Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation

Abstract

Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field.

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• Resource frugal optimizer for quantum machine learning
• Synergistic Dynamical Decoupling and Circuit Design for Enhanced Algorithm Performance on Near-Term Quantum Devices
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Improving the Performance of Digitized Counterdiabatic Quantum Optimization via Algorithm-Oriented Qubit Mapping
• Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models
• Quantum homotopy analysis method with quantum-compatible linearization for nonlinear partial differential equations
• Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
• High-fidelity dimer excitations using quantum hardware
• Application of Quantum Pre-Processing Filter for Binary Image Classification with Small Samples
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Constraint-Aware Quantum Optimization via Hamming Weight Operators
• Tomography-assisted noisy quantum circuit simulator using matrix product density operators
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• The Dual Role of Low-Weight Pauli Propagation: A Flawed Simulator but a Powerful Initializer for Variational Quantum Algorithms
• Circuit-Noise-Resilient Virtual Distillation