User:Shaanvi D/Quantum machine learning

Quantum embedding
Quantum embedding also known as quantum encoding, is the process of translating classical bits to quantum bits (qubits). The quantum gates are used to convert classical bits to qubits. The classical bits 0,1 in qubits are represented by $$|0\rangle$$,$$|1\rangle$$ or the superposition of $$|0\rangle$$ and $$|1\rangle$$. The classical bits are converted into qubits in the Hilbert space by using a quantum feature map. For example, a classical bit x is converted into quantum state $$|X\rangle $$ with the help of quantum circuit. Depending upon the data, algorithms used for data embedding, there are many quantum embedding methods such as Basis embedding, Amplitude embedding, Angle embedding, Q-Sample embedding etc. . In quantum machine learning ,every process is reversible process, we can decode the encoded data when it is required.

Basis embedding
Basis embedding is designed to do arithmetic operations on the real number. First the real number is approximated to a binary number and then the binary bit is translated into qubits in the computational basis. For example, a real number 3,4 is converted into its binary equivalent 11, 100  and then this bit is translated as $$|11\rangle$$,$$|100\rangle$$ in computational basis and arithmetic operation is applied.

Amplitude embedding
Also known as wave function encoding the data is encoded into the amplitude of a wave function. This type of embedding is used when we don't required more calculation in the vector state. Amplitude embedding is used in supervised learning and unsupervised learning to classify the data.

Angle embedding
Also known as Tensor product embedding and Qubit embedding, angle embedding is the basic form of translating bits to qubits. In angle embedding, each bits is represented by a qubits, so the qubits are not entangled. Quantum neural networks takes the advantage of angle embedding for processing data.

NISQ Circuit
As the name suggests, there is noise in the device's processor, and is the intermediate state between a universal fault-tolerant quantum computer and today's best supercomputer. Also, the term NISQ is more related to the hardware than to the software. NISQ can handle data between 20 to a few hundred qubits. NISQ era has begun and will last till the system can respond to the failure of hardware or software. Due to the noise, there is decoherence of quantum states, so to fully utilize the power of the NISQ processor, at present, we use quantum algorithms with less complex structure as the algorithms should run in a short period of time before decoherence occurs. The theoretical research shows promising quantum supremacy, but there is a practical challenge which is limited quantum resources like qubits number, circuit depth.

Variation Quantum Algorithms (VQAs)
VQAs are one of the most studied quantum algorithms as researchers expect that all the needed applications for the quantum computer will be using the VAQs and also VAQs seem to fulfill the expectation for gaining quantum supremacy. VQAs is a mixed quantum-classical approach where the quantum processor prepares quantum states and measurement is made and the optimization is done by a classical computer. VAQs are considered best for NISQ as  VAQs are noise tolerant compared to other algorithms and give quantum superiority with only a few hundred qubits. Researchers have studied circuit-based algorithms to solve optimization problems and ground state energy of complex system which were difficult to solve or required a large time to do computational using a classical computer.

Variation Quantum Circuits (VQCs)
Variation Quantum Circuits also known as Parametrized Quantum Circuits (PQCs) are based on Variation Quantum Algorithms (VQAs). VQCs consist of three parts, preparation of initial states, quantum circuit and measurement. Researchers are extensively studying VQCs, as it uses the power of quantum computation to learn in a short time and also use fewer parameters than its classical counterparts. It is theoretically and numerically proven that we can approximate non-linear functions on quantum circuits like that in neural network. Due to VQCs superiority, neural network has been replaced by VQCs in Reinforcement Learning tasks and Generative Algorithms. The intrinsic nature of quantum devices towards decoherence, random gate error and measurement errors caused to have high potential to limit the training of the variation circuits. Training the VQCs on the classical devices before employing them on quantum devices helps to overcome the problem of decoherence noise that came through the number of repetitions for training.

Quantum Binary Classifier
Pattern reorganization is one of the important task of machine learning, binary classification is one of the tool or algorithms to find pattern. Binary classification is used in supervised learning and in unsupervised learning. In quantum machine learning, classical bits are converted in qubits and they are map to Hilbert space, complex value data are used in quantum binary classifier to used the advantage of Hilbert space. By exploiting, the quantum mechanic properties such as superposition, entanglement, interference the quantum binary classifier produces the accurate result in short period of time.

