- Fundamentals
- Also: quantum supremacy
- Also: quantum computational advantage
Quantum Advantage Claims
Quantum advantage claims are experimental demonstrations where a quantum device solves a specific problem faster than classical computers, though the practical relevance and classical hardness of such benchmarks remain actively debated.
A quantum advantage claim is a published experimental result asserting that a quantum device has solved a specific computational task faster or more efficiently than the best known classical algorithm. These claims attract significant scientific and media attention, but their interpretation requires careful scrutiny.
History of Notable Claims
Google (2019): Google’s Sycamore processor sampled from a random circuit output distribution in 200 seconds, which Google claimed would take 10,000 years on a classical supercomputer. This was widely reported as “quantum supremacy.” IBM subsequently disputed the classical estimate, arguing Summit could perform the sampling in days. Later improvements to classical simulation algorithms brought the classical runtime further down.
USTC (2020, 2021): The University of Science and Technology of China demonstrated Gaussian boson sampling using the Jiuzhang device, claiming a 100-trillion-fold speedup over classical methods. A followup experiment with Jiuzhang 2.0 increased the claimed advantage. Classical simulation algorithms have continued to improve against these benchmarks.
IBM (ongoing): IBM’s quantum utility demonstrations focus on simulating quantum systems (such as the kicked Ising model) and comparing to classical methods, arguing that quantum devices can outperform classical simulation for specific physically motivated problems on ~100-qubit devices.
Why Claims Are Contested
Improving classical algorithms. When a quantum advantage claim appears, classical algorithm researchers are motivated to develop better simulation methods. Advantage claims in random circuit sampling and boson sampling have been progressively weakened by classical improvements. An advantage valid in 2019 may not hold in 2024.
Problem selection. Most advantage demonstrations use problems specifically designed to be hard classically and easy quantumly. These problems, such as random circuit sampling or Gaussian boson sampling, have no known practical applications. Demonstrating an advantage on a practically useful problem (chemistry, optimization, machine learning) has not yet occurred.
Verification difficulty. If a quantum device solves a problem that is classically intractable, you cannot verify the answer classically. This creates a fundamental tension: the problems most amenable to quantum advantage claims are also the problems where independent verification is hardest.
Hardware noise. NISQ devices produce noisy outputs. A claim of quantum advantage over classical simulation of the ideal circuit may not hold if the quantum device’s output is actually easy to classically simulate due to noise.
Quantum Advantage vs Quantum Utility
“Quantum advantage” traditionally means a provable speedup on a problem with practical value. “Quantum supremacy” (now less favored due to its connotations) meant any computational task done faster. “Quantum utility” is a newer term used by IBM to describe cases where quantum computation produces useful results competitive with or better than classical methods, without necessarily being strictly faster.
The terminology shift reflects a pragmatic move: strict quantum advantage on practical problems remains elusive, while demonstrating usefulness on real physics problems is achievable today.
What a Valid Claim Requires
A credible quantum advantage claim should specify the exact problem and input distribution, provide the best known classical algorithm and its runtime on the best available hardware, demonstrate the quantum result is accurate (not just fast), and be reproducible by independent groups. Very few existing claims meet all these criteria.
Looking Forward
Fault-tolerant quantum computers running algorithms like Shor’s (for factoring) or QPE-based chemistry simulation are expected to provide clear, practical advantages that classical algorithms cannot match. These require logical qubits with error rates below the fault-tolerance threshold and are likely a decade or more away at scale.