Journal ArticleDOI

# Adiabatic Superconducting Artificial Neural Network: Basic Cells.

Abstract: We consider adiabatic superconducting cells operating as an artificial neuron and synapse of a multilayer perceptron (MLP). Their compact circuits contain just one and two Josephson junctions, respectively. While the signal is represented as magnetic flux, the proposed cells are inherently nonlinear and close-to-linear magnetic flux transformers. The neuron is capable of providing a one-shot calculation of sigmoid and hyperbolic tangent activation functions most commonly used in MLP. The synapse features by both positive and negative signal transfer coefficients in the range ~ (-0.5,0.5). We briefly discuss implementation issues and further steps toward multilayer adiabatic superconducting artificial neural network which promises to be a compact and the most energy-efficient implementation of MLP.
Topics: , Artificial neuron (58%), Josephson effect (51%), Adiabatic process (51%)

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Adiabatic superconducting artificial neural network: Basic cells
Igor I. Soloviev, Andrey E. Schegolev, Nikolay V. Klenov, Sergey V. Bakurskiy, Mikhail Yu. Kupriyanov, Maxim V.
Tereshonok, Anton V. Shadrin, Vasily S. Stolyarov, and Alexander A. Golubov
Citation: Journal of Applied Physics 124, 152113 (2018); doi: 10.1063/1.5042147
View online: https://doi.org/10.1063/1.5042147
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Adiabatic superconducting articial neural network: Basic cells
Igor I. Soloviev,
1,2,3,a)
Andrey E. Schegolev,
1,2,4,5
Nikolay V. Klenov,
1,2,4,5,6
Sergey V. Bakurskiy,
1,2,3
Mikhail Yu. Kupriyanov,
1
Maxim V. Tereshonok,
2,5
3
Vasily S. Stolyarov,
3,6,7,8
and Alexander A. Golubov
3,9
1
Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, 119991 Moscow, Russia
2
MIREARussian Technological University, 119454 Moscow, Russia
3
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
4
Physics Department, Lomonosov Moscow State University, 119991 Moscow, Russia
5
Moscow Technical University of Communications and Informatics (MTUCI), 111024 Moscow, Russia
6
Dukhov Research Institute of Automatics (VNIIA), 127055 Moscow, Russia
7
Institute of Solid State Physics RAS, 142432 Chernogolovka, Russia
8
Solid State Physics Department, KFU, 420008 Kazan, Russia
9
Faculty of Science and Technology and MESA+ Institute of Nanotechnology, 7500 AE Enschede,
The Netherlands
(Received 30 May 2018; accepted 25 July 2018; published online 26 September 2018)
We consider adiabatic superconducting cells operating as an articial neuron and synapse of a multi-
layer perceptron (MLP). Their compact circuits contain just one and two Josephson junctions,
respectively. While the signal is represented as magnetic ux, the proposed cells are inherently non-
linear and close-to-linear magnetic ux transformers. The neuron is capable of providing the one-
shot calculation of sigmoid and hyperbolic tangent activation functions most commonly used in
MLP. The synapse features both positive and negative signal transfer coefcients in the range
(0:5, 0:5). We briey discuss implementation issues and further steps toward the multilayer adi-
abatic superconducting articial neural network, which promises to be a compact and the most
https://doi.org/10.1063/1.5042147
I. INTRODUCTION
Articial neural network (ANN) is the key technology in
the fast developing area of articial intelligence. It has been
gress requires an increase in complexity and depth of ANNs.
However, modern implementations of the neural networks
are commonly based on conventional computer hardware
which is not well suited for neuromorphic operation. This
leads to excessive power consumption and hardware over-
head. Ideal basic elements of ANNs should combine the mul-
tiple properties like one-shot calculation of their functions,
operation with energy near the thermal noise oor, and nano-
scale dimensions.
The most energy ef cient computing today can be per-
formed using the superconductor digital technology.
