The discussion below applies only to gate-based quantum computer architectures. The quantum annealing-based devices produced by the Canadian company D-Wave can solve production-scale optimization problems today.

The first practical demonstration of a quantum supremacy experiment was realized by Google in 2019 by executing on a quantum computer a task that cannot be reproduced using the fastest existing super-computers in a reasonable amount of time. While this experiment marked a huge achievement, the task itself was sampling from a probability distribution which is prohibitively hard to recreate classically. This could possibly be useful for generating random numbers but, in general, is not of much practical interest. The term Quantum Advantage is reserved for demonstrating quantum supremacy for a task of practical interest and when realized, will mark the next major milestone for the field of quantum computing.

The capabilities of a quantum device can be characterized by scale, quality, and speed. The scale is measured by the number of qubits. The quality is a function of the qubit connectivity, the fidelity of the quantum gates, and the precision of measurements. The speed is roughly given by how fast quantum circuits can be generated in real time using classical computing resources and then executed using quantum computing resources on a quantum device. While depending on the quantum technology used, these numbers differ, we have seen in recent years improvements, even by orders of magnitude for these parameters. This progress and also some very recent results from IBM indicate that quantum advantage will be achieved soon.

An important question is what will be the first concrete practical application for which quantum advantage will be achieved? There are several constraints that apply here, first we assume that error correction is not yet available, which rules out many well-known quantum algorithms like Grover and Shor. Many of the promising applications in Machine Learning require the existence of QRAM, a device that does not exist yet. For large-scale optimization tasks, while promising quantum heuristics exist, the case for quantum advantage has not been made convincingly enough theoretically. Simulation of physical systems for chemistry is one instance of a problem for which the input data size is small enough such that it can be easily loaded on current NISQ devices, while the existing classical solutions are known to scale exponentially with system size. This makes many of us believe that chemistry will be the first field where quantum computers will deliver real value. Please use this link to contact us, if you want to learn more about our investigations on solving chemistry problems using quantum computers.