Superconducting Circuits without Inductors Based on Bistable Josephson Junctions

Abstract

Magnetic flux quantization in superconductors allows the implementation of fast and energy-efficient digital superconducting circuits. However, information representation in magnetic flux severely limits the functional density and is a long-standing problem. Here, we introduce the concept of superconducting digital circuits that do not utilize magnetic flux and have no inductors. We argue that neither the use of geometric nor kinetic inductance is promising for the scaling down of superconducting circuits. The key idea of our approach is the utilization of bistable Josephson junctions, allowing the representation of information through the Josephson energy. Since the proposed circuits are composed only of Josephson junctions, they can be called all-Josephson junction (all-JJ) circuits. We present a methodology for the design of circuits consisting of conventional and bistable junctions. We analyze the principles of the circuit's functioning, ranging from simple logic cells to an 8-bit parallel adder. The utilization of bistable junctions in the all-JJ circuits is promising for the simplification of schematics and a decrease of the JJ count, leading to space efficiency.

Dynamic Processes in a Superconducting Adiabatic Neuron with Non-Shunted Josephson Contacts

“…In Figure 1a, we schematically showed the corresponding normalized values. Earlier in [18][19][20][21][22], it was demonstrated how it is necessary to change the quantron to obtain a computationally effective transfer characteristic (activation function). In this case, the quantron is actually a single-contact Josephson superconducting interferometer for which it is assumed that the critical current of its Josephson contact can change under the influence of an external signal.…”

“…The symmetry of the potential in (7), and, consequently, the dynamic processes in the system, significantly depends on the inductances included in the parameters a and b of the system under consideration. For a shunted Josephson junction [21], the following relation should be satisfied: l a = 1 + l. Having fixed this condition, we analyzed the changes in the potential during the operation of the S C -neuron. Note that the input signal smoothly changes the potential of the system between two stable equilibrium positions near φ = 0 and ϕ = 2π.…”

“…Thus, the established relationships between the inductances of the circuit show how to control the potential relief, providing bistable states of the neuron. If the capacitance and resistance can be neglected, then the inertia-less mode of the neuron takes place, when the output current immediately follows the control flux [18][19][20][21][22]. The presence of capacitance will lead to nontrivial dynamics in the phase space, which will also depend on the initial conditions of the phase and its velocity.…”

“…The values of the shoulder inductances and the inductive coupling coefficients affect the "delay" of the supplied flux at the device input. The quantity l a is responsible for the tilt of the symmetry axis of the sigmoid relative to the horizontal axis [21].…”

“…Unfortunately, the existing prototypes of adiabatic superconducting network cells are quite large in size [19][20][21]. By eliminating the resistive shunting of Josephson junctions from the proposed schemes, we will significantly reduce their size and energy dissipation per operation.…”