Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond

Abstract

Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction-representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classical resources it consumes), but whether classical components are crucial to an underlying model of the computation. We then take a broader view of this question, reviewing a number of hybrid algorithms and discussing what makes them hybrid, as well as the history of how they emerged and considerations related to hardware. This leads into a natural discussion of what the future holds for these algorithms. To answer this question, we turn to the use of specialized processors in classical computing. The classical trend is not for new technology to completely replace the old, but to augment it. We argue that the evolution of quantum computing is unlikely to be different: Hybrid algorithms are likely here to stay well past the NISQ era and even into full fault tolerance, with the quantum processors augmenting the already powerful classical processors which exist by performing specialized tasks.

Improved Iterative Quantum Algorithm for Ground‐State Preparation

“…It was also remarked that the condition (19) was impractical since the eigenvalues of  were required to be estimated in advance. Thus, a practical strategy is provided to choose 𝜇 by demonstrating the equivalence between the imaginary time evolution (ITE) and the algorithm proposed in Section 2.1.…”

“…VQE obtains the ground state with a proper choice of ansatz, a suitable cost function and a controllable classical optimization. [16][17][18][19] Nevertheless, VQE may face obstacles such as highly depending on the expressibility of the chosen ansatz and the so-called barren plateau which makes the optimization track detract from the global minimum. [20] In order to circumvent the barren plateau, imaginary time evolution (ITE) is an alternative which drives an initial state to the ground state after long time evolution.…”

Understanding domain-wall encoding theoretically and experimentally

“…While this is an area with great promise, available devices exist in relatively early stages of development, which is often termed the noisy intermediate-scale quantum [12] era of quantum computing. In these early stages, it is crucial to be able to get the most out of these devices through, among other things, optimal encoding of problems [13].…”

A Preprocessing Perspective for Quantum Machine Learning Classification Advantage in Finance Using NISQ Algorithms

“…Qubits will lose their entanglement, and so will also lose the information. These devices make up the NISQ era [ 9 ] and limit the use of quantum algorithms or hybrid algorithms to be useful [ 10 ].…”