Way back in the ancient era of 2001, long before the days of iPhones, back when TV was in black and white and dinosaurs still roamed the earth, I delivered a talk on quantum computing at DEF CON 9.0. In the conclusion I offered some projections about the growth of quantum computing based on reported growth of qubits to date. Between the first qubit in 1995 and the 8 qubit system announced before my talk in 2001, qubits were doubling about every 2 years.
I drew a comparison with Moore’s law that computers double in power every 18 months, or as 2(years/1.5). A feature of quantum computers is that the power of a quantum computer increases as the power of the number of qubits, which is itself doubling at some rate, then two years, or as 22(years/2), or, in ASCII: Moore’s law is 2^(Y/1.5) and Gessel’s law is 2^2^(Y/2).
As far as I know, nobody has taken up my formulation of quantum computing power as a time series double exponential function of the number of qubits in a parallel structure to Moore’s law. It seems compelling, despite obviously having a few (minor) flaws. A strong counter argument to my predictions is that useful quantum computers require stable, actionable qubits, not noisy ones that might or might not be in a useful state when measured. Data on stable qubit systems is still too limited to extrapolate meaningfully, though a variety of error correction techniques have been developed in the past two decades to enable working, reliable quantum computers. Those error correction techniques work by combining many “raw” qubits into a single “logical” qubit at around a 10:1 ratio, which certainly changes the regression substantially, though not the formulation of my “law.”
I generated a regression of qubit growth along the full useful quantum computer history, 1998–2023, and performed a least-squares fit to an exponential doubling period and got 3.376 years, quite a bit slower than the heady early years’ 2.0 doubling rate. On the other hand, fitting an exponential curve to all announcements in the modern 2016–2023 period yields a doubling period of only 1.074 years. The qubit doubling period is only 0.820 years if we fit to just the most powerful quantum computers released, ignoring various projects’ lower-than-maximum qubit count announcements; I can see arguments for either though selected the former as somewhat less aggressive.
From this data, I offer a formulation of what I really hope someone else somewhere will call, at least once, “Gessel’s Law,” P = 22(y/1.1) or, more generally given that we still don’t have enough data for a meaningful regression, P = 22(y/d); quantum computational power will grow as 2 to the power 2 to the power years over a doubling period which will become more stable as the physics advance.
Gidney & Ekra (of Google) published How to factor 2048-bit RSA integers in 8 hours using 20 million noisy qubits, 2021-04-13. So far for the most efficient known (as in not hidden behind classification, should such classified devices exist) explicit algorithm for cracking RSA. The qubit requirement, 2×10⁷, is certainly daunting, but with a doubling time of 1.074 years, we can expect to have a 20,000,000 qubit computer by 2042. Variations will also crack Diffie-Hellman and even elliptic curves, creating some very serious security problems for the world not just from the failure of encryption but the exposure of all so-far encrypted data to unauthorized decryption.
Based on the 2016–2023 all announcements regression and Gidney & Ekra, we predict RSA 2048 will fall on 2042-01-15 at 2am., a prediction not caveated by the error correction requirement for stable qubits as they count noisy, raw, cubits as I do. As a validity check, my regression predicts “Quantum Supremacy” right at Google’s 2022 announcement.