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.
In recent years, significant progress has been made in building quantum computers by several companies. Despite the progress, these noisy intermediate-scale quantum (NISQ) computers still suffer from several noises and errors such as measurement errors, multi-qubit gate errors, and worse, short decoherence times. Though quantum computer vendors are releasing better quantum computers in terms of Quantum Volume, the quantum device still remains far from quantum supremacy in practical problems. The Quantum Approximate Optimization Algorithm (QAOA) was suggested to potentially demonstrate a computational advantage in combinatorial optimization problems on NISQ computers. In this paper, we optimize the QAOA circuits and to scale the problem size on IBM quantum processors. In addition, we study the effect of the length of the QAOA ansatz on IBM quantum processors and discuss optimal implementation methods for scalable QAOA. We test our implementations on the MaxCut problems.
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