Israel F. Araujo

The initialization of quantum states or Quantum State Preparation (QSP) is a basic subroutine in quantum algorithms. In the worst case, general QSP algorithms are expensive due to the application of multi-controlled gates required to build the quantum state. Here, we propose an algorithm that detects whether a given quantum state can be factored into substates, increasing the efficiency of compiling the QSP circuit when we initialize states with some level of unentanglement. The simplification is done by eliminating controls of quantum multiplexers, significantly reducing circuit depth and the number of CNOT gates with a better execution and compilation time than the previous QSP algorithms. Considering efficiency in terms of depth and number of CNOT gates, our method is competitive with the methods in the literature. However, when it comes to run-time and compilation efficiency, our result is significantly better, and the experiments show that by increasing the number of qubits, the gap between the temporal efficiency of the methods increases.

This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational quantum autoencoders, which depend on stochastic optimization and face challenges such as shot noise, barren plateaus, and non-convex optimization landscapes, our deterministic method substantially reduces the complexity and computational overhead of quantum data compression. We evaluate the performance of the compressor through numerical experiments, demonstrating its ability to achieve high fidelity in quantum state reconstruction compared to variational quantum algorithms. Furthermore, we demonstrate the practical utility of the Schmidt quantum compressor in one-class classification tasks.

This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational quantum autoencoders, which depend on stochastic optimization and face challenges such as shot noise, barren plateaus, and non-convex optimization landscapes, our deterministic method substantially reduces the complexity and computational overhead of quantum data compression. We evaluate the performance of the compressor through numerical experiments, demonstrating its ability to achieve high fidelity in quantum state reconstruction compared to variational quantum algorithms. Furthermore, we demonstrate the practical utility of the Schmidt quantum compressor in one-class classification tasks.

We provide a method for compiling approximate multicontrolled single qubit gates into quantum circuits. Without ancilla qubits, the total number of elementary gates to decompose an n-qubit multicontrolled gate is proportional to 32n elementary operations. The proposed decomposition depends on an optimization technique that minimizes the CNOT gate count for multitarget and multicontrolled CNOT and SU(2) gates. We also provide an approximate decomposition with ancilla qubits with lower-circuit complexity. Computational experiments show the reduction of CNOT gates when multicontrolled U(2) gates are applied. As multicontrolled single-qubit gates serve as fundamental components of quantum algorithms, the proposed decomposition offers a comprehensive solution that can significantly decrease the count of elementary operations employed in quantum computing applications.

Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data and has substantial impacts on performance outcomes. In this study, we present neural quantum embedding (NQE), a method that efficiently optimizes quantum embedding beyond the limitations of positive and trace-preserving maps by leveraging classical deep-learning techniques. NQE enhances the lower bound of the empirical risk, leading to substantial improvements in classification performance. Moreover, NQE improves robustness against noise. To validate the effectiveness of NQE, we conduct experiments on IBM quantum devices for image data classification, resulting in a remarkable accuracy enhancement from 0.52 to 0.96. In addition, numerical analyses highlight that NQE simultaneously improves the trainability and generalization performance of quantum neural networks, as well as of the quantum kernel method.

We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits without ancilla qubits. The total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n, and the previous best approximate approach without auxiliary qubits requires 32nk elementary operations, where k is a function that depends on the error threshold. The proposed decomposition depends on an optimization technique that minimizes the CNOT gate count for multi-target and multi-controlled CNOT and SU(2) gates. Computational experiments show the reduction in the number of CNOT gates to apply multi-controlled U(2) gates. As multi-controlled single-qubit gates serve as fundamental components of quantum algorithms, the proposed decomposition offers a comprehensive solution that can significantly decrease the count of elementary operations employed in quantum computing applications.