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International Conference on Microwave, Antenna and Communication (MAC)

A Generative model to represent real time classical data as quantum state

Indraneel Borgohain, Charles D. Conner, Bharat S. Rawal

Published Mar 24, 2023• 0 citations
Publisher

Abstract

Existence of quantum systems in superposition states gives an exponential advantage over classical system in both time and space. In this paper we will look at reconstructing real time classical data as a pure quantum state. Each classical data sample eg. each pixel location in an images is indexed by a$\mathbf{n}$bit string representing one of the basis superposition states. The amplitude of the state which represents probability of measuring the state can be encoded as the normalized value of the sample at that location. A parameterized circuit[2] is used to prepare the quantum state as superposition of basis states from initial ground state. Each basis state corresponds to a sample classical data (eg. a pixel in case of an image). Quantum amplitude estimation based on Grovers algorithm[15] is used to estimate the amplitudes of each of these states. The parameters of the circuit is adjusted to minimize a loss function using classical gradient descent algorithm. The normalized amplitude at the output of our circuit is multiplied by a normalization factor that can also be tuned to represent the original data sample. This enables us to use the original real time data in our loss function computation. Section 1 of the paper gives a brief introduction. Section II covers the related works. Section III talks about amplitude encoding. Section IV describes quantum state preparation using supervised Learning. Section V describes implementation of the algorithms and finally Section VI gives the final conclusion of the research paper along with a result from the algorithm.

DOI
10.1109/mac58191.2023.10177087

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Existence of quantum systems in superposition states gives an exponential advantage over classical system in both time and space. In this paper we will look at reconstructing real time classical data as a pure quantum state. Each classical data sample eg. each pixel location in an images is indexed by an\mathbf{n}nbit string representing one of the basis superposition states. The amplitude of the state which represents probability of measuring the state can be encoded as the normalized value of the sample at that location. A parameterized circuit[2] is used to prepare the quantum state as superposition of basis states from initial ground state. Each basis state corresponds to a sample classical data (eg. a pixel in case of an image). Quantum amplitude estimation based on Grovers algorithm[15] is used to estimate the amplitudes of each of these states. The parameters of the circuit is adjusted to minimize a loss function using classical gradient descent algorithm. The normalized amplitude at the output of our circuit is multiplied by a normalization factor that can also be tuned to represent the original data sample. This enables us to use the original real time data in our loss function computation. Section 1 of the paper gives a brief introduction. Section II covers the related works. Section III talks about amplitude encoding. Section IV describes quantum state preparation using supervised Learning. Section V describes implementation of the algorithms and finally Section VI gives the final conclusion of the research paper along with a result from the algorithm.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent 2n2^n2n-dimensional data using only nnn qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
This research explores the integration of quantum computing with classical machine learning to enhance data classification tasks using Quantum Neural Networks (QNN) and Parameterized Quantum Circuits (PQC). The hybrid approach leverages the advantages of both quantum and classical systems to improve the efficiency and accuracy of data processing. In this model, data is encoded into qubits using amplitude encoding, representing input vectors as amplitudes of quantum states. The QNN is initialized by placing the qubits in superposition using Hadamard gates, followed by data encoding with parameterized rotational gates that map classical data to quantum states using rotation angles. PQC plays a central role by applying layers of parameterized quantum operations to process data in the quantum space. These parameters are optimized during the training process, where a quadratic loss function minimizes the error between the predicted quantum states and the true class labels using gradient descent. Experiments conducted on the MNIST dataset show that the hybrid the hybrid quantum-classical neural network (QCNN) with PQC achieves a classification accuracy of over 95%, highlighting its potential in machine learning applications. The results demonstrate that integrating quantum computing with classical machine learning enhances performance in complex data analysis tasks due to the exponential growth of quantum state space and the parallelism of quantum systems, making hybrid models promising for computer vision and classification tasks.
A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of M entries, each represented by n bits, the method requires O(n) qubits and O(Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.
Abstract Machine learning is widely believed to be a promising practical application of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies crucially on gradients of model parameters. Such an approach lacks provable convergence to global minima and will become infeasible as quantum learning models scale up. Here, we introduce quantum automated learning, where no variational parameter is involved and the training process is converted to quantum state preparation. In particular, we encode training data into unitary operations and iteratively evolve a random initial state under these unitaries and their inverses, with a target-oriented perturbation towards higher prediction accuracy sandwiched in between. Under rea- sonable assumptions, we rigorously prove that the evolution converges exponentially to the desired state corresponding to the global minimum of the loss function. We show that such a training process can be understood from the perspective of preparing quantum states by imaginary time evolution, where the data-encoded unitaries together with target-oriented perturbations would train the quantum learning model in an automated fashion. We further prove that the introduced quantum automated learning paradigm features universal representation power and good generalization ability with the generalization error upper bounded by the ratio between a logarithmic function of the Hilbert space dimension and the number of training samples. In addition, we carry out extensive numerical simulations on real-life images and quantum data to demonstrate the effectiveness of our approach and validate the assumptions. Our results establish an unconventional quantum learning strategy that is gradient-free with provable and explainable trainability, which would be crucial computing in machine learning scenarios.