Quantum CNN has high test accuracy on data sets, but has limitations

In the 2022 Nobel Prize announced on October 4, three scientists, Alain Aspect, John F. Clause and Anton Zeilinger, won the physics award for their quantum entanglement, attracting attention from the outside world to the field of quantum research. and discussion.

Among them, research investment represented by quantum computing has increased significantly in recent years. People have begun to explore using quantum methods to subvert existing technologies in fields such as security and network communications. classical computing techniques.

Some researchers believe that the core of quantum computing lies in "solving classic problems through lower computational cost technology." With the parallel development of deep learning and quantum computing research in recent years, Many researchers have also begun to pay attention to the intersection of these two fields: quantum deep learning.

Recently, Holly Emblem, Head of Insights at Xbox Game Studio Rare, discussed the current state of quantum deep learning in a new article "Quantum Deep Learning: A Quick Guide to Quantum Convolutional Neural Networks" Research and applications are introduced, with a focus on the advantages and limitations of quantum convolutional neural networks (QCNN) compared with classical computing methods.

1 The difference between classical computing and quantum computing

First introduce an important concept about the difference between classical computing and quantum computing. When a program is executed on a classical computer, a compiler converts the program statements into binary bits; in quantum computing, unlike a classical computer where bits represent either a 1 or a 0 at any time, qubits can be in either state. "Hovering" between states, the qubit collapses to one of its two ground states, 1 or 0, only when it is measured.

This property is called superposition and plays a crucial role in quantum computing tasks. Through superposition, quantum computers can perform tasks in parallel without requiring a fully parallel architecture or GPU to perform. The reason for this is that when each overlay state corresponds to a different value, if an operation is performed on the overlay state, the operation is performed on all states at the same time.

Here is an example of superposition of quantum states:

The superposition of quantum states is exponential, a and b refer to the probability amplitude, which gives gives the probability of projecting to a state once a measurement is performed. Among them, superposition quantum states are created by using quantum logic gates.

Caption: Ragsxl’s IQM quantum computer in Espoo, Finland

2 Entanglement and Bell states

Superposition is very important in quantum physics, and another key principle is entanglement.

Entanglement refers to the behavior that creates or causes interaction between two or more particles in a way that means that the quantum states of these particles can no longer act independently of each other. Description, even from a distance. When particles are entangled, if one particle is measured, the other particle with which it is entangled will immediately be measured in the opposite state (these particles have no local state).

As the understanding of qubits and entanglement develops, the discussion of Bell states continues. The following shows the maximum entangled state of qubits:

|00　 → β → 1 √ 2 (|00　 |11　) = |β00　,

|01　 → β → 1 √ 2 (|01　 | 10　) = |β01　

##|10　 → β → 1 √ 2 (|00　 - |11　) = |β10　

|11　 → β → 1 √ 2 (|01　 - |10　) = |β11　

Use quantum circuits to create Bell states:

Caption: Bell state circuit at Perry’s Temple of Quantum Computing

In the Bell state circuit shown, it takes a qubit input and applies Hadamard gates and CNOT gates to create an entangled Bell state.

Currently, Bell states have been used to develop a series of quantum computing applications; among them, Hegazy, Bahaa-Eldin and Dakroury proposed that Bell states and ultra-dense coding can be used to achieve " "Unconditional Security" theory.

3 Convolutional Neural Network and Quantum Convolutional Neural Network

François Chollet pointed out in Python deep learning that the convolutional neural network (CNN ) are popular in tasks such as image classification due to their ability to build pattern hierarchies, such as representing lines first and then the edges of those lines. This allows CNNs to build on information between layers and represent complex Visual data.

CNNs have convolutional layers, consisting of filters that "slide" through the input and produce "feature maps" that allow patterns in the input to be detected. At the same time, CNN can use pooling layers to reduce the size of feature maps, thereby reducing the resources required for learning.

