IBM Updated 2025-07-16
As of the 2020's, a slumbering giant.
But the pre-Internet impact of IBM was insane! Including notably:
Politician Updated 2025-07-16
Measurement-based quantum computer Updated 2025-07-16
TODO confirm: apparently in the paradigm you can choose to measure only certain output qubits.
This makes things irreversible (TODO what does reversibility mean in this random context?), as opposed to Circuit-based quantum computer where you measure all output qubits at once.
TODO what is the advantage?
Rabi cycle Updated 2025-07-16
TCP/IP Updated 2025-07-16
Lagrangian vs Hamiltonian Updated 2025-07-16
The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:
This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.
Length contraction Updated 2025-07-16
Suppose that a rod has is length measured on a rest frame (or maybe even better: two identical rulers were manufactured, and one is taken on a spaceship, a bit like the twin paradox).
Question: what is the length than an observer in frame moving relative to as speed observe the rod to be?
The key idea is that there are two events to consider in each frame, which we call 1 and 2:
  • the left end of the rod is an observation event at a given position at a given time: and for or and for
  • the right end of the rod is an observation event at a given position at a given time : and for or and for
Note that what you visually observe on a photograph is a different measurement to the more precise/easy to calculate two event measurement. On a photograph, it seems you might not even see the contraction in some cases as mentioned at en.wikipedia.org/wiki/Terrell_rotation
Measuring a length means to measure the difference for a single point in time in your frame ().
So what we want to obtain is for any given time .
In summary, we have:
By plugging those values into the Lorentz transformation, we can eliminate , and conclude that for any , the length contraction relation holds:
The key question that needs intuitive clarification then is: but how can this be symmetric? How can both observers see each other's rulers shrink?
And the key answer is: because to the second observer, the measurements made by the first observer are not simultaneous. Notably, the two measurement events are obviously spacelike-separated events by looking at the light cone, and therefore can be measured even in different orders by different observers.

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