of pulses required to
implement an arbitrary operation [35] within a given fermion parity subspace:

$\mathcal{N}(\mathcal{L}_{e/o})=\lceil\frac{\pi}{\arccos{(\mathcal{L}_{e/o})}}\rceil+1.$
(34)


# A Biomedical Entity Extraction Pipeline for
Oncology Health Records in Portuguese

Hugo Sousa  INESC TEC, FCUPPortoPortugal<EMAIL_ADDRESS>,  Arian
Pasquali  INESC TECPortoPortugal<EMAIL_ADDRESS>,  Alípio Jorge
INESC TEC, FCUPPortoPortugal<EMAIL_ADDRESS>,  Catarina Sousa Santos
INESC TECPortoPortugal<EMAIL_ADDRESS>and  Mário Amorim Lopes
INESC TECPortoPortugal<EMAIL_ADDRESS>
(2023)

###### Abstract.

Textual health records of cancer patients are usually protracted and highly
unstructured, making it very time-consuming for health professionals to get a
complete overview of the patient’s therapeutic course. As such limitations can
lead to suboptimal and/or inefficient treatment procedures, healthcare
providers would greatly benefit from a system that effectively summarizes the
information of those records. With the advent of deep neural models, this
objective has been partially attained for English clinical texts, however, the
research community still lacks an effective solution for languages with
limited resources. In this paper, we present the approach we developed to
extract procedures, drugs, and diseases from oncology health records written
in European Portuguese. This project was conducted in collaboration with the
Portuguese Institute for Oncology which, besides holding over $10$ years of
duly protected medical records, also provided oncologist expertise throughout
the development of the project. Since there is no annotated corpus for
biomedical entity extraction in Portuguese, we also present the strategy we
followed in annotating the corpus for the development of the models. The final
models, which combined a neural architecture with entity linking, achieved
$F_{1}$ scores of $88.6$, $95.0$, and $55.8$ per cent in the mention
extraction of procedures, drugs, and diseases, respectively.

Biomedical Entity Recognition, Data Mining, Oncology Electronic Health Records

††copyright: acmcopyright††journalyear: 2023††copyright:
licensedothergov††conference: The 38th ACM/SIGAPP Symposium on Applied
Computing; March 27-March 31, 2023; Tallinn, Estonia††booktitle: The 38th
ACM/SIGAPP Symposium on Applied Computing (SAC ’23), March 27-March 31, 2023,
Tallinn, Estonia††price: 15.00††doi: 10.1145/3555776.3578577††isbn:
978-1-4503-9517-5/23/03††ccs: Computing methodologies Information
extraction††ccs: Information systems Data mining††ccs: Information systems
Decision support systems††ccs: Information systems Document structure

##  1\. Introduction

The effectiveness achieved by artificial intelligence (AI) systems in recent
years has led to an increase in practical applications in healthcare support.
To give an example, the number of FDA-approved AI medical algorithms has grown
rapidly in recent years (Ebrahimian et al., 2022). Such growth would not be
possible without the digitization of healthcare, which has significantly
increased the number of clinical records stored in digital collections. These
longitudinal records – known as electronic health records (EHRs) – compile all
available patient-specific information, such as previous conditions,
diagnoses, treatments, prescriptions, laboratory test results, radiological
images, and phenotypic and genotypic features (Jensen et al., 2012; Bibault et
al., 2016). As a result, much potential lurks within EHRs (Wang et al.,
2018a). First, from an integrated healthcare standpoint, by providing
clinicians with instant and portable access to all up-to-date patient
information, EHRs streamline local and remote care delivery, potentially
leading to better-informed decision-making (Graber et al., 2017; Jensen et
al., 2012; Bibault et al., 2016). Second, the possible benefits of mining
these records for research purposes are endless. Current research of AI
methods in the clinical context includes: variant reporting (Bibault et al.,
2016); public health and environmental impact surveillance (Boland et al.,
2021; Lee, 2018); and precision (or personalized) Medicine (Fagherazzi, 2020).

