Abstract
In this work, we present a Quantum Hopfield Associative Memory (QHAM) and demonstrate its capabilities in simulation and hardware using IBM Quantum Experience.. The QHAM is based on a quantum neuron design which can be utilized for many different machine learning applications and can be implemented on real quantum hardware without requiring mid-circuit measurement or reset operations. We analyze the accuracy of the neuron and the full QHAM considering hardware errors via simulation with hardware noise models as well as with implementation on the 15-qubit ibmq_16_melbourne device. The quantum neuron and the QHAM are shown to be resilient to noise and require low qubit overhead and gate complexity. We benchmark the QHAM by testing its effective memory capacity and demonstrate its capabilities in the NISQ-era of quantum hardware. This demonstration of the first functional QHAM to be implemented in NISQ-era quantum hardware is a significant step in machine learning at the leading edge of quantum computing.
Highlights
Background on quantum neuron designSeveral artificial neuron designs have been developed to apply this classical machine learning paradigm to quantum machine learning applications[6,28,34,35]
Quantum machine learning models have been developed for generic quantum neural n etworks[6,7,8], quantum dynamic neural networks[9], continuous-variable quantum neural networks[10], quantum convolutional neural networks[11,12], and quantum Hopfield neural n etworks[13]
Quantum machine learning research has recently been centered around the use of variational quantum algorithms as machine learning models[14,15,16,17] due to their high expressibility and rapid trainability compared to classical networks[17]
Summary
Several artificial neuron designs have been developed to apply this classical machine learning paradigm to quantum machine learning applications[6,28,34,35]. We base our system on the quantum neuron developed by Cao et al.[6] and modify their structure for implementation in IBMQ in a single, uninterrupted quantum circuit. Each classical neuron state xi can be mapped to a qubit in state |0 or |1. Mapping each neuron state to the probability of measuring|1 in the qubit, xi = −1 corresponds to a pure|0 state ( P(|1 ) = 0 ). Any non-classical value of xi ∈ (−1, 1) can be represented as a superposition state, such as xi being represented by |si
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