Meanwhile, in the US, the Univac Solid State computer[1] used similar principles in its patented[3] "Solid State Logic"[2], and was also released in 1958.
My understanding is that the magnetic amplifiers used in the V2 rocket kicked off a lot of interesting uses of magnetic cores.
[1] https://en.wikipedia.org/wiki/UNIVAC_Solid_State
Magnetic amps were indeed used in the V2 in the control electronics.
But they substantially predate World War II and were once widely deployed and widely understood. The technology goes back to at least the late 19th century. It was used in many of the places where we'd use an amplifier today, like to run signals in a factory where hydraulics are not practical.
They can be quite fast - if the AC supply is well into the 10s of KHz they can reproduce audio range frequencies.
Some of the first electronic radio transmitters were based on the magnetic amplifier. The radio pioneer Reginald Fessenden developed a system using his Alexanderson alternator (a super-high-speed AC generator) which produced high power (many kilowatts) of AC at the target carrier frequency of around 30 kHz. He then fed the output of that, through a large magnetic amplifier, governing the kilowatts of generator output, with a small control current from a switch or microphone -- amplitude modulation. That was c. 1916.
During WWII, Germany used magnetic amplifiers in many different kinds of military equipment, because they had the advantage of being much more rugged and reliable than the electronic devices available at that time.
After WWII, the technology of magnetic amplifiers was one of many technologies that USA took from Germany and provided to US companies (like also the Soviet Union did with their part of Germany, but while USA took the technical documentation and samples of the products, the Soviet Union moved entire factories to Russia, piece by piece).
I wrote an article on the history of magnetic amplifiers: https://spectrum.ieee.org/the-vacuum-tubes-forgotten-rival
The quick summary is that magnetic amplifiers started in the US in 1901, but Germany came up with much better magnetic alloys during World War II. This led to a post-war boom in mag amps, which were used in industrial control, aerospace, and computers such as the Univac Solid State. These magnetic materials also led to core memory. Transistors mostly killed off mag amps, although PC power supplies used them into the 1990s.