1
The rst ever practical logic gates capable of operating down
to and below the Landauer thermal limit
2
were realized
recently
3
on the basis of adiabatic superconductor logic.
Besides the several attempts to the implementation of the
superconducting ANNs proposed since the 1990s,
412
the
cuits was presented only recently.
13,14
In this paper, we con-
sider operation principles of adiabatic superconducting basic
cells which comply with the above-mentioned properties for
ANN implementation. We focus on a particular multilayer
perceptron (MLP) because of a wide range of its applicability
and well-developed learning algorithms for such a network.
II. BASIC CELLS
The basic element of superconducting circuits is the
Josephson junction. Its characteristic energy typically lies
below aJ level while switching frequency is several hundred
GHz. Contrary to semiconductor transistor, the Josephson
junction is not fabricated in a substrate but between two
superconductor layers deposited on a substrate utilized as a
mechanical support. This provides opportunity for supercon-
ducting circuits to benet from 3D topology which can be
especially suitable for deep ANNs. The minimal feature size
of superconducting circuits is progressively decreased down
to nanoscales in recent years.
15
Another attractive feature of the Josephson junction is its
inherently strong nonlinearity. Indeed, the current owing
through the junction, I, is commonly related to the supercon-
ducting phase difference between the superconducting banks,
w
,as
I ¼ I
c
sin
w
, (1)
where I
c
is the junction critical current. We show below that
this current-phase relation (CPR) having both linear and non-
linear parts is well suited for implementation of supercon-
ducting arti cial neuron with one-shot calculation of sigmoid
or hyperbolic tangent activation functions
σ (x) ¼
1
1 þ e
x
, (2a)
a)
isol@phys.msu.ru
JOURNAL OF APPLIED PHYSICS 124, 152113 (2018)
0021-8979/2018/124(15)/152113/5/$30.00 124, 152113-1 Published by AIP Publishing. or τ (x) ¼ tanh (x), (2b) utilized in MLP and superconducting synapse enabling signal transfer with both positive and negative coefcients. Unlike most of their predecessors, 49,11,12 both cells are oper- ating in a pure superconducting mode featured by minimal power consumption. A. Articial neuron One of the simplest superconducting cells is parametric quantron proposed in 1982 for adiabatic operation. 16 It is the superconducting loop consisted of a Josephson junction and a superconducting inductance. According to the Josephson junction CPR (1), the relation between the input magnetic ux and the Josephson junction phase in its circuit has a simple expression: w þ l sin w ¼ f in , (3) where we use normalization of current to critical current of the Josephson junction, I c , and input magnetic ux Φ in to the magnetic ux quantum Φ 0 , f in ¼ 2πΦ in =Φ 0 , inductance, L, is normalized to characteristic inductance, l ¼ L=L c , L c ¼ Φ 0 =2πI c , accordingly. It is seen from (1) and (3) that the current circulating in the loop has a tilted sine dependence on input magnetic ux. The way to transform this dependence close to the desired one [(2a) or (2b)] is the addition of a linear term compensat- ing the sine slope on the initial section (where sin w w )in the vicinity of zero input ux, f in 0. This can be done by attaching another superconducting loop with a part of its inductance, l out , being common with the initial circuit [see Fig. 1(a)]. The synthesized cell was named a sigma-cell 13 because its transformation of mag- netic ux can be very close to sigmoid function. Here, we are interested in a transfer function, f out ( f in ), where output magnetic ux, f out , is proportional to output current, f out ¼ l out i out . The system of equations describing the proposed cell is as follows: w þ l sin w ¼ f in =2 þ l out i out , (4a) w þ l sin w ¼ f in þ l a i a , (4b) where l a is the attached inductance. The corresponding system implicitly dening the