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Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the calculation of the eigenvalues of unitary matrices. The QPE algorithm has been combined with Kitaev's algorithm and the inverse quantum Fourier transform (IQFT) which are utilized as a fundamental component of such quantum algorithms. In this paper, we explore the computational challenges of implementing QPE algorithms on noisy intermediate-scale quantum (NISQ) machines using the IBM Q Experience (e.g., the IBMQX4, 5qubit quantum computing hardware platform). Our experimental results indicate that the accuracy of finding the phase using these QPE algorithms is severely constrained by the NISQ computer's physical characteristics such as coherence time and error rates. To mitigate these physical limitations, we propose implementing a modified solution by reducing the number of controlled rotation gates and phase shift operations, thereby increasing the accuracy of the finding phase in near-term quantum computers.

This paper investigates the application of quantum computing technology to airline gate-scheduling quadratic assignment problems (QAP). We explore the quantum computing hardware architecture and software environment required for porting classical versions of these type of problems to quantum computers.We discuss the variational quantum eigensolver and the inclusion of space-efficient graph coloring to the Quadratic Unconstrained Binary Optimization (QUBO). These enhanced quantum computing algorithms are tested with an 8 gate and 24 flight test case using both the IBM quantum computing simulator and a 27 qubit superconducting transmon IBM quantum computing hardware platform.

Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have shown that choosing an effective parameterized quantum circuit (PQC) or ansatz for a VQA is crucial to its overall performance, especially on near-term devices. In this paper, we utilize pulse-level access to quantum machines, our understanding of their twoqubit interactions, and, more importantly, our knowledge of VQAs, to customize the design of two-qubit entanglers. Our analysis shows that utilizing customized pulse gates for ansatze reduces state preparation times by more than half, maintains expressibility relative to standard ansatze, and produces PQCs that are more trainable through local cost function analysis. Our algorithm performance results show that in three cases, our PQC configuration outperforms the base implementation. Experiments using IBM Quantum hardware demonstrate that our pulse-based PQC configurations are more capable of solving MaxCut and Chemistry problems compared to a standard configuration. INDEX TERMSQuantum computing, variational quantum algorithms (VQAs), parameterized quantum circuits (PQCs), pulse level control, hamiltonian tomography, barren-plateaus VOLUME 4, 2016 1 This article has been accepted for publication in IEEE Transactions on Quantum Engineering.