This paper presents a simple and fast method to represent vector and matrix using quantum state. Two application examples of the method presented in this paper are given as follows. 1. Applying the method directly to design quantum loading scheme that evades the efficiency bottleneck of classical computer. CPU and memory are the most important two parts of computer, "CPU + Memory=Computer". Loading scheme is defined as loading data into registers of CPU from memory, it connects CPU and memory as a whole machine. Classical loading scheme has time complexity O(N) in terms of arbitrary algorithm, it is the efficiency bottleneck of classical computer. By contrast, quantum loading scheme presented in this paper has time complexity O(logN)! 2. The method is also suitable to represent image and brings many advantages to image compression.
This paper presents a simple and fast method to represent vector and matrix using quantum state. Two application examples of the method presented in this paper are given as follows. 1. Applying the method directly to design quantum loading scheme that evades the efficiency bottleneck of classical computer. CPU and memory are the most important two parts of computer, "CPU + Memory=Computer". Loading scheme is defined as loading data into registers of CPU from memory, it connects CPU and memory as a whole machine. Classical loading scheme has time complexity O(N) in terms of arbitrary algorithm, it is the efficiency bottleneck of classical computer. By contrast, quantum loading scheme presented in this paper has time complexity O(logN)! 2. The method is also suitable to represent image and brings many advantages to image compression.
Vector is the general format of input data of most algorithms. Designing unitary operation to load all information of vector into quantum registers of quantum CPU from classical memory is called quantum loading scheme (QLS). QLS assembles classical memory and quantum CPU as a whole computer, which will be important for further quantum computation. We present a QLS based on path interference with time complexity O(logN), while classical loading scheme has time complexity O(N), that is the efficiency bottleneck of classical computer.
Quantum image computing has attracted attention due to its vast storage and faster processing of image data than classical computers. Although classical computing power has grown substantially in the last decade, its abilities have plateaued, struggling to meet the needs of huge datasets. Quantum computers, on the other hand, take advantage of unique qualities like quantum parallelism, superposition, and entanglement to provide faster solutions to complicated problems. Managing huge image data in classical systems necessitates significant memory and hardware resources, which makes quantum computing a possible alternative. Several approaches have arisen for encoding and compressing classical images in the quantum processor. However, one of the most significant limitations is the complexity of quantum state preparation, which translates pixel coordinates to corresponding quantum circuits. Current approaches for representing large-scale images require a huge number of quantum resources including qubit, and qubit connection, which presents significant hurdles. Therefore, this article aims to overview the pixel intensity and state preparation circuit that needs fewer connections, i.e., quantum gates to represent quantum image data, and then explore and design effective compression and processing methods for medium and high-resolution images. This work specializes in emerging quantum models’ potential for enhancing image representation and compression capabilities. It also conducts a comprehensive study of quantum image representation and compression techniques, categorizing existing methods by grayscale and color image types and evaluating their methods, strengths, and limitations. It focuses on crucial difficulties, such as high qubit requirements and complex state preparation, that limit scalability for huge images. This paper also assesses each model’s compression efficacy, which will help future research focus on efficient circuit designs with lower complexity for medium to high-resolution images. It is an essential reference for advancing quantum image processing research since it provides a systematic framework for evaluating quantum image compression and representation algorithms.
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an n-qubit state ψ consists of its inner products with O(2n) stabilizer states. A quantum state initially specified by its 2n entries in the computational basis can be compressed to this form in time O(2npoly(n)), and, subsequently, the compressed description can be used to additively approximate the expectation value of an arbitrary observable. Our compression scheme directly gives a new protocol for the vector in subspace problem with randomized one-way communication complexity that matches (up to polylogarithmic factors) the optimal upper bound, due to Raz. We obtain an exponential improvement over Raz's protocol in terms of computational efficiency.