transfer function through dependencies of f out , f in on w has the following form: f out ¼ l out f in 2l a sin w 2(l a þ l out ) , (5a) f in ¼ 2 l a þ l out l a þ 2l out  w þ l þ l a l out l a þ l out  sin w  : (5b) Vanishing of the derivative d f out =d f in at f in ¼ 0 corre- sponds to the condition: l a ¼ 1 þ l: (6) One can t (5) to sigmoid function (2a) taking (6) into account with the two tting parameters: l, l out . The result of tting is shown in Fig. 1(b). The found optimal values, l ¼ 0:125, l out ¼ 0:3, provide conformity of the sigma-cell transfer function with sigmoid one with stan- dard deviation at the level of 10 3 . Sigmoid function (2a) was scaled as σ (1:173x) in our tting process. The transfer function f out ( f in ) (5) was normalized by 2πl out =(l a þ 2l out ) to t a unit height and shifted by a half period. The latter can be obtained by application of a constant bias ux to the circuit, f b ¼2π(l a þ l out )=(l a þ 2l out ). While sigmoid activation function is commonly used for input data dened in the positive domain, for data dened on the whole numeric axis around zero, it is convenient to use hyperbolic tangent. Application of additional bias ux provid- ing π phase shift into the loop containing Josephson junction moves the center of the nonlinear part of the cell transfer func- tion to zero. This allows one to obtain the desired shape of activation function (2b).Theπ phase shift can also be imple- mented using the πJosephson junction 1720 with π shift of its CPR (1), I ¼I c sin ( w ), instead of the standard one. One needs to correspondingly change the sign of the terms containing sine function in (5) to perform the tting FIG. 1. (a) Scheme of an articial neuron cell. (b) The cell transfer function (line) tted to sigmoid and hyperbolic tangent functions (dots). Scaling of the functions (2) is shown in the gure. The transfer function f out ( f in )is normalized by 2πl out =(l a þ 2l out ) and shifted by 2π(l a þ l out )=(l a þ 2l out ) on the ux axis to t (2a), and normalized to πl out =(l a þ 2l out ) with no addi- tional shift on ux axis to t (2b). The optimal values of parameters are l ¼ 0:125, l out ¼ 0:3, l a ¼ 1:125. Consistency of curves in both cases is at the level of 10 3 . Hyperbolic tangent activation function is tted with π shift in the Josephson junction CPR (1). 152113-2 Soloviev et al. J. Appl. Phys. 124, 152113 (2018) procedure. The tting result is presented in Fig. 1(b). Hyperbolic tangent function was scaled as tanh (0:586x) while the transfer function f out ( f in ) was normalized by a factor of two lower value than the previous time, πl out =(l a þ 2l out ). With the same values of parameters l, l out , and zero bias ux, we obtained the same conformity of the curves. B. Articial synapse Synapse modulates the weight of a signal arriving at the neuron. In our case, the signal corresponds to magnetic ux and, therefore, synapse can be implemented simply as a transformer of magnetic ux with desired coupling factor. Summation of signals can be provided by connecting the transformers to a single superconducting input loop of the neuron. However, this solution suits for ANN with a certain and unchangeable conguration. In most cases, a congurable ANN would be preferable. The selected conguration of inter-neuron connections should be maintained during its entire use if the feature space dimensions do not vary. However, the weight values should be congurable if we want to train the ANN on the y. The best way to meet this requirement is utilization of some non- volatile memory elements. In superconducting circuits, such an element can be implement ed by using the ferromagnetic (F) materials. In particular, introduction of F-layers into the Josephson junction weak link area allows us to modulate its critical current. 