Although most successful applications of AI in healthcare have been for image-
based diagnosis and detection (Liu et al., 2019), most of EHRs are primarily
composed of free-text clinical narratives describing the patient’s history,
which opens up a wide range of possibilities for natural language processing
(NLP) applications. Nevertheless, due to their unstructured nature, harnessing
the information within these records is not straightforward. When compared
with a more structured representation, the free-text format has the advantage
of allowing the medical staff to communicate more naturally, providing
adequate freedom for clear human-to-human communication. On the other hand,
since the amount of text grows with the patient’s interactions with healthcare
professionals, the documents quickly reach dozens and hundreds of pages. This
problem is aggravated in patients with persistent diseases, such as cancer,
where the number of pages can run into the thousands. Such lengthy documents
are intractable for the clinical staff to handle, especially in an emergency
setting where time is scarce to take action. In such a scenario, a tool that
would automatically and reliably summarize the patient’s therapeutic path
would be a great asset for improving healthcare services.

An important step to achieve such summarization is the
identification/extraction of the biomedical entities in the text – such as
diseases, medical procedures, or drugs. Although some systems were developed
for general-purpose clinical texts written in English – including Apache
cTAKES111https://ctakes.apache.org/, CLAMP222https://clamp.uth.edu/, and more
notably IBM Watson Health333https://www.ibm.com/watson-health – the same can
not be said for languages with relatively low-resources, where effective
extraction of medical entities remains a challenge (AlShuweihi et al., 2021).
The lack of effectiveness is mainly attributed to the scarcity or nonexistence
of publicly available data, which limits the development of tools for clinical
texts (such as the pre-training of large language models for the clinical
setting). Apart from that, the heterogeneity of clinical narratives is also a
major problem. For instance, while the clinical note that results from a
scheduled appointment is descriptive and syntactically correct, the same is
not true for notes from the emergency service where itemized text is prevalent
and the use of abbreviations and acronyms more frequent. Therefore, a model
that is trained in scheduled appointment documents would (most likely) present
a much lower effectiveness in emergency service documents. In practice, this
means that to achieve an effective system, one must annotate a corpus within
the domain/institution where the model will be deployed. Since the current
state-of-the-art systems (which are based on deep neural models) require large
amounts of annotated data to attain high effectiveness, this is a major
bottleneck in system development.

Faced with the aforementioned issues while developing a system for the
extraction of biomedical entities for the Portuguese Institute for Oncology
(IPO) in Porto, Portugal’s largest oncology center, we created an efficient
approach for the annotation of a medical corpus that can be extrapolated for
any medical domain and institution to quickly achieve a corpus that can be
used to train a deep neural model. In this paper, we describe how the Unified
Medical Language System (UMLS) metathesaurus was employed to accelerate and
minimize the required resources for the annotation process of the corpus.
Furthermore, in this paper, we also show that by combining three named entity
recognition models – for the identification of procedures, drugs, and diseases
– with entity linking on UMLS we were able to achieve relevant effectiveness
for European Portuguese. As this approach is only limited by the availability
of a pre-trained large language model and the availability of the language on
the UMLS knowledge base, this approach can also be extrapolated to other
languages and domains.

In summary, the main contributions of this work are the following:

  1. (i)

we present an efficient strategy for the annotation of clinical narratives
with biomedical entities that accelerates the annotation process;

  2. (ii)

we present a methodology to achieve efficient biomedical entity extraction for
Portuguese that can be adapted to other languages with equivalent resources;

  3. (iii)

finally, we present a real-life case study with results obtained by applying
such a strategy for the extraction of biomedical entities on free-text
oncology narratives written in European Portuguese.

The remainder of the paper is structured as follows: in Section 2 we frame the
presented work in the context of the current research. Section 3 describes the
developed methodology for the annotation of clinical texts along with the
corpus that resulted from applying it in IPO Porto documents. In section 4 we
present the prediction pipeline that was implemented on IPO Porto and present
the experimental procedure that led us to that architecture in Section 5.
Finally, Section 6 and 7 concludes the paper by discussing possibilities for
future research, respectively.