In recent years, quantum image computing has gained significant attention due to its ability to provide more data storage and process faster than classical computation. These are possible due to the unique properties of quantum mechanism of parallelism, superposition, and entanglement. Compressing and representing classical image data in the quantum domain, as well as state label preparation complexity, is still a challenging issue. The existing techniques typically directly connect the pixel values and their corresponding state label connection without exploring quantum bits i.e. qubits and connection pattern correlation. As a result, the required number of quantum resources, such as gates and qubits to implement quantum circuits, is quite high. This thesis proposes several novel approaches by exploiting correlations within qubits/connections in the state preparation within pixel domain and transform domain. The existing quantum methods need qubits, and quantum gates to represent both pixel intensity and their corresponding position i.e. state preparation information. To reduce the number of qubits and gates required for state preparation, transformation and quantization are applied to the image data. This is because the transformed coefficients are concentrated in a smaller region compared to the pixel domain, allowing the number of state-preparation qubits to be significantly lower. Theoretical analysis and experimental results show that it provides better compression and representation than existing approaches. To represent the quantized transformed coefficient using the existing quantum representing approach, two control gates are needed, one for opening and another for closing the connection to locate each quantized transformed state value. Due to the repetitive use of the same control gates to locate each quantized state connection, a significant number of quantum resources are still required. Furthermore, resetting the output effect of each quantized transformed coefficient state connection on the qubit introduces redundancy in control gate usage and increases circuit complexity. To address state complexity challenges of the quantized transform coefficient approach, a novel reset gate is introduced that can perform the same task for closing the connection of state position. It modifies the closing state connection that nullifies the previous quantized transformed coefficient state connection effect on the next one, eliminating the need for repetitive use of control gates. Although using the reset gate instead of control gate, the proposed approach improves the compression performance, still, this approach requires higher quantum resources to locate the state position of the quantized transformed coefficient alongside. To address this, a novel control gate state connection approach is proposed. It modifies the quantized transformed coefficient connections by discarding ‘0’ values in the state preparation stage, since only input ‘1’ influences the output. This approach significantly reduces the circuit complexity. The experimental results confirm its superior performance in quantum image compression and representation. The required number of qubits for representing large magnitude of coefficient is sometimes higher for high quality images. To address this, a non-zero state connection of pixel values circuit is proposed on top of the block truncation coding compression approach. This approach is easy to implement, cost-effective, and memory-efficient and requires fewer qubits compared to the transformed-based approach. However, this approach requires more connections to complete the whole image circuit. Recently, an autoencoder-based approach has been used to compress quantum images. The main limitation of the autoencoder approach is that it is only applicable to small-scale images with unclear state compression mechanisms. To overcome this limitation, a parameterized position-aware lossy quantum autoencoder is proposed by utilizing the least significant bit (LSB) as a control qubit for optimized state-label information management. We have used a block-based position-aware LSB control qubit approach to improve further compression efficiency. Comparative analysis shows that it outperforms the existing quantum autoencoder approach in terms of gate efficiency as well as image quality.
Quantum Image Representation represents a promising frontier in Machine Learning and image processing. It provides unique opportunities to revolutionize how classical images can be represented as a quantum state using a reasonable number of qubits. This research investigates three state-of-theart Quantum Image Representation techniques to determine their benefits in obtaining a quantum state representing the classical image. By implementing and comparing these techniques, we explore their potential for encoding classical images. Subsequently, the Variational Classifier is applied to investigate whether these encoding types offer advantages over traditional data loading functions. Despite observed efficiency gains, distinguishing significant advantages over traditional data loading techniques remains challenging.
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a novel method for creating quantum states that approximately encode images as amplitudes, based on recently proposed techniques that convert matrix product states to quantum circuits. The numbers of gates and qubits in our method scale logarithmically in the number of pixels given a desired accuracy, which make it suitable for near term quantum computers. Finally, we experimentally demonstrate our technique on 8 qubits of a trapped ion quantum computer for complex images of road scenes, making this the first large instance of full amplitude encoding of an image in a quantum state.