1,21,22 This phenomenon was already proposed for utilization in articial synapse of superconducting spiking ANN. 12 In our case of MLP, we can also make use of it. The synapse scheme presented in Fig. 2(a) is nearly a mirrored scheme of the proposed neuron [Fig. 1(a)]. The only differences are the addition of the second Josephson junction and the possibility to independently modulate criti- cal currents of the magnetic junctions (marked by boxes), e.g., by application of tuning magnetic eld. For MLP, it is required to provide both positive and negative weights of signal. Our synapse is designed accord- ing to this requirement. The input current, i in , induced in inductance l in by input magnetic ux, f in , is split toward the two Josephson junctions. Magnitude of currents i 1 , i 2 in each branch correspond to critical currents of the junc- tions, i c1 , i c2 , so that the sign of output circulating current, i cir ¼ (i 1 i 2 )=2 (and the direction of output magnetic ux, f out ), is determined by their ratio. Maximum in equality of i c1 , i c2 provides maximum output signal, while equal critical currents correspond to zero transfer coefcient. It is convenient to present the system of equations for the synapse cell in terms of Josephson junctions phase sum, w þ ¼ ( w 1 þ w 2 )=2, and phase difference, w ¼ ( w 1 w 2 )=2: w þ þ l 2 þ l in  i in þ f in ¼ 0, (7a) w þ li cir ¼ 0: (7b) Furthermore, introducing the sum Σi c ¼ i c1 þ i c2 and differ- ence Δi c ¼ i c1 i c2 of the critical currents and taking (1) into account one can represent (7) in the following form: w þ þ l 2 þ l in  ðΣi c sin w þ cos w þ Δi c sin w cos w þ Þ þ f in ¼ 0; (8a) w þ l 2 (Σi c sin w cos w þ þ Δi c sin w þ cos w ) ¼ 0: (8b) The dependence of the phase difference on the phase sum, w ( w þ ), can be obtained 23,24 from (8b) with corresponding function f ( w , w þ ) ¼ w þ l 2 (Σi c sin w cos w þ þ Δi c sin w þ cos w ), (9) as follows: w ¼ ð πsgnΔi c 0 H[ f (x; w þ )sgn Δ i c ]dx; (10) where H(x) is the Heaviside step function. Equations (7a), (8a), and (10) implicitly dene the cell transfer function FIG. 2. (a) Scheme of an articial synapse cell. Magnetic Josephson junc- tions are marked by boxes. (b) Synapse cell transfer function for the values of parameters: l in ¼ 2, l ¼ 4, Σi c ¼ 1, and Δi c as shown in the gure. Vertical dotted line shows the boundary of highly linear range where stan- dard deviation from the linear function is at the level of 10 3 . This range corresponds to maximum output magnetic ux of the optimized neuron cell. 152113-3 Soloviev et al. J. Appl. Phys. 124, 152113 (2018) f out ( f in ) through dependencies f out ¼ 2li cir ¼2 w ( w þ ) and f in [ w ( w þ ), w þ ]on w þ . Here, we are interested in the range of the phase sum, w þ [ [0, π=2), where the transfer function might be linear. Figure 2(b) shows synapse cell transfer function for dif- ferent values of critical currents difference in the range Δi c [ [ 0:9, 0:9]. The critical current sum is Σi c ¼ 1. With the xed critical currents, the shape of the transfer function is determined by inductances l in , l. In accordance with (7a), an increase in input inductance l in increases the amplitude of nonlinearity of the dependence of input current on input ux i in ( f in ) making it more tilted. This is in complete analogy with parametric quantron scheme (3). The slope of the linear part of the transfer func- tion is correspondingly decreased. However, this gives a stretching of this linear part, which is of use for us, and con- traction of the nonlinear part. Increase in inductance l provides the same effect [see (7a)]. At the same time, it increases the nonlinearity of the dependence of output ux on phase sum [see (8b)] which vice versa increases the slope of the linear part though making it less linear. The goal of optimization of the transfer function f out ( f in ) is the maximum modulation of its slope alongside with the high linearity among the possibly wider range of input ux. In our case, the values of inductances were chosen to be l in ¼ 2, l ¼ 4. With these parameters magnetic ux can be transferred through the synapse with coefcients in the range (0:5, 0:5) depending on the critical currents difference. For maximum output magnetic ux of optimized neuron, 2πl out =(l a þ l out ) 1:1, maximum standard deviation of the synapse transfer function from the linear function is at the level of 10 3 . In the whole shown range [0, π], it is of an order of magnitude worse. III. DISCUSSION Both considered cells operate in a pure superconducting regime. Evolution of their states is fully physically reversible. Therefore, they can be operated adiabatically with energy per operation down to the Landauer limit. 