A quantum Hopfield associative memory implemented on an actual quantum processor

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.

Community detection in brain connectomes with hybrid quantum computing

“…This approach differs from ours in that the optimization problem is encoded in a Hopfield network instead of an Ising-like system 55 , 56 . In practice, the resulting Hopfield encoding can be optimized by any available procedure including but not limited to QA 57 and have, in fact, already been implemented on actual quantum processing units 58 . Successful applications of this approach include image restoration 59 , pattern-recalling 60 and recognition of genetic sequences 56 .…”

“…As far as we know, nonetheless, its application to community detection problems remains unexplored. New optimization strategies such as the Hopfield network encoding and the usage of alternative quantum processing units deserve further study 58 , 61 . Moreover, in future studies we will expand individual analysis of brain connectomes to multi-layer connectomes 14 and to common eigenspaces of networks from population studies 9 .…”

Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments

“…One of the first quantum associative memories based on a Hopfield network (HN) approach was proposed in 2000 [ 69 ]. Recently, a physical realization based on an actual quantum processor was provided [ 101 ]. As shown before, the HN energy function is identical to the QUBO problem, which can be solved by applying the quantum strategies in Section 4.7 .…”

A quantum algorithm for track reconstruction in the LHCb vertex detector

“…The DP Hamiltonian has been employed in track reconstruction algorithms based on the optimisation of Hopfield networks [27,28,32,33]: nevertheless, these approaches become unfeasible in high hit multiplicity conditions due to the scaling of the size of the network. Several quantum versions of the Hopfield network are available in the literature, trying to exploit the unique features of quantum computation to achieve an advantage [34][35][36][37][38]. Our quantum algorithm follows a similar approach to Rebentrost et al [38], in which the optimisation of a Hopfield network is turned into a matrix inversion problem and solved with the Harrow-Hassadim-Lloyd (HHL) algorithm (also known as quantum algorithm for linear systems of equations), which has the potential of achieving an exponential advantage with respect to its classical counterpart [23].…”