A variant of QAE algorithm by Suzuki et al. called maximum likelihood amplitude estimation (MLAE) achieves the amplitude estimation by varying depths of Grover operators and post-processing for maximum likelihood estimation without the additional controlled operations and QFT. However, MLAE requires running multiple circuits of different depths of Grover operators. On the other hand, quantum multi-programming (QMP) is a computing method that executes multiple quantum circuits concurrently on a quantum computer. The quantum circuits executed concurrently can be different and even have different circuit depths. The main motivation of the QMP is that the number of qubits of NISQ computers is much greater than their quantum volume. In this work, using QMP in conjunction with MLAE makes it possible to run MLAE using a single circuit, thus requiring sampling much fewer times. We validate this algorithm for a numerical integration problem using NVIDIA’s open-source platform CUDA Quantum (simulator), Qiskit (simulator) and Quantinuum H2 device.
Growing interest in quantum machine learning has resulted into very innovative algorithms and vigorous studies that demonstrate their power. These studies, although very useful, are often designed for fault-tolerant quantum computers that are far from reality of today's noise-prone quantum computers. While companies such as IBM have ushered in a new era of quantum computing by allowing public access to their quantum computers, quantum noise as well as decoherence are daunting obstacles that not only degrade the performance of quantum algorithms, but also make them infeasible for running on current-era quantum processors. We address the feasibility of a quantum machine learning algorithm on IBM quantum processors to shed light on their efficacy and weaknesses to design noise-aware algorithms that work around these limitations. We compare and discuss the results by implementing a quantum convolutional filter on a real quantum processor as well as a simulator.
Since the publication of the Quantum Amplitude Estimation (QAE) algorithm by Brassard et al., 2002, several variations have been proposed, such as Aaronson et al., 2019, Grinko et al., 2019, and Suzuki et al., 2020. The main difference between the original and the variants is the exclusion of Quantum Phase Estimation (QPE) by the latter. This difference is notable given that QPE is the key component of original QAE, but is composed of many operations considered expensive for the current NISQ era devices. We compare two recently proposed variants (Grinko et al., 2019 and Suzuki et al., 2020) by implementing them on the IBM Quantum device using Qiskit, an open source framework for quantum computing. We analyze and discuss advantages of each algorithm from the point of view of their implementation and performance on a quantum computer.
This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002) in conjunction with Grover’s algorithm. However, QAE is daunting to implement on NISQ devices since it typically relies on Quantum Phase Estimation (QPE), which requires many ancilla qubits and controlled operations. To mitigate these challenges, a recently published QAE algorithm (Suzuki et al., 2020), which does not rely on QPE, requires a much smaller number of controlled operations and does not require ancilla qubits. We implement this new algorithm for numerical integration on IBM quantum devices using Qiskit and optimize the circuit on each target device. We discuss the application of this algorithm on two qubits and its scalability to more than two qubits on NISQ devices.
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