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Chapman & Hall/CRC eBooks

Quantum Associative Memory

Andreas Wichert

Published Nov 28, 2023• 0 citations
Publisher

Abstract

Quantum associative memory (QuAM) in the domain of quantum computation is a model with a capacity exponential in the number of neurons. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem where the classical data must be read and after the measurement the superposition collapses. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem. The efficient preparation of data is possible in part for spares data. However, the input destruction problem is not solved till today, and usually theoretical speed ups are analyzed by ignoring the input problem, which is the main bottleneck for data encoding. The naming of the phases is in analogy to a living organism that prepares itself during the sleep for an active day. The advantage of quantum approach is present in the active phase.

DOI
10.1201/9781003374404-14

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Quantum associative memory (QuAM) in the domain of quantum computation is a model with a capacity exponential in the number of neurons. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem where the classical data must be read and after the measurement the superposition collapses. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem. The efficient preparation of data is possible in part for spares data. However, the input destruction problem is not solved till today, and usually theoretical speed ups are analyzed by ignoring the input problem, which is the main bottleneck for data encoding. The naming of the phases is in analogy to a living organism that prepares itself during the sleep for an active day. The advantage of quantum approach is present in the active phase.
Quantum memory is proposed as an analogue to classical computer memory, like the random-access memory (RAM). RAM is a form of computer memory that can be read and changed in any order, typically used to store working data. In quantum machine learning domain, the usage of quantum random access memory (qRAM) is proposed to avoid input destruction problem. The method of qRAM is related to the entanglement of the index qubits that are in the superposition with the patterns. The method of qRAM is related to the entanglement of the index qubits that are in the superposition with the patterns. As in the method of the entanglement of the index qubits, the qubits of qRAM are entangled during the reading operation and have to be un-computed after computation.
We have entered the Noisy Intermediate-Scale Quantum Era. A plethora of quantum processor prototypes allow evaluation of potential of the Quantum Computing paradigm in applications to pressing computational problems of the future. Growing data input rates and detector resolution foreseen in High-Energy LHC (2030s) experiments expose the often high time and/or space complexity of classical algorithms. Quantum algorithms can potentially become the lower-complexity alternatives in such cases. In this work we discuss the potential of Quantum Associative Memory (QuAM) in the context of LHC data triggering. We examine the practical limits of storage capacity, as well as store and recall errorless efficiency, from the viewpoints of the state-of-the-art IBM quantum processors and LHC real-time charged track pattern recognition requirements. We present a software prototype implementation of the QuAM protocols and analyze the topological limitations for porting the simplest QuAM instances to the public IBM 5Q and 14Q cloud-based superconducting chips.
We have entered the Noisy Intermediate-Scale Quantum Era. A plethora of quantum processor prototypes allow evaluation of potential of the Quantum Computing paradigm in applications to pressing computational problems of the future. Growing data input rates and detector resolution foreseen in High-Energy LHC (2030s) experiments expose the often high time and/or space complexity of classical algorithms. Quantum algorithms can potentially become the lower-complexity alternatives in such cases. In this work we discuss the potential of Quantum Associative Memory (QuAM) in the context of LHC data triggering. We examine the practical limits of storage capacity, as well as store and recall errorless efficiency, from the viewpoints of the state-of-the-art IBM quantum processors and LHC real-time charged track pattern recognition requirements. We present a software prototype implementation of the QuAM protocols and analyze the topological limitations for porting the simplest QuAM instances to the public IBM 5Q and 14Q cloud-based superconducting chips.
Using quantum algorithms to carry out ML tasks is what is known as Quantum Machine Learning (QML) and the methods developed within this field have the potential to outperform their classical counterparts in solving certain learning problems. The development of the field is partly dependent on that of a functional quantum random access memory (QRAM), called for by some of the algorithms devised. Such a device would store data in a superposition and could then be queried when algorithms require it, similarly to its classical counterpart, allowing for efficient data access. Taking an axiomatic approach to QRAM, this thesis provides the main considerations, assumptions and results regarding QRAM and yields a QRAM handbook and comprehensive introduction to the literature pertaining to it.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
It is widely believed that the real parallel computation achieved by quantum computers has an enormous computing potential. In order to expand its applicable field, we have investigated the fusion of quantum and neural computations. As a first step of implementing learning function on quantum computers, we have proposed a novel quantum associative memory (QuAM) by considering an analogy between neural associative network and qubit network. The memorizing procedure of the QuAM is realized with a Hamiltonian derived from qubit-qubit interactions, and the retrieving procedure is based on the adiabatic Hamiltonian evolution. The memory capacity of the QuAM has been nominally estimated as 2N-1where N is a number of qubits, but its retrieve property has not been discussed in our previous study. This paper proposes a retrieving process for the QuAM and evaluates its performance in detail. The results indicate that the average of the retrieving probability is over 50% even when the qubit network memorizes 2N-1patterns and thus the QuAM is successfully implemented.