Quantum computing makes use of quantum resources provided by the underlying quantum nature of matter to enhance classical computation. However, current Noisy Intermediate-Scale Quantum (NISQ) era in quantum computing is characterized by the use of quantum processors comprising from a few tens to, at most, few hundreds of physical qubits without implementing quantum error correction techniques. This limits the scalability in the implementation of quantum algorithms. Digital-analog quantum computing (DAQC) has been proposed as a more resilient alternative quantum computing paradigm to outperform digital quantum computation within the NISQ era framework. It arises from adding the flexibility provided by fast single-qubit gates to the robustness of analog quantum simulations. Here, we perform a careful comparison between digital and digital-analog paradigms under the presence of noise sources. The comparison is illustrated by comparing the performance of the quantum Fourier transform algorithm under a wide range of single-and two-qubit noise sources. Indeed, we obtain that, when the different noise channels usually present in superconducting quantum processors are considered, the fidelity of the QFT algorithm for the digital-analog paradigm outperforms the one obtained for the digital approach. Additionally, this difference grows when the size of the processor scales up, constituting consequently a sensible alternative paradigm in the NISQ era. Finally, we show how the DAQC paradigm can be adapted to quantum error mitigation techniques for canceling different noise sources, including the bang error.
We propose a new hybrid quantum algorithm based on the classical Ant Colony Optimization algorithm to produce approximate solutions for NP-hard problems, in particular optimization problems. First, we discuss some previously proposed Quantum Ant Colony Optimization algorithms, and based on them, we develop an improved algorithm that can be truly implemented on near-term quantum computers. Our iterative algorithm codifies only the information about the pheromones and the exploration parameter in the quantum state, while subrogating the calculation of the numerical result to a classical computer. A new guided exploration strategy is used in order to take advantage of the quantum computation power and generate new possible solutions as a superposition of states. This approach is specially useful to solve constrained optimization problems, where we can implement efficiently the exploration of new paths without having to check the correspondence of a path to a solution before the measurement of the state. As an example of a NP-hard problem, we choose to solve the Quadratic Assignment Problem. The benchmarks made by simulating the noiseless quantum circuit and the experiments made on IBM quantum computers show the validity of the algorithm.
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