Quantum Supremacy: Experiments & Meaning
Defining Quantum Supremacy
Quantum supremacy — also called quantum advantage — is the milestone at which a programmable quantum computer performs a computation that no classical computer can replicate in a feasible amount of time. John Preskill coined the term in a 2012 lecture, drawing a parallel to the concept of supremacy in other scientific domains. The milestone is scientific rather than practical: the problems used to claim supremacy are specifically designed to be hard for classical computers while easy for quantum ones, not to solve commercially useful tasks. Nevertheless, demonstrating quantum supremacy is a crucial proof that quantum computers can outperform classical ones for a well-defined task, confirming that the theoretical promise of quantum speedup is realizable in engineered hardware (Preskill, “Quantum computing and the entanglement frontier,” arXiv:1203.5813, 2012). The distinction between “supremacy” and “advantage” has become increasingly important as the field matures and shifts focus to practical applications. The term “quantum advantage” is now preferred by many researchers because it describes the more meaningful goal of outperforming classical computers on practically relevant problems.
Google Sycamore (2019)
In October 2019, the Google Quantum AI team published a landmark paper in Nature announcing that their 53-qubit Sycamore processor had achieved quantum supremacy. Sycamore performed 1 million samples from the output distribution of a random quantum circuit in 200 seconds. The team estimated that the same task would take the world’s most powerful classical supercomputer (Summit at Oak Ridge) approximately 10,000 years, using a state vector simulation approach requiring 128 petabytes of memory. The paper, led by John Martinis and Frank Arute, received immediate and intense scrutiny (Arute et al., “Quantum supremacy using a programmable superconducting processor,” Nature, 2019). IBM immediately challenged the result: a team led by Edwin Pednault argued that an improved classical algorithm — based on tensor network contraction — could simulate the same task in 2.5 days on Summit, not 10,000 years. This debate highlighted a persistent theme in supremacy research: classical algorithms and hardware keep improving, meaning the bar for quantum supremacy is a moving target. Despite the controversy, the Sycamore experiment remains a landmark engineering achievement demonstrating precise control of a 53-qubit processor with low error rates. The experiment used a square lattice of transmon qubits with tunable couplers, achieving simultaneous single-qubit and two-qubit gate fidelities above 99.5%.
USTC Zuchongzhi (2021)
In October 2021, Chinese researchers at the University of Science and Technology of China (USTC) led by Jian-Wei Pan published results on their 56-qubit Zuchongzhi processor. The team performed random circuit sampling and claimed a speedup 1 million times greater than Sycamore’s. Their classical simulation estimated 8 years on the fastest supercomputer. Zuchongzhi used superconducting qubits similar in design to Sycamore but with improved connectivity and gate fidelities. The USTC team had previously (2020) demonstrated Gaussian boson sampling with photonic qubits, claiming quantum advantage for a different computational primitive (Zhong et al., “Quantum computational advantage using photons,” Science, 2020). The Zuchongzhi result confirmed that random circuit sampling supremacy is reproducible across different hardware platforms. The 66-qubit Zuchongzhi 2.0 followed in 2022 with further improved fidelity, demonstrating the rapid pace of Chinese quantum hardware development.
Supremacy Versus Advantage
The term “quantum advantage” is increasingly preferred to “quantum supremacy” because it describes the more meaningful goal of outperforming classical computers on practically relevant problems. The distinction matters: supremacy experiments use synthetic benchmarks selected for classical hardness, while advantage requires solving a problem people actually care about. In 2023, IBM demonstrated what they called “quantum utility” — using a 127-qubit Eagle processor to compute magnetic properties of materials that are challenging for classical methods, with accuracy validated by experimental data. This represented a shift from synthetic benchmarks to scientifically relevant calculations, even though classical simulation was still possible with sufficient effort (Kim et al., “Evidence for the utility of quantum computing before fault tolerance,” Nature, 2023). The utility-scale milestone has been adopted by several hardware vendors as a more meaningful metric than raw qubit count or supremacy claims. The quantum utility demonstration showed that quantum computers can already contribute to scientific discovery in specific domains, even without full fault tolerance.
Gaussian Boson Sampling
In parallel to the superconducting qubit race, photonic quantum computing has pursued supremacy through Gaussian Boson Sampling (GBS). Xanadu’s 2025 Borealis processor demonstrated GBS with 216 squeezed states, claiming a quantum advantage for a specific sampling task. Unlike random circuit sampling, GBS may have practical applications: the output distribution encodes the Hafnian of a matrix, which relates to graph problems like perfect matching and molecular vibronic spectra. This connection to practical problems gives GBS a potential path from supremacy to advantage. Photonic approaches have the additional advantage of operating at room temperature, though they face challenges with loss and scalability. Recent advances in photon sources and detectors have improved GBS fidelity significantly.