2 For standard working temperature of superconducting circuits, T ¼ 4:2 K, this limit corresponds to the energy, k B T ln 2 4 10 23 J (where k B is the Boltzmann constant). Estimations show that the bit energy can be as low as 10 21 J for adiabatic superconductor logic at clock frequency of 10 GHz. 25 This is million times less than characteristic energy consumed by a semiconductor transistor. In one hand, taking into account the fact that modern implementation of neuron based on complementary- metal-oxide semiconductor (CMOS) technology requires a few dozens of transistors, the possible gap between power consumption of semiconductor and superconductor ANN is increased by an order. On the other hand, penalty for super- conducting circuits cooling is typically several hundred W/W that cancels out the two to three orders of supremacy. Nevertheless, the proposed adiabatic superconducting ANN can be up to 10 4 10 5 times more energy efcient than its semiconductor counterparts. One should note some peculiarities of the proposed concept. First of all, there is no power supply in these circuits and so the signal vanishes. Therefore, there is a need for a ux amplier which can be implemented on a base of some standard adiabatic cell like adiabatic quantum ux parame- tron (AQFP). 1,26 However, such aspects as the linearity of amplication, the distance of signal propagation without amplication, and related issues of achievable fan-in and fan-out should be additionally considered. Another feature is the periodicity of sigma-cell based neuron transfer function. Corresponding issues can be miti- gated by a signal normalization. Along with the use of standard superconducting inte- grated circuits fabrication process, the proposed cells require utilization of magnetic Josephson junctions which are rela- tively new to superconducting technology. Nevertheless, modern developments of cryogenic magnetic memory 1,27 and superconducting logic circuits with controlled functional- ity 28,29 promise their fast introduction. In particular case of the proposed synapse, one could benet from implementation of the magnetic Josephson junc- tion controlled by direction of magnetic eld, like the Josephson magnetic rotary valve 30 with heterogeneous area of weak link. Such a valve is featured by high critical current for a certain direction of its F-layer magnetization and low critical current for the direction rotated by 90 . Two such junctions in close proximity to each other with mutual rota- tion on 90 relative to their axes directed along the boundary of inhomogeneity allow one to obtain high critical current for one junction and low critical current for another one with the same direction of magnetizations of their F-layers. In this case, rotation of their magnetizations leads to a correspond- ing decrease and increase of Josephson junctions critical currents which means modulation of synapse weight, accord- ing to Fig. 2. Utilization of the rotary valve reduces the number of control lines required to program the magnetic Josephson junctions by half. However, their total number, which is twice the number of synapses, remains huge for practical ANNs. Therefore, the effective synapse control is another urgent task on the way to multilayer adiabatic superconducting ANN. IV. CONCLUSION In this paper, we considered operation principles of adiabatic superconducting basic cells for implementation of multilayer perceptron. These are articial neuron and synapse which are nonlinear and