NISQ Circuit as Quantum Model
As the depth of the quantum circuit advances on NISQ devices, the noise level rises, posing a significant challenge to accurately computing costs and gradients on training models. The noise tolerance will be improved by using the quantum perceptron and the quantum algorithm on the currently accessible quantum hardware.

A regular connection of similar components known as neurons forms the basis of even the most complex brain networks. Typically, a neuron has two operations: the inner product and an activation function. As opposed to the activation function, which is typically nonlinear, the inner product is a linear process. With quantum computing, linear processes may be easily accomplished additionally,  due to the simplicity of implementation, the threshold function is preferred by the majority of quantum neurons for activation functions.

Quantum Convolution Neural Network
A novel design for multi-dimensional vectors that uses circuits as convolution filters is QCNN. It was inspired by the advantages of CNNs and the power of QML. It is made using a combination of a variational quantum circuit(VQC) and a deep neural network (DNN), fully utilizing the power of extremely parallel processing on a superposition of a quantum state with a finite number of qubits. The main strategy is to carry out an iterative optimization process in the NISQ devices, without the negative impact of noise, which is possibly incorporated into the circuit parameter, and without the need for quantum error correction.

The quantum circuit must effectively handle spatial information in order for QCNN to function as CNN. The convolution filter is the most basic technique for making use of spatial information. One or more quantum convolutional filters make up a quantum convolutional neural network (QCNN), and each of these filters transforms input data using a quantum circuit that can be created in an organized or randomized way. Three parts that make up the quantum convolutional filter are:  the encoder, the parameterized quantum circuit (PQC), and the measurement. The quantum convolutional filter can be seen as an extension of the filter in the traditional CNN because it was designed with trainable parameters.

Quantum neural networks take advantage of the hierarchical structures, and for each subsequent layer, the number of qubits from the preceding layer is decreased by a factor of two. For n input qubits, these structure have O(log(n)) layers, allowing for shallow circuit depth. Additionally, they are able to avoid "barren plateau," one of the most significant issues with PQC-based algorithms, ensuring trainability .Despite the fact that the QCNN model does not include the corresponding quantum operation, the fundamental idea of the pooling layer is also offered to assure validity. In QCNN architecture, the pooling layer is typically placed between succeeding convolutional layers. Its function is to shrink the representation's spatial size while preserving crucial features, which allows it to reduce the number of parameters, streamline network computing, and manage over-fitting. Such process can be accomplished applying full Tomography on the state to reduce it all the way down to one qubit and then processed it in subway. The most frequently used unit type in the pooling layer is max pooling, although there are other types as well. Similar to conventional feed-forward neural networks, the last module is a fully connected layer with full connections to all activations in the preceding layer. Translational invariance, which requires identical blocks of parameterized quantum gates within a layer, is a distinctive feature of the QCNN architecture.

Dissipative Quantum Neural Network
Dissipative QNNs (DQNNs) are constructed from layers of qubits coupled by perceptron called building blocks, which have an arbitrary unitary design. Each node in the network layer of a DQNN is given a distinct collection of qubits, and each qubit is also given a unique quantum perceptron unitary to characterize it. The input states information are transported through the network in a feed-forward fashion, layer-to-layer transition mapping on the qubits of the two adjacent layers, as the name implies. Dissipative term also refers to the fact that the output layer is formed by the ancillary qubits while the input layers are dropped while tracing out the final layer. When performing a broad supervised learning task, DQNN are used to learn a unitary matrix connecting the input and output quantum states. The training data for this task consists of the quantum state and the corresponding classical labels.

Inspired by the extremely successful classical Generative adversarial network(GAN), dissipative quantum generative adversarial network (DQGAN) is introduced for unsupervised learning of the unlabeled training data. The generator and the discriminator are the two DQNNs that make up a single DQGAN. The generator's goal is to create false training states that the discriminator cannot differentiate from the genuine ones, while the discriminator's objective is to separate the real training states from the fake states created by the generator. The relevant features of the training set are learned by the generator by alternate and adversarial training of the networks that aid in the production of sets that extend the training set. DQGAN has a fully quantum architecture and is trained in quantum data.

Experiment:

 * Quantum convolution neural network are used for pattern recognition, classification on the classical data , decentralizing feature extraction for automatic speech recognition , scalable QCNN, Data-Driven Time Propagation.