##  2\. Related Work

The aim of biomedical NER (BioNER) (Kim et al., 2019) is to identify the spans
of biomedical entities in a clinical text. Not long ago, the best-performing
systems relied on hand-crafted rules to capture different characteristics of
entity classes (Leser and Hakenberg, 2005; Campos et al., 2012). However,
these features frequently result in highly specialized tools that can only be
used in the domains for which they were designed. Recently, the developments
in NLP, in particular with large language models such as BERT (Vaswani et al.,
2017), BioBERT (Lee et al., 2020), or PubMedBERT (Gu et al., 2021), have
mitigated this problem. Moreover, training deep learning architectures such as
Long Short-Term Memory (LSTM) and Conditional Random Field (CRF) on top of the
large language models word representations, had greatly improved the
effectiveness of BioNER for English texts over the last few years (Habibi et
al., 2017; Giorgi and Bader, 2018; Wang et al., 2018b; Yoon et al., 2019).

In that vein, a few deep-learning-based NLP approaches have been developed to
support clinical decision-making in cancer-related contexts using unstructured
clinical texts. These have been tested in several medical fields and
applications, such as but not limited to: senology, to identify and pinpoint
local and distant recurrence for breast cancer (Karimi et al., 2021);
endocrinology, to improve the diagnosis of thyroid cancer (Zhang et al.,
2022); urology, to stratify the risk of developing urinary incontinence
following partial or full prostate removal (Bozkurt et al., 2020); and
clinical trial screenings, to select patients based on prognosis and
propensity to changes in therapeutic courses (Kehl et al., 2021).
Additionally, a BERT-based model – MetBERT – was also created for the
prediction of metastatic cancer from clinical notes (Liu et al., 2022).

Nevertheless, developing effective BioNER models for low-resource languages
remains a challenge (Névéol et al., 2018; Lerner et al., 2020). This is
primarily because harnessing the power of deep learning models requires a
substantial amount of data. However, because clinical texts contain highly
sensitive information, ethical and legal constraints make it hard to make
corpora available. Yet another issue is the specificity of the data, which
limits its applicability. For example, the only clinical text corpus released
for European Portuguese (Lopes et al., 2019) does not resemble the clinical
notes we found at IPO, as the latter were more disaggregated/itemized and did
not follow the traditional semantic structure of a narrative. Consequently,
application projects are forced to develop a corpus for the data with which
the application will go into production. In this regard, some efforts have
been made to develop methodologies to simplify the annotation of the clinical
corpus. For instance, in a similar challenge to ours, Silvestri et al. (2022)
used active learning and distant supervision to annotate clinical texts
written in Italian. In this work, we adopted a more general strategy that
requires less computational power.

##  3\. Corpus Development

IPO Porto has been keeping electronic health records of its patients for more
than $10$ years. We were able to work with a sufficient sample, under
confidentiality, and on-site. Among the many files that describe each
patient’s journey through the hospital, there is one of particular interest
for this project, the clinical diary.

The clinical diary contains a textual description of every action or
interaction the patient had in the hospital. This includes any treatment,
procedure, appointment, plan of action, and other information deemed relevant
by the health professionals. It is a very descriptive file and, thereby, a
rich source of information. Adversely, it can become very long, repetitive,
and hard to be efficiently read by humans in the loop.

###  3.1. Sampling Process

For the development of the corpus, we selected $80$ fairly short clinic
diaries. In practical terms, this meant sampling documents that were between
the first and second quartile in terms of the number of pages, which
materialized in documents ranging from $52$ to $97$ A4 equivalent pages long.
This is significant because we wanted to reflect a rich variety of clinical
note-writing styles as possible in the corpus (which vary with the person that
writes them). Yet another benefit of sampling from a variety of relatively
small documents is that it increases the exposure to different patients.
Consequently, this increases the number of biomedical entities that will be
present in the final corpus.

###  3.2. Preprocessing

The clinical diary is composed of clinical notes that are delimited by
headers. Important metadata, including the date and the context in which the
note was written, is contained in the headers. Since the status of the patient
does not change in every interaction that he/she has with the medical staff,
it is common that the clinical notes overlap in content. Furthermore, there is
information (such as comorbidities and pathological antecedents) that is
frequently repeated throughout the clinical diary. To avoid multiple
annotations of the same content, we segmented the clinical notes into
sentences with the segtok sentence segmenter444https://github.com/fnl/segtok.
From the $80$ clinic diaries, we collected a total of $36,512$ unique
sentences.

Yet another important specificity of clinical notes is the frequent use of
acronyms and abbreviations which are commonly employed by clinical staff.
Although there has been some work towards using word embeddings/deep neural
models to handle the acronyms and abbreviations (Liu et al., 2015; Li et al.,
2019) we found it sufficiently simple and robust to build a glossary of the
acronyms and abbreviations found in our corpus. In the current version, the
glossary contains $183$ entries. However, it can be manually extended to
include new acronyms and abbreviations that may appear in future documents.

