I presume that you refer to the difference between point particles and fields. The wave function in QM is essentially a classical field), where for every point in space you have a set of numbers describing the quantum state. This state evolved in time according to the time-dependent Schrodinger equation, until “something classical” happens, at which point you have to throw dice to pick one of the preferred states (also known as the wave-function collapse or the MWI world split).
The part of QM which is just the evolution of the Schrodinger equation is computationally equivalent to that of modeling diffusion or heat flow: the equation structure is very similar, with complex numbers instead of reals. The “measurement” part (calculating an outcome) is nearly trivial, just pick one of the outcomes (or one of the worlds, if you are a fan of MWI), according to the Born rule.
While it is true that there are many shortcuts to solving the Schrodinger equation numerically, and a set of these shortcuts is what tends to be studied in most QM courses, there is no substitution for numerical evolution in a general case.
Quantum computing is a rather different beast from the regular quantum physics, just like classical computing is different from classical physics: computing is an abstraction level on top, it lets you think only about the parts of the problem that are relevant, and not worry about the underlying details. Quantum computing is no more about quantum mechanics than the classical computer science is about the physics of silicon gates.
One final piont. It is a general observation that understanding of any scientific topic is greatly enhanced by teaching it, and teaching it to an ultimate idiot savant, a computer, is bound to probe your understanding of the topic extensively. So, if you want to learn QM, get your hands dirty with one of the computational projects like this one, and if you want to learn quantum computing, write a simulation of the Schor’s algorithm or something similar.
I presume that you refer to the difference between point particles and fields. The wave function in QM is essentially a classical field), where for every point in space you have a set of numbers describing the quantum state. This state evolved in time according to the time-dependent Schrodinger equation, until “something classical” happens, at which point you have to throw dice to pick one of the preferred states (also known as the wave-function collapse or the MWI world split).
The part of QM which is just the evolution of the Schrodinger equation is computationally equivalent to that of modeling diffusion or heat flow: the equation structure is very similar, with complex numbers instead of reals. The “measurement” part (calculating an outcome) is nearly trivial, just pick one of the outcomes (or one of the worlds, if you are a fan of MWI), according to the Born rule.
While it is true that there are many shortcuts to solving the Schrodinger equation numerically, and a set of these shortcuts is what tends to be studied in most QM courses, there is no substitution for numerical evolution in a general case.
Quantum computing is a rather different beast from the regular quantum physics, just like classical computing is different from classical physics: computing is an abstraction level on top, it lets you think only about the parts of the problem that are relevant, and not worry about the underlying details. Quantum computing is no more about quantum mechanics than the classical computer science is about the physics of silicon gates.
One final piont. It is a general observation that understanding of any scientific topic is greatly enhanced by teaching it, and teaching it to an ultimate idiot savant, a computer, is bound to probe your understanding of the topic extensively. So, if you want to learn QM, get your hands dirty with one of the computational projects like this one, and if you want to learn quantum computing, write a simulation of the Schor’s algorithm or something similar.