A generalization of the new quantum block representation by basis states (QBRBS) is presented and analyzed. This representation facilitates the manipulation of signals by providing a flexible block size to store signal elements. Furthermore, QBRBS uses quantum superposition and entangled qubits to store signal values on the basis states of qubit registers instead of probability amplitude, enabling accurate information retrieval after finite measurements. A detailed analysis exposed a polynomial growth in qubit complexity and decreased quantum complexity on the presented quantum block format. The geometric, statistical, element-value, element-value block, and block position operations are described. Simulation experiments show the feasibility and capabilities of the block representation to achieve data hiding applications. A quantum steganography scheme exploiting the QBRBS features is presented. Finally, the quantum circuit and simulation verification are performed using Qiskit.
A generalization of the new quantum block representation by basis states (QBRBS) is presented and analyzed. This representation facilitates the manipulation of signals by providing a flexible block size to store signal elements. Furthermore, QBRBS uses quantum superposition and entangled qubits to store signal values on the basis states of qubit registers instead of probability amplitude, enabling accurate information retrieval after finite measurements. A detailed analysis exposed a polynomial growth in qubit complexity and decreased quantum complexity on the presented quantum block format. The geometric, statistical, element-value, element-value block, and block position operations are described. Simulation experiments show the feasibility and capabilities of the block representation to achieve data hiding applications. A quantum steganography scheme exploiting the QBRBS features is presented. Finally, the quantum circuit and simulation verification are performed using Qiskit.
We present the first quantum version of the one-dimensional integer wavelet S-Transform (QIST). This version is based on a new Quantum Block Representation by Basis States (QBRBS) and the design of a quantum rounding operator. The QBRBS format facilitates storing and manipulating pairs of signal elements, decreasing the use of additional qubits and gates. Also, the quantum rounding operator exploits the features of the S-Transform to avoid nonlinearities. Complete quantum circuits for addition, subtraction, and halving operations were developed. The complexity analysis showed a polynomial quantum complexity, O(n), and a time complexity of O(1). The experiments performed on MATLAB and Qiskit verify the theoretical results coinciding with the results of the classical version. Finally, the new quantum transform’s feasibility and accuracy enable new quantum developments in information hiding, compression, and IoT applications.
Quantum Mean Filtering (QMF) leverages quantum properties for efficient filtering but faces challenges such as storage overhead, garbage information, boundary conditions, and iterative filtering limitations. Therefore, this paper proposes an improved QMF using Quantum Block Representation by Basis States (QBRBS) and an entire shift operation. The proposed method decreases storage requirements, eliminates garbage information, handles boundary conditions, enables iterative filtering, and reduces quantum complexity. Comparative analysis shows that QBRBS-based QMF outperforms traditional QMF in terms of storage efficiency, measurement complexity, iterative capabilities, and quantum circuit complexity, significantly enhancing the practicality of quantum filtering.
Quantum signal processing offers a possible solution to store and process massive signals efficiently. As the foundation of quantum signal processing, quantum signal representation (QSR) that stores color information using basis states, is convenient to retrieve accurately signals from quantum systems. But the existing QSRs are only focus on integer signals (i.e., images) and are difficult to be directly operated by quantum Fourier transform (QFT) and quantum wavelet transform (QWT). Thus, we propose four models of QSR for integer, real, and complex signals. Furthermore, we design quantum implementation circuits of type conversions of QSR with complexityO(1). Type conversions of QSR are illustrated by general processes of QFT and Haar QWT, and demonstrate that the proposed QSRs are suitable for QFT and QWT.
There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around 90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.
In recent years, quantum image computing draws a lot of attention due to storing and processing image data faster compared to classical computers. A number of approaches have been proposed to represent the quantum image inside a quantum computer. Representing and compressing medium and big-size images inside the quantum computer is still challenging. To address this issue, we have proposed a block-wise DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) approach to represent and compress the gray-scale image efficiently to save computational time and reduce the quantum bits (qubits) for the state preparation. In this work, we have demonstrated the capability of block-wise DCT and DWT transformation inside the quantum domain to investigate their relative performances. The Quirk simulation tool is used to design the corresponding quantum image circuit. In the proposed DCT-EFRQI approach, a total of 17 qubits are used to represent the coefficients, the connection between coefficients and state (i.e., auxiliary), and their position for representing and compressing grayscale images inside a quantum computer. Among those, 8 qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position including one auxiliary qubit. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of rate-distortion performance.
Currently, quantum steganography schemes utilizing the least significant bit (LSB) approach are primarily optimized for fixed-point data processing, yet they encounter precision limitations when handling extended floating-point data structures owing to quantization error accumulation. To overcome precision constraints in quantum data hiding, the EPlsb-MFQS and MVlsb-MFQS quantum steganography algorithms are constructed based on the LSB approach in this study. The multichannel floating-point quantum representation of digital signals (MFQS) model enhances information hiding by augmenting the number of available channels, thereby increasing the embedding capacity of the LSB approach. Firstly, we analyze the limitations of fixed-point signals steganography schemes and propose the conventional quantum steganography scheme based on the LSB approach for the MFQS model, achieving enhanced embedding capacity. Moreover, the enhanced embedding efficiency of the EPlsb-MFQS algorithm primarily stems from the superposition probability adjustment of the LSB approach. Then, to prevent an unauthorized person easily extracting secret messages, we utilize channel qubits and position qubits as novel carriers during quantum message encoding. The secret message is encoded into the signal’s qubits of the transmission using a particular modulo value rather than through sequential embedding, thereby enhancing the security and reducing the time complexity in the MVlsb-MFQS algorithm. However, this algorithm in the spatial domain has low robustness and security. Therefore, an improved method of transferring the steganographic process to the quantum Fourier transformed domain to further enhance security is also proposed. This scheme establishes the essential building blocks for quantum signal processing, paving the way for advanced quantum algorithms. Compared with available quantum steganography schemes, the proposed steganography schemes achieve significant improvements in embedding efficiency and security. Finally, we theoretically delineate, in detail, the quantum circuit design and operation process.