###  3.3. Annotation with UMLS

Table 1.  How the UMLS semantic types were grouped for our three entity types. TUI stands for “Type Unique Identifier”. | TUI | Name
---|---|---
Procedures | T058 | Health Care Activity
T059 | Laboratory Procedure
T060 | Diagnostic Procedure
T061 | Therapeutic or Preventive Procedure
Drugs | T121 | Pharmacologic Substance
T122 | Biomedical or Dental Material
T195 | Antibiotic
T200 | Clinical Drug
Diseases | T019 | Congenital Abnormality
T020 | Acquired Abnormality
T033 | Finding
T037 | Injury or Poisoning
T046 | Pathologic Function
T047 | Disease or Syndrome
T048 | Mental or Behavioral Dysfunction
T049 | Cell or Molecular Dysfunction
T050 | Experimental Model of Disease
T184 | Sign or Symptom
T190 | Anatomical Abnormality
T191 | Neoplastic Process
Table 2.  Distribution of the corpus statistics over train, validation, and
test sets within the three entity types (procedures, drugs, and diseases).
_Sent_ , _B_ , _I_ , and _O_ stand for the number of sentences, begin tokens,
inside tokens, and outside tokens, respectively.

|  | Procedures |  | Drugs |  | Diseases |  | Aggregated
---|---|---|---|---|---|---|---|---
|  | Sent | B | I | O |  | Sent | B | I | O |  | Sent | B | I | O |  | Sent | B | I | O
Train |  | 2,398 | 2,091 | 1,225 | 39,333 |  | 1,236 | 1,128 | 6 | 16,529 |  | 1,870 | 1,651 | 512 | 26,616 |  | 4,219 | 4,870 | 1,743 | 62,328
Validation |  | 599 | 610 | 311 | 8,717 |  | 309 | 285 | 2 | 4,163 |  | 467 | 395 | 141 | 5,738 |  | 1,055 | 1,290 | 454 | 13,503
Test |  | 701 | 821 | 452 | 13,992 |  | 377 | 445 | 1 | 6,737 |  | 608 | 734 | 210 | 11,743 |  | 1,318 | 2,000 | 663 | 25,755
Total |  | 3,698 | 3,522 | 1,988 | 62,042 |  | 1,922 | 1,858 | 9 | 27,429 |  | 2,945 | 2,780 | 863 | 44,097 |  | 6,592 | 8,160 | 2,860 | 101,586

To greatly reduce manual annotation effort we start by automatically
annotating the sentences. For this purpose, the Unified Medical Language
System (UMLS) metathesaurus (Bodenreider, 2004) was used as a knowledge base
for biomedical entity identification. UMLS contains an ontology that maps each
biomedical entity (referred to as “concept” in UMLS jargon) to a semantic
group, which is a high-level categorization of the entities. Examples of
semantic groups are “Clinical Drug”, “Pathologic Function”, and “Diagnostic
Procedure”. To determine the semantic groups of interest in our project, we
followed a two-step process. First, we asked the oncology team to pre-select
the semantic groups to be extracted based on the description of the semantic
group555The semantic groups and their respective definition can be found in
https://lhncbc.nlm.nih.gov/ii/tools/MetaMap/Docs/SemGroups_2018.txt. We then
annotated 300 sentences with the entities within the initial set of semantic
groups and presented the result of the annotation to the oncology team. In
conjunction, we parsed all sentences and iteratively updated the set of
semantic groups to add concepts that were not annotated (that is, false
negatives). The final set of semantic groups was then grouped into three
types: procedures, drugs, and diseases. Table 1 presents the mapping between
semantic groups and the defined entity types666For the complete semantic type
mappings see
https://lhncbc.nlm.nih.gov/ii/tools/MetaMap/documentation/SemanticTypesAndGroups.html.
Our initial automatic labeling step aims to catch as many true entities as
possible even if at the cost of including many false entities. By following
this procedure, we ultimately produced a high-recall classifier, and
therefore, reduce the annotation effort of the specialists to eliminate the
false entities.

