Quantum computing scaling laws (sometimes abbreviated asQC scaling laws) are a set of observations describing theexponential growth of various aspects ofquantum computer development. The most important scaling laws in quantum computing are Rose's law, Neven's law, and Schoelkopf's law. These laws are named after prominent quantum computing researchers and predict continued improvement in quantum computer performance in the coming years. However, it is important to note that these laws are more empirical rules of thumb and predictions based on observations rather than immutable truths, and technological development may bring unexpected challenges and breakthroughs.[a]
Rose's law observes that the number ofqubits on chips doubles roughly every 18 months.[1][2] The law is often described as the quantum-computing equivalent ofMoore's law.[3][4] The term was coined by Steve Jurvetson after meeting D-Wave founder Geordie Rose.[5] This law attempts to measure rapid processor scaling, though different quantum computing technologies may follow different trajectories depending on their design constraints.[4][5]
Neven's law states that the computational power of quantum computers appears to be growing at adoubly exponential rate.[6] In other words, not only is computational power increasing exponentially—that exponential growth is itself accelerating exponentially.[6]
The law is named forHartmut Neven, Google's Quantum AI team lead, named one ofFast Company's Most Creative People of 2020.[7] He has remarked: "It's not one company versus another, but rather, humankind versus nature—or humankind with nature."[8] Neven's law suggests thatquantum advantage may emerge much sooner than linear or simple exponential models predict, thanks to compounding improvements.[6][8]
Some authors have noted that the conceptual basis of Neven's law—compounding exponential trends due to qubit growth andHilbert space scaling—was discussed earlier. For example,Jonathan Dowling illustrated in Schrödinger's Killer App (2013) that qubit counts could grow exponentially and that the size of Hilbert space grows exponentially with the number of qubits, calling this “super-exponential” growth.[9][10][11] A 2020 memorial article in Nature Photonics referred to this combined idea as the “Dowling–Neven law”, although this term is not widely used in the literature.[9]
Schoelkopf's law observes thatdecoherence times in quantum computing roughly improve tenfold every three years.[12][13][14] Decoherence time indicates how long a quantum state remains stable enough for computation.[12][13] After that, interference from the environment causes the state to decay, losing quantum information.[14] Extending coherence is critical for running complex quantum algorithms reliably.[13][15] Named afterRobert J. Schoelkopf, this scaling law addresses one of quantum computing's most fundamental challenges.[12][15]
p. 391: "The growth in the number of qubits, as per Moore's law, is exponential by year. Because the size of the Hilbert space, vertical scale, is exponential in the number of qubits, it is therefore super exponential.", pp. 402–403: "The quantum computers will follow a quantum version of Moore's law, outlined above, exponential growth in the number of qubits, and a consequent super-exponential growth in the dimension of the Hilbert space where all the quantum computational power is.
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