Caption: Convolutional neural network demonstrated by Cecbur

Definition After understanding the classic CNN, we can explore how quantum CNN (Quantum Convolutional Neural Network, QCNN) utilizes these traditional methods and extends them.

Garg and Ramakrishnan believe that a common approach to developing quantum neural networks is to develop a "hybrid" approach that introduces so-called "quantum convolutional layers," which are Transformations based on stochastic quantum circuits appear as add-on components in classical CNNs.

Shown below is a hybrid QCNN developed by researchers such as Yanxuan Lü and tested on the MNIST handwritten digits dataset:

Research In the paper "A Quantum Convolutional Neural Network for Image Classification," the researchers used quantum circuits and entanglement as part of a classical model to obtain input images and generate predictions as outputs.

In this method, QCNN takes image data as input and encodes it into a quantum state |x>, and then uses quantum convolution and a pooling layer to transform it to extract features; finally, a fully connected layer of strongly entangled circuits is used for classification, and predictions are obtained through measurements.

Where optimization is handled through stochastic gradient descent (SGD), which can be used to reduce the difference between training data labels and QCNN predicted labels. Focusing on quantum circuits, the gates used in the quantum convolutional layer are as follows, including rotation operators and CNOT gates.

Measure a subset of qubits in the pooling layer, and the result determines whether to apply single qubit gates to adjacent bits:

The fully connected layer consists of a "universal single qubit gate" and a CNOT gate that generates entangled states. To compare QCNN with other methods, the researchers used the MNIST data set with simulated QCNN. Following the typical approach, we created a training/test dataset and developed a QCNN consisting of the following layers:

• 2 Quantum Convolutional Layers
• 2 Quantum pooling layers
• 1 Quantum fully connected layer

This QCNN pair The test set accuracy of the data set reached 96.65%, and after testing on the data from Papers with Code, the highest accuracy score of this data set in classic CNN could reach 99.91%.

It should be noted that only two types of MNIST data sets were classified in this experiment, which means that there will be limitations in fully comparing its performance with other MNIST model performance.

4 Feasibility Assessment and Summary

Although researchers have developed methods in QCNN, a key issue in the field currently is the hardware required to implement the theoretical model Doesn't exist yet. In addition, hybrid methods also face challenges in testing methods that simultaneously introduce quantum evolution layers into classical CNN calculations.

If we consider that one of the advantages of quantum computing is that it can solve "classically intractable problems with computationally cheaper techniques", then an important aspect of these solutions is It lies in "quantum acceleration". Some researchers believe that the advantage of quantum machine learning compared with classical implementation is that quantum algorithms are expected to have polynomial or even exponential acceleration times.

However, one limitation of the QCNN method shown above is that when we need algorithms (such as QCNN) that consistently decode/encode classical data and measurements, "quantum acceleration" "The gains are limited; and currently, there is not much information on how to design the best encoding/decoding and protocols that require minimal measurements to benefit from "quantum acceleration."

Entanglement has been proven to be an important property of quantum machine learning. The research mentioned in this article on QCNN using strong entanglement circuits can generate entangled states as its fully connected layer, making The model is able to make predictions. Not only that, entanglement is also used to assist deep learning models in other fields, such as using entanglement to extract important features from images, and using entanglement in data sets may mean that models can learn from smaller training data sets than previously expected. etc.

This article provides a comparison of classical deep learning methods and quantum deep learning methods, and discusses the use of quantum layers (including strongly entangled circuits) to generate predicted QCNN, analyzing the benefits of quantum deep learning and limitations, and introduces the more general application of entanglement in machine learning, which also means that we can start to think about the next step of quantum deep learning, especially the application of QCNN in more fields. In addition, quantum hardware is also constantly improving, and companies such as PsiQuantum have even proposed the goal of developing a quantum processor with one million qubits.

As research in the fields of deep learning and quantum computing continues, we can expect to see further developments in quantum deep learning.

The above is the detailed content of Quantum CNN has high test accuracy on data sets, but has limitations. For more information, please follow other related articles on the PHP Chinese website!