To extract the concepts that were within the final set of semantic groups, we
used the QuickUMLS toolkit777https://github.com/Georgetown-IR-Lab/QuickUMLS
(Soldaini and Goharian, 2016), which implements fast string matching with the
UMLS concepts. From the set of $36,512$ sentences, QuickUMLS identified
concepts in $9,912$ of them.

###  3.4. Specialized Curation

Since the set of semantic groups to be extracted by UMLS was selected to
maximize recall, the annotation produced by UMLS included a lot of vague terms
(such as ”blood” or ”pain”) that are not useful for oncologists. To curate the
annotations, we presented the annotations to the oncology team and instructed
them to validate the annotations, i.e., remove false positives. This is a
significant boost in the manual annotation effort as it does not require the
specialist to read the entire sentence, but only to look at the entities that
were annotated by UMLS. However, the annotators were also allowed to add
missing entities, in case they drew their attention while parsing the UMLS
annotations.

Note that, since the annotation produced by UMLS covers a wide range of
concepts, the revision by the specialist can be interpreted as the selection
of the entities he/she wants the pipeline to identify. Therefore, the
resulting dataset will be tailored to the necessities and requirements of the
institution.

After the curation of the specialists and the removal of all the sentences
that did not have any annotation, we were left with $6,592$ sentences, in
which, $3,689$ contained procedures mentions, $1,922$ contained drugs
mentions, and $2,945$ contained diseases mentions. As the goal was to train a
NER model, the annotation was stored in the Inside-Outside-Beginning format
(Ramshaw and Marcus, 1995). The last row of Table 2 shows how the sentences
and the begin/inside/outside tokens were distributed over the datasets that
only contained one entity type (“Procedures”, “Drugs”, and “Diseases”
columns), and the dataset with all the entity types (“Aggregated” column). The
remaining rows of the table present the distribution over the train,
validation, and test set. This split was performed randomly at the sentence
level of the “Aggregated” dataset. First, $20\%$ of the sentences were set
aside for test. Then, the remaining $80\%$ of sentences were partitioned so
that $80\%$ of the documents were used to train the models and $20\%$ to
validate them.

##  4\. Prediction Pipeline

To model the biomedical entity identification task we designed a pipeline that
conceptually can be segmented into three components: a pre-trained language
model to provide embeddings for the input text; the NER model(s) to identify
the entities of interest; and entity linking with UMLS to ensure that entities
that were found by the NER models refer to biomedical entities. Figure 1
presents a graphical illustration of the architecture we used on our specific
application for IPO Porto.

For the pre-trained language model, we employed the
BERTimbau888https://huggingface.co/neuralmind/bert-base-portuguese-cased
(Souza et al., 2020) language model, which was built by training the BERT
(Devlin et al., 2019) architecture in a mixture of Brazilian and European
Portuguese texts999There is currently no large-language model trained
exclusively on European Portuguese texts.. For the identification of the
entities, we trained three models – one for each entity type – using the
architecture proposed by Ma and Hovy (2016). This model architecture was
tailored for sequence labeling, relying on a convolutional neural network
(LeCun et al., 1989) for character encoding, a bi-directional long-short term
memory (Hochreiter and Schmidhuber, 1997) to aggregate character and word
representations, and a sequential conditional random field (Lafferty et al.,
2001) to jointly classify all words of a sentence. Lastly, all the entities
identified by the NER models are looked for in the UMLS (a process commonly
referred to as entity linking) with the list of semantic types we deemed
relevant in the automatic annotation phase (see Table 1). If the entity is
found in the UMLS and its semantic group is part of the set that is relevant,
the entity is kept, otherwise, it is discarded.

Figure 1. Graphical representation of the proposed pipeline.

An important remark is that although we use a NER model for procedures, drugs,
and diseases, the final class of the entity is defined by the metadata in the
UMLS. More precisely, by its semantic group, which is then mapped to the class
by the map in Table 1. Conceptually, the three NER models can be interpreted
as just one NER model that classifies the tokens as BEGIN, INSIDE, and OUTSIDE
rather than classifying the tokens as B-PROCEDURE, B-DRUG, et cetera.

