IEEE Circuits and Systems Magazine - Q1 2021 - 24

have been used to implement arithmetic units based
on RNS [81], [89].
A. Superconductor Logic Devices
The AQFP superconductor logic family was proposed
as a breakthrough technology towards building energyefficient computing systems [90]. The dynamic energy
dissipation of AQFP logic can be drastically reduced
due to the adiabatic switching operations by using AC
bias/excitation currents for both the clock signal and
power supply.
The circuit in Fig. 13, from [91], represents a typical
simple AQFP gate that acts as a buffer. The QuantumFlux-Parametron (QFP) is a two-junction Superconducting Quantum Interference Device (SQUID). It is based on
superconducting loops containing two Josephson junctions (J 1 and J 2) and two inductors (L 1 and L 2), which
are shunted by an inductor L q in the center node. An
excitation current I x is applied, which changes the potential energy of the QFP from a single well to a double
well. Consequently, the final state of the QFP, depending
only on the direction of the input current I in, is one of

Iin

Lx1

Lx2

k2
L1

J2
Lq

Iout

" 0 "

" 1 "

Figure 13. Circuit of an AQFP gate-Josephson junctions
(J 1 and J 2).

Control
Signal

(a)

(b)

Figure 14. Diagram of states of a 2 # HPP switch. (a) Bar
state. (b) Cross state.
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

two states: the " 0 " state with an SFQ in the left loop or
the " 1 " state with an SFQ in the right loop (see Fig. 13). A
large output current, in the direction defined by the final
state of the QFP, is generated in L q .
One major advantage of AQFP is the energy efficiency
potential. For example, experimental results show that
the energy dissipation per junction of an 8-bit AQFPbased Carry Look-ahead Adder (CLA) is only 24 k B T [92]
(approximately 100 # 10 -21 Joule for a temperature of
25 oC), being a correct operation demonstrated at a
1-GHz clock frequency. The robustness of AQFP technology has been demonstrated against circuit parameter
variations, as well as the potential towards implementing very large-scale integrated circuits using AQFP devices. A more systematic and automatic synthesis framework, as well as synthesis results on a larger number of
benchmark circuits, is presented in [90]. The automatic
synthesis on 18 benchmark circuits, including 11 circuits from the ISCAS-85 benchmark suite and a 32-bit
RISC-V Arithmetic Logic Unit (ALU), is performed using
a standard cell library of AQFP technology, with 4-phase
clock signals. The results compare an AQFP 10 kA/cm 2
standard cell library with a TSMC 12 nm FinFET one. The
results show the consistent energy benefit of the AQFP
technology, which is able to achieve an up to 10-fold
improvement in energy consumption per clock cycle in
comparison to the 12 nm TSMC technology [90].
Recent research has highlighted the interest in nonconventional arithmetic also for AQFP technology. In
addition to the ultra-high energy efficiency, it is pointed
out that this technology has two characteristics that
make it especially suitable for implementing SC [79].
One is its deep pipelining nature, since each AQFP logic
gate is connected to an AC clock signal, thus requiring a
clock phase, which makes it difficult to avoid Read after
Write (RAW) hazards in conventional binary computing.
The other is the opportunity to obtain a true Random
Number Generation (RNG) using single AQFP buffers.
B. Integrated Nanophotonics
Integrated nanophotonics is another emergent technology that takes advantage of nonconventional arithmetic,
in particular RNS [93], [94]. The inherent parallelism of
RNS and the energy efficiency of integrated photonics can
be combined to build high-speed RNS-based arithmetic
units supported on integrated photonics switches. RNS
arithmetic is performed through spatial routing optical
signals in 2 # 2 Hybrid Photonic-Plasmonic (HPP) switches, following a computing-in-the-network paradigm. The
block diagram of these 2 # 2 HPP switches is represented
in Fig. 14. It is fabricated by using indium tin oxide (ITO)
as the active index modulation material [95]. In the bar
state, the light will propagate straight into the bar arm
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