Tunable Quantum Neural Networks in the QPAC-Learning Framework

In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class

Iterative Qubits Management for Quantum Index Searching in a Hybrid System

Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs attempt to deploy their applications that aim to achieve a quantum speedup. Grover's algorithm and quantum phase estimation are the foundations of many applications with the potential for such a speedup. While these algorithms, in theory, obtain marvelous performance, deploying them on existing quantum devices is a challenging task. For example, quantum phase estimation requires extra qubits and a large number of controlled operations, which are impractical due to low-qubit and noisy hardware. To fully utilize the limited onboard qubits, we propose IQuCS, which aims at index searching and counting in a quantum-classical hybrid system. IQuCS is based on Grover's algorithm. From the problem size perspective, it analyzes results and tries to filter out unlikely data points iteratively. A reduced data set is fed to the quantum computer in the next iteration. With a reduction in the problem size, IQuCS requires fewer qubits iteratively, which provides the potential for a shared computing environment. We implement IQuCS with Qiskit and conduct intensive experiments. The results demonstrate that it reduces qubits consumption by up to 66.2%

Quantum Approximate Counting with Nonadaptive Grover Iterations

Approximate Counting refers to the problem where we are given query access to a function f : [N] ? {0,1}, and we wish to estimate K = #{x : f(x) = 1} to within a factor of 1+? (with high probability), while minimizing the number of queries. In the quantum setting, Approximate Counting can be done with O(min (?{N/?}, ?{N/K} / ?) queries. It has recently been shown that this can be achieved by a simple algorithm that only uses "Grover iterations"; however the algorithm performs these iterations adaptively. Motivated by concerns of computational simplicity, we consider algorithms that use Grover iterations with limited adaptivity. We show that algorithms using only nonadaptive Grover iterations can achieve O(?{N/?}) query complexity, which is tight

Quantum Fourier Iterative Amplitude Estimation

Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several quantum algorithms have been proposed to achieve this goal. In this paper, we present an application of Quantum Machine Learning (QML) and Grover's amplification algorithm to build a new tool for estimating Monte Carlo integrals. Our method, which we call Quantum Fourier Iterative Amplitude Estimation (QFIAE), decomposes the target function into its Fourier series using a Parametrized Quantum Circuit (PQC), specifically a Quantum Neural Network (QNN), and then integrates each trigonometric component using Iterative Quantum Amplitude Estimation (IQAE). This approach builds on Fourier Quantum Monte Carlo Integration (FQMCI) method, which also decomposes the target function into its Fourier series, but QFIAE avoids the need for numerical integration of Fourier coefficients. This approach reduces the computational load while maintaining the quadratic speedup achieved by IQAE. To evaluate the performance of QFIAE, we apply it to a test function that corresponds with a particle physics scattering process and compare its accuracy with other quantum integration methods and the analytic result. Our results show that QFIAE achieves comparable accuracy while being suitable for execution on real hardware. We also demonstrate how the accuracy of QFIAE improves by increasing the number of terms in the Fourier series. In conclusion, QFIAE is a promising end-to-end quantum algorithm for Monte Carlo integrals that combines the power of PQC with Fourier analysis and IQAE to offer a new approach for efficiently approximating integrals with high accuracy.Comment: 17 pages, 5 figures, 2 table