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Low Temperature Physics

A neuron based on a single flux qubit

N. V. Klenov, A. V. Kuznetsov, Andrey E. Schegolev, Igor I. Soloviev, Sergey V. Bakurskiy, M. Yu. Kupriyanov, Maxim V Tereshonok

Published Jul 1, 2019• 9 citations
Publisher

Abstract

The concept of creating an element base for superconducting quantum neural networks based on only a single flux qubit is presented. The behavior of the activation function is analyzed for different variants of the “quantum neuron” implementation (based on three-contact, two-contact, and five-contact interferometers), and the conditions at which this activation function is close to a sigmoid curve are determined. The prospects of using energy-efficient upgrades to the rapid single-flux-quantum logic to control the transfer and activation functions when operating a quantum neural network based on the proposed elements are discussed.

DOI
10.1063/1.5111305

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The concept of creating an element base for superconducting quantum neural networks based on only a single flux qubit is presented. The behavior of the activation function is analyzed for different variants of the “quantum neuron” implementation (based on three-contact, two-contact, and five-contact interferometers), and the conditions at which this activation function is close to a sigmoid curve are determined. The prospects of using energy-efficient upgrades to the rapid single-flux-quantum logic to control the transfer and activation functions when operating a quantum neural network based on the proposed elements are discussed.
Josephson digital or analog ancillary circuits are an essential part of a large number of modern quantum processors. The natural candidate for the basis of tuning, coupling, and neromorphic co-processing elements for processors based on flux qubits is the adiabatic (reversible) superconducting logic cell. Using the simplest implementation of such a cell as an example, we have investigated the conditions under which it can optionally operate as an auxiliary qubit while maintaining its "classical" neural functionality. The performance and temperature regime estimates obtained confirm the possibility of practical use of a single-contact inductively shunted interferometer in a quantum mode in adjustment circuits for q-processors.
We explore the dynamics of an adiabatic neural cell of a perceptron artificial neural network in a quantum regime. This mode of cell operation is assumed for a hybrid system of a classical neural network whose configuration is dynamically adjusted by a quantum co-processor. Analytical and numerical studies take into account non-adiabatic processes as well as dissipation, which leads to smoothing of quantum coherent oscillations. The obtained results indicate the conditions under which the neuron possesses the required sigmoid activation function.
A novel superconducting neuron circuit and two types of variable synapses, which are based on superconducting quantum interferometer devices (SQUIDs), are presented. A neuron circuit with good input-output isolation and steep threshold characteristics is accomplished using a combination of a single-junction SQUID coupled to a double-junction SQUID. The quantum state of the single-junction SQUID represents the neuron state, and the output voltage of the double-junction SQUID, which is operated in a nonlatching mode with shunt resistors, is a sigmoid-shaped function of the input. Both variable synapse circuits are composed of multiple shunted double-junction SQUIDs. The first type changes its conductance value by using both superconducting and voltage states. The second variable synapse circuit changes its output current digitally by switching its bias currents. Besides numerical simulations of the circuit characteristics, we have fabricated superconducting neural chips in a Nb/AlO/sub x//Nb Josephson junction technology. The fundamental operation of each element and a 2-bit neural-based A/D converter have been successfully tested. A learning system with a variable synapse is also discussed.>
Quantum computing enables quantum neural networks (QNNs) to have great potential to surpass artificial neural networks. The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We present two quantum neuron examples based on the proposed framework. The quantum resources required to construct a single quantum neuron are polynomial in function of the input size. Finally, both IBM Quantum Experience results and numerical simulations illustrate the effectiveness of the proposed framework.
Google’s AlphaGo represents the impressive performance of deep learning and the backbone of deep learning is the workhorse of highly versatile neural networks. Each network is made up of layers of interconnected neurons and the nonlinear activation function inside each neuron is one of the key factors that account for the unprecedented achievement of deep learning. Learning how to create quantum neural networks has been a long time pursuit since 1990’s from many researchers, unfortunately without much success. The main challenge is to know how to design a nonlinear activation function inside the quantum neuron, because the laws in quantum mechanics require the operations on quantum neurons be unitary and linear. A recent discovery uses a special quantum circuit technique called repeat-until-success to make a nonlinear activation function inside a quantum neuron, which is the hard part of creating this neuron. However, the activation function used in that work is based on the periodic tangent function. Because of this periodicity, the input to this function has to be restricted to the range of [0, π/2), which is a serious constraint for its applications in real world problems. The function’s periodicity also makes its neurons not suited for being trained with gradient descent as its derivatives oscillate. The purpose of our study is to propose a new nonlinear activation function that is not periodic so it can take any real numbers and its neurons can be trained with efficient gradient descent. Our quantum neuron offers the full benefit as a quantum entity to support superposition, entanglement, interference, while also enjoys the full benefit as a classical entity to take any real numbers as its input and can be trained with gradient descent. The performance of the quantum neurons with our new activation function is analyzed on IBM’s 5Q quantum computer and IBM’s quantum simulator.
Two classes of superconducting devices have been proposed as quantum bits (qubits) for realizing quantum logic operations. The flux qubits based on a superconducting quantum interference device (SQUID) appear to be particularly promising owing to the macroscopic nature of the qubit and potential integration with high-speed control circuitry in the form of rapid single-flux quantum electronics. Recent progress is discussed and near-term challenges mentioned. The radio frequency SQUID-based qubit offers a prospect for a reliably manufacturable scalable approach.