##  5\. Experiments

###  5.1. Evaluation

For the evaluation and comparison of the models, we employed the strict and
relaxed Precision, Recall, and $F_{1}$ metrics. Whereas the strict metrics
only count exact matches, the relaxed metrics consider the overlaps between
the predictions and the annotations as being correct. Therefore, by presenting
both we are able to attain a more comprehensive understanding of the model’s
effectiveness.

Naturally, for the dataset, we used the corpus that is described in Section 3.
To provide a detailed overview of the model’s effectiveness, besides
presenting the result on the Aggregated dataset (the dataset that contains the
annotation of all the entity types) we also analyze the results of the model
on the Procedures, Drugs, and Diseases datasets. The train, validation, and
test partitions are present in Table 2.

###  5.2. Models

To evaluate the importance of the components in our prediction pipeline we run
experiments with three modeling settings: just using the UMLS predictions;
just using the NER predictions; and using the full pipeline prediction. Bellow
follows a detailed description of the three approaches.

#### UMLS

For the baseline model we used UMLS as introduced in Section 3. That is, we
used the QuickUMLS tool to search for concepts belonging to the semantic
groups that were deemed relevant for each entity type (see Table 1). This is a
simple baseline that can be easily reproduced and therefore, provide a
reference metrics that can serve as a base for comparison in future research.

#### NER

The joint NER task is approached by first aggregating the predictions of three
separate, but structurally identical, NER models. One for identifying mentions
to procedures, another for diseases and a third for drugs. This serves to
evaluate the effectiveness of the NER models without doing entity linking with
UMLS. As we use three different models, one token may be classified with two
entity types. That is, a token can be classified as B-DRUG and B-DISEASE. In
that case, we check the raw values outputted by the NER models and keep the
entity with the highest value.

#### NER & UMLS

Lastly, the NER & UMLS is the model described in Section 4 that does entity
linking of the entities predicted by the NER model.

###  5.3. Implementation Details

The pipeline was implemented in Python. In particular, we used the QuickUMLS
toolkit to implement the UMLS entity linking, and Spark NLP to train and
implement the NER models. All the experiments were run on a server with an AMD
EPYC 7351P processor and NVIDIA GeForce GTX 1080 Ti GPU.

###  5.4. Training

As stated in Section 4, three NER models were trained for the identification
of procedures, drugs, and diseases. Before training, we randomly sampled a set
of $20$ hyperparameter configurations to train each of the models. The
hyperparameters that were tuned are: the dropout rate, which was sampled from
$\\{0.0$, $0.1$, $0.2$, $0.3$, $0.4$, $0.5\\}$; the batch size, which was
sampled from $\\{4$, $8$, $16$, $32$, $64$, $128\\}$; and the learning rate,
which was sampled from $\\{0.001$, $0.003$, $0.005$, $0.01$, $0.03$, $0.05$,
$0.1\\}$. For each hyperparameter configuration, we trained the model for $30$
epochs and stored the weights of the epoch in which the model had the best
micro $F_{1}$ score in the validation set. After training the $20$ models for
each entity type, we kept the model with the best validation $F_{1}$ as our
final model.

###  5.5. Results

Table 3.  Results of evaluating the three models on test partition of the
datasets. In bold and underlined are highlighted the best strict and relaxed
$F_{1}$, respectively.

|  | UMLS |  | NER |  | NER & UMLS
---|---|---|---|---|---|---
|  | Strict | Relaxed |  | Strict | Relaxed |  | Strict | Relaxed
|  | P | R | F1 | P | R | F1 |  | P | R | F1 | P | R | F1 |  | P | R | F1 | P | R | F1
Procedures |  | 65.4 | 96.7 | 78.0 | 68.5 | 99.9 | 81.3 |  | 75.2 | 80.8 | 77.9 | 81.0 | 87.0 | 83.9 |  | 95.0 | 83.1 | 88.6 | 98.2 | 85.6 | 91.4
Drugs |  | 75.8 | 92.5 | 83.3 | 76.2 | 93.0 | 83.7 |  | 74.5 | 95.2 | 83.6 | 74.5 | 95.2 | 83.6 |  | 98.6 | 91.6 | 95.0 | 98.6 | 91.6 | 95.0
Diseases |  | 67.6 | 97.2 | 79.7 | 70.1 | 99.8 | 82.4 |  | 57.4 | 46.0 | 51.1 | 87.1 | 69.7 | 77.4 |  | 67.5 | 47.5 | 55.8 | 95.7 | 66.8 | 78.7
Aggregated |  | 44.5 | 97.0 | 61.0 | 47.3 | 99.7 | 64.2 |  | 62.3 | 68.0 | 65.0 | 75.7 | 81.8 | 78.6 |  | 79.8 | 67.3 | 73.0 | 92.3 | 77.4 | 84.2