close-to-linear superconducting trans- formers of magnetic ux, respectively. Both cells are capable of operation in the adiabatic regime featured by ultra-low power consumption at the level of 4 to 5 orders of magnitude less than that of their modern semiconductor counterparts (including cooling power penalty). The proposed neuron cell contains just a single Josephson junction. The neuron provides one-shot calculation of either sigmoid or hyperbolic tangent activation function. The certain type of this function is deter- mined by the type of utilized Josephson junction and can also be switched on the y by application of magnetic ux. The synapse is implemented with two magnetic Josephson 152113-4 Soloviev et al. J. Appl. Phys. 124, 152113 (2018) ##### Citations More filters Journal ArticleDOI 12 Apr 2019-Physical Review B Abstract: We have used spin-polarized neutron reflectometry to investigate the magnetization profile of superlattices composed of ferromagnetic Gd and superconducting Nb layers. We have observed a partial suppression of ferromagnetic (F) order of Gd layers in [$\mathrm{Gd}({d}_{F})/\mathrm{Nb}(25 \mathrm{nm}){\mathrm{]}}_{12}$superlattices below the superconducting (S) transition of the Nb layers. The amplitude of the suppression decreases with increasing${d}_{F}. By analyzing the neutron spin asymmetry we conclude that the observed effect has an electromagnetic origin---the proximity-coupled S layers screen out the external magnetic field and thus suppress the F response of the Gd layers inside the structure. Our investigation demonstrates the considerable influence of electromagnetic effects on the magnetic properties of S/F systems. 15 citations Journal ArticleDOI Nikolay V. Klenov1, Yury Khaydukov1, S. V. Bakurskiy1, R. Morari2 +6 moreInstitutions (3) Abstract: We present a study of magnetic structures with controllable effective exchange energy for Josephson switches and memory applications. As a basis for a weak link we propose to use a periodic structure composed of ferromagnetic (F) layers spaced by thin superconductors (s). Our calculations based on the Usadel equations show that switching from parallel (P) to antiparallel (AP) alignment of neighboring F layers can lead to a significant enhancement of the critical current through the junction. To control the magnetic alignment we propose to use a periodic system whose unit cell is a pseudo spin valve of structure F1/s/F2/s where F1 and F2 are two magnetic layers having different coercive fields. In order to check the feasibility of controllable switching between AP and P states through the whole periodic structure, we prepared a superlattice [Co(1.5 nm)/Nb(8 nm)/Co(2.5 nm)/Nb(8 nm)]6 between two superconducting layers of Nb(25 nm). Neutron scattering and magnetometry data showed that parallel and antiparallel alignment can be controlled with a magnetic field of only several tens of Oersted. 14 citations Journal ArticleDOI 03 Sep 2019-Physical Review B Abstract: We investigate the behavior of the critical temperature{T}_{c}$in superconductor/ferromagnet/superconductor (S/F/S) trilayers in the dirty limit as a function of the ferromagnetic layer thickness${d}_{f}$and the S/F interface transparency. We perform${T}_{c}$calculations using the general self-consistent multimode approach based on the Usadel equations in Matsubara Green's functions technique, and compare the results with the single-mode approximation, widely used in literature. Both methods produce similar results for sufficiently low interface transparency. For transparent interfaces, we obtain a qualitatively different${T}_{c}({d}_{f})$behavior. Using the multimode approach, we observe multiple 0-$\ensuremath{\pi}$transitions in critical temperature, which cannot be resolved by the single-mode approximation. We also calculate the critical S layer thickness at given${d}_{f}\$ when an S/F/S trilayer still has a nonzero critical temperature. Finally, we establish the limits of applicability of the single-mode approximation.

