# Quantum Advantage

The term “quantum advantage” can refer to the experimental demonstration of a quantum algorithm solving a real-world problem on a quantum computer faster than any classical algorithm running on any classical computer. Because quantum computing terminology is not standardized, the term may also be applied to theoretical speedups – those that have not been demonstrated experimentally – as well as to problems with no known real-world utility.

The promise of such computational advantages for real-world problems fuels investments into relevant organizations. Although academic institutions favor exponential speedups, enterprises value any edge over competitors, including quadratic and quartic speedups.

## What is Quantum Advantage?

Although the term “quantum advantage” was initially applied to speed, other potential advantages have been discovered. As noted on our “Quantum Computer Technology: Architecture, Advantages and Disadvantages” page, these other advantages include:

- The enhanced precision of computation over classically-intractable problems that currently need to be solved approximately
- The tremendous compression of classical data, which is advantageous for the storage and transmission of such data
- Advancements in science from the simulation of quantum systems in ways that would otherwise be impossible
- The generation of quantum cryptographic keys for the encryption, secure transmission, and decryption of classical data

Other advantages have been cited that result from quantum computing being primarily cloud services. Although these advantages apply to other cloud services, as well, they can be thought of as advantages over on-premises high performance computing (HPC) resources. As noted on our “Quantum-as-a-Service: Definition, Advantages and Examples” page, these advantages include:

- No purchase, installation, or maintenance expenses
- Pay only for consumed resources, not idle resources
- Scale up or down, as needed
- Easy switching to other technologies
- Global collaboration
- Provider expertise

Furthermore, quantum computers are generally recognized as consuming less energy than HPC resources. This is financially advantageous if the hardware is on-site, and it is the more environmentally-responsible option regardless of location.

## Quantum Supremacy vs. Quantum Advantage

In comparing the terms quantum advantage vs quantum supremacy, it must be noted that the terms are often used interchangeably. In regard to their most common uses, however, there are distinctions in their definitions:

- “Quantum supremacy” most commonly refers to the experimental demonstration of a quantum algorithm solving a problem on a quantum computer that is infeasible for any supercomputer within a reasonable amount of time.
- “Quantum advantage” most commonly refers to the experimental demonstration of a quantum algorithm solving a real-world problem on a quantum computer faster than any classical algorithm on any classical computer.

The key differences between these definitions, therefore, are:

- “Supremacy” can be demonstrated on any problem, regardless of its usefulness, whereas “advantage” is concerned with useful, real-world problems.
- “Supremacy” does not require quantum error correction (QEC), whereas “advantage” requires QEC for the results to be useful.
- “Supremacy” has no relevance for commercial activity, whereas “advantage” is highly relevant for commercial activity.
- “Advantage” can also apply, as previously noted, to benefits that are not associated with the duration of computation.

In summary, “Supremacy” usually has one straightforward meaning, which involves solving problems that supercomputers cannot, whether the problems need to be solved or not. A Techopedia article titled “Quantum Advantage” adds that the parameters of “supremacy” experiments ought to be “reasonable.” Either way, “advantage” is the far more versatile and practical term.

Besides its versatility, Nature correspondence titled “Instead of ‘supremacy’ use ‘quantum advantage’” highlights another reason for the shift in recent years to the increased use of “advantage.” Despite objections, however, the term “supremacy” remains in use for extreme demonstrations of quantum computation.

## Quantum Advantage in Optimization

Quantum advantage in optimization retains the definition of quantum advantage, but applied specifically to solving optimization problems. One reason for this distinction is the classical intractability of many of these problems, all of which have real-world applicability. As these problems scale in size, their complexity can grow much faster.

Hybrid classical-quantum algorithms exist that, like classical algorithms, have scaling problems. The reason for the increased attention, therefore, is the discovery of the applicability of the Rydberg states of neutral atoms to solve certain classically-intractable problems without scaling issues. This is now being looked at as potentially the quickest realization of true quantum advantage.