The Classical Competition
Classical simulation techniques continue to improve, pushing the frontiers of what is verifiably quantum. Tensor network methods based on matrix product states can simulate random circuits with hundreds of qubits as long as the circuit is shallow enough that entanglement remains bounded. Supercomputers with GPU acceleration can simulate 40+ qubit circuits directly through state vector methods. Specialized algorithms, like those using Schrödinger-Feynman hybrid techniques, partition large circuits into smaller pieces that are simulated separately and recombined. The ongoing competition between quantum hardware and classical simulation methods means that maintaining a supremacy claim requires continuous hardware improvement — a pattern that has played out in every supremacy experiment to date. The development of tensor network algorithms specifically optimized for random circuit sampling has narrowed the gap between quantum and classical performance significantly.
Random Circuit Sampling
The standard computational primitive for quantum supremacy is random circuit sampling: given a random quantum circuit on n qubits with depth d, sample bitstrings from the output distribution. Classical simulation of this task requires one of two approaches. State vector simulation stores the full 2ⁿ amplitude vector — 128 petabytes for 53 qubits — which exceeds the memory capacity of current supercomputers. Tensor network methods contract the circuit as a tensor network, which can reduce memory requirements but increases computation time exponentially with circuit depth. The hardness of simulating random circuits has been analyzed extensively by Aaronson and Arkhipov (2011), who provided complexity-theoretic evidence that approximate sampling from random quantum circuits is classically hard under plausible conjectures (“The computational complexity of linear optics,” Theory of Computing, 2011). The hardness proof relies on the conjecture that the permanent of random Gaussian matrices is hard to approximate, connecting quantum supremacy to well-studied computational hardness assumptions.
Cross-Entropy Benchmarking
Cross-entropy benchmarking (XEB) is the standard method for verifying quantum supremacy. The linear XEB score compares the measured output distribution against the ideal (classically computed) distribution for the quantum circuit. If the score exceeds approximately 0.1%, the output is unlikely to come from any efficiently computable classical distribution. The XEB score also serves as a fidelity metric: it measures how close the actual quantum processor is to ideal behavior, with noise reducing the score. The Google Sycamore experiment achieved a linear XEB score of 0.2%, sufficiently above the threshold to claim supremacy. Patch XEB, an improved verification technique, reduces the classical computational cost of computing the reference distribution by splitting the circuit into independently verifiable patches.
Impact on Quantum Roadmaps
Quantum supremacy demonstrations have shaped hardware development roadmaps across the industry. Google’s 2019 result validated the superconducting qubit approach and justified continued scaling investment, directly leading to the Willow processor and the 1,000+ qubit roadmap. USTC’s results demonstrated that multiple hardware platforms can achieve supremacy, reducing technology risk for the broader field. The supremacy milestones have also influenced government policy: the US National Quantum Initiative reauthorization in 2023 referenced supremacy results when justifying increased funding. Critically, the supremacy results shifted the conversation from “if” quantum advantage is possible to “when” it will be practically useful. Hardware vendors now compete on error rates, qubit quality, and utility-scale demonstrations rather than raw qubit counts. The focus has moved from supremacy to fault-tolerant quantum computing, with concrete roadmaps from IBM (Blue Jay by 2033), Google (2029 utility-scale target), and Microsoft (topological qubit milestones).
Frequently Asked Questions
Did Google actually achieve quantum supremacy? Google’s 2019 Sycamore result demonstrated a clear speedup over classical state-vector simulation. IBM showed improved classical algorithms could simulate it faster than Google claimed, but the result remains a landmark quantum engineering achievement.
What is the difference between quantum supremacy and quantum advantage? Supremacy is the scientific milestone of outperforming classical computers on any problem. Advantage means outperforming them on a practically useful problem.
What is random circuit sampling? Random circuit sampling is the task of generating samples from the output distribution of a random quantum circuit — a problem designed to be hard for classical computers.
How is quantum supremacy verified? Through cross-entropy benchmarking, which compares the output distribution against the ideal distribution to confirm genuinely quantum behavior.
Has quantum supremacy been replicated? Yes — USTC’s Zuchongzhi (2021) replicated supremacy with random circuit sampling, and multiple photonic experiments have claimed advantage through Gaussian Boson Sampling.
Related: Quantum Computing Guide | Quantum Error Correction | Quantum Algorithms Guide