8 citations

Journal ArticleDOI
TL;DR: It is argued that such superlattices can be used as tunable kinetic inductors designed for artificial neural networks representing the information in a “current domain”, based on calculations based on the Usadel equations.
Abstract: We present both theoretical and experimental investigations of the proximity effect in a stack-like superconductor/ferromagnetic (S/F) superlattice, where ferromagnetic layers with different thicknesses and coercive fields are made of Co. Calculations based on the Usadel equations allow us to find the conditions at which switching from the parallel to the antiparallel alignment of the neighboring F-layers leads to a significant change of the superconducting order parameter in superconductive thin films. We experimentally study the transport properties of a lithographically patterned Nb/Co multilayer. We observe that the resistive transition of the multilayer structure has multiple steps, which we attribute to the transition of individual superconductive layers with the critical temperature, T c, depending on the local magnetization orientation of the neighboring F-layers. We argue that such superlattices can be used as tunable kinetic inductors designed for artificial neural networks representing the information in a "current domain".

8 citations

Journal ArticleDOI
Michael L. Schneider1, Kenneth Segall2Institutions (2)
TL;DR: It is found that the fan-out should be limited only by junction count and circuit size limitations, and a fan-in level on the order of a few 100-to-1 should be achievable based on current technology.
Abstract: Neuromorphic computing has the potential to further the success of software-based artificial neural networks (ANNs) by designing hardware from a different perspective. Current research in neuromorphic hardware targets dramatic improvements to ANN performance by increasing energy efficiency and speed of operation and even seeks to extend the utility of ANNs by natively adding functionality such as spiking operation. One promising neuromorphic hardware platform is based on superconductive electronics, which has the potential to incorporate all of these advantages at the device level in addition to offering the potential of near lossless communications both within the neuromorphic circuits and between disparate superconductive chips. Here, we explore one of the fundamental brain-inspired architecture components, the fan-in and fan-out as realized in superconductive circuits based on Josephson junctions. From our calculations and WRSPICE simulations, we find that the fan-out should be limited only by junction count and circuit size limitations, and we demonstrate results in simulation at a level of 1-to-10 000, similar to that of the human brain. We find that fan-in has more limitations, but a fan-in level on the order of a few 100-to-1 should be achievable based on current technology. We discuss our findings and the critical parameters that set the limits on fan-in and fan-out in the context of superconductive neuromorphic circuits.

7 citations

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Abstract: This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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Abstract: Ultra-low-power adiabatic quantum flux parametron (QFP) logic is investigated since it has the potential to reduce the bit energy per operation to the order of the thermal energy. In this approach, nonhysteretic QFPs are operated slowly to prevent nonadiabatic energy dissipation occurring during switching events. The designed adiabatic QFP gate is estimated to have a dynamic energy dissipation of 12% of IcΦ0 for a rise/fall time of 1000 ps. It can be further reduced by reducing circuit inductances. Three stages of adiabatic QFP NOT gates were fabricated using a Nb Josephson integrated circuit process and their correct operation was confirmed.

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K. K. Likharev1Institutions (1)
Abstract: Fundamental limitations on the energy dissipated during one elementary logical operation are discussed. A model of a real physical device (parametric quantron) based on the Josephson effect in superconductors is used throughout the discussion. This device is shown to be physically reversible, and moreover it can serve as the clementary cell of a logically reversible computer, both these properties being necessary to achieve the fundamental limits of energy dissipation. These limits due to classical and quantum statistics are shown to lie well below the earlier estimates,k B T and ηϑ, respectively.

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Abstract: To realize functionality similar to that of their biological inspirations, advanced neuromorphic systems require massive interconnectivity, extreme energy efficiency, and complex signaling mechanisms. The authors propose an integrated optoelectronic platform combining superconducting electronics with photonic signaling, to enable neuromorphic computing beyond the scale of the human brain.

122 citations

Journal ArticleDOI
TL;DR: A new form of artificial synapse based on dynamically reconfigurable superconducting Josephson junctions with magnetic nanoclusters in the barrier is demonstrated, which provides a significant step toward a neuromorphic platform that is faster, more energy-efficient, and thus can attain far greater complexity than has been demonstrated with other technologies.
Abstract: Neuromorphic computing promises to markedly improve the efficiency of certain computational tasks, such as perception and decision-making. Although software and specialized hardware implementations of neural networks have made tremendous accomplishments, both implementations are still many orders of magnitude less energy efficient than the human brain. We demonstrate a new form of artificial synapse based on dynamically reconfigurable superconducting Josephson junctions with magnetic nanoclusters in the barrier. The spiking energy per pulse varies with the magnetic configuration, but in our demonstration devices, the spiking energy is always less than 1 aJ. This compares very favorably with the roughly 10 fJ per synaptic event in the human brain. Each artificial synapse is composed of a Si barrier containing Mn nanoclusters with superconducting Nb electrodes. The critical current of each synapse junction, which is analogous to the synaptic weight, can be tuned using input voltage spikes that change the spin alignment of Mn nanoclusters. We demonstrate synaptic weight training with electrical pulses as small as 3 aJ. Further, the Josephson plasma frequencies of the devices, which determine the dynamical time scales, all exceed 100 GHz. These new artificial synapses provide a significant step toward a neuromorphic platform that is faster, more energy-efficient, and thus can attain far greater complexity than has been demonstrated with other technologies.

112 citations

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