The results of the final models on the test set of the datasets are presented
in Table 3. In a general overview of the effectiveness of the three models,
one can observe that the NER & UMLS model presents the best strict and relaxed
$F_{1}$ in all the datasets except for the Diseases, where the UMLS model
presents the best results. However note that while the strict $F_{1}$ of the
NER & UMLS model for the identification of Diseases is 23.9 percentage points
worst than the UMLS model, when we compare the relaxed $F_{1}$ score the
difference is only 3.7 percentage points. Upon close inspection, we found that
UMLS has a tendency to annotate the entities along with its attributes, for
example “benign prostatic hyperplasia”, while the NER & UMLS models focus more
on the key words, in the previous example, it only identified “hyperplasia” as
a disease101010Please note that we present the examples in English for the
reader’s convenience. However, these excerpts have been translated from
European Portuguese.. Another aspect that might be hurting the NER performance
is the wide variety of concepts fitted under the “Diseases” category (see
Table 1). Further segmenting this category might yield better results, however
further studies would be required to validate this hypothesis. Apart from
that, we can see that the NER & UMLS model presents an $F_{1}$ score of 88.6%
and 95.5% on the identification of Procedures and Drugs, respectively.

Another interesting remark that can be made upon inspection of Table 3 is the
fact that the NER models greatly benefit from the entity linking with UMLS.
This is mostly due to the removal of false entities that were identified by
the NER models that do not find any match on UMLS, which results in a major
boost in precision. However, by comparing the NER and the NER & UMLS models on
the Procedures and Diseases datasets, one can see that the linking with UMLS
also increased the recall of the NER models. This effect is due to the fact
that in the NER & UMLS model the entity type is defined by the semantic group
of the entity and not by the model that identified the entity. Therefore,
linking with the UMLS is also useful to classify the entity type. The same
effect was not observed in the ”Drugs” dataset, where the recall got worst
after linking with UMLS. However, this dataset is also the smallest so further
studies would be necessary to have a better understanding of this phenomenon.

##  6\. Conclusion

This work describes the methodology employed to achieve effective results for
biomedical entity identification in oncology texts written in European
Portuguese when no initial annotated corpus was available. That includes the
annotation of a clinical corpus with the UMLS metathesaurus, the data pipeline
created, and the training of three NER models for the identification of
procedures, drugs, and diseases. Even though the methodology was employed for
European Portuguese texts, it can be adapted to other languages with
comparable resources. More precisely, the span and applicability of this
methodology are dependent on three main aspects, namely: the availability of
the UMLS metathesaurus for the language;111111See
https://www.nlm.nih.gov/research/umls/knowledge_sources/metathesaurus/release/abbreviations.html#LAT
for the complete list of languages supported by UMLS. the availability and
effectiveness of a large language model for the language; and the
accessibility to clinical texts. Given these three components, the reader
should be able to extrapolate this methodology to his/her project.

##  7\. Future Research

The presented models are part of a bigger pipeline that ends up feeding a
dashboard that summarizes the patient therapeutic path. Arrangements are being
made so that a production test is conducted for this dashboard on the IPO
emergency service. This test will expose the pipeline predictions to a panel
of oncology specialists (much broader than those that developed the approach)
which will not only provide a qualitative evaluation of the pipeline but also
more fine-grained feedback that will allow a quantitative study.

A path we are keen to explore is the effectiveness impact of swapping the
general purpose BERTimbau (Souza et al., 2020) model by the BioBERTpt
(Schneider et al., 2020) model, or even train/fine-tune BERT on European
Portuguese texts has it has been shown to yield better results (Unanue et al.,
2017; Newman-Griffis and Zirikly, 2018). This seems a natural route to further
improve the performance of the system.

###### Acknowledgements.

This work is financed by National Funds through the Portuguese funding agency,
FCT - Fundação para a Ciência e a Tecnologia, within project Grant
#LA/P/0063/2020.

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