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The predictive success of quantum mechanics underpins many areas of modern science, even as the exact simulation of large, interacting quantum systems remains beyond the reach of classical computation.

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The goal of benchmarking is to determine how far the output of a noisy system is from its ideal behavior; this becomes exceedingly difficult for large quantum systems where classical simulations become intractable.

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Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers.

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Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term.

Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian.

Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies.

We introduce a volumetric benchmark for near-term quantum platforms based on the generation and verification of genuine entanglement across n-qubits using graph states and direct stabilizer measurements.

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems.

The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers.

Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior.

One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE).

Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance.

Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver.

High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer.

Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise.

Superconducting transmon qubits are of great interest for quantum computing and quantum simulation.

The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors.

Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge.