First of all consider a computer is incomplete without a program, so lets just think of a programmed computer—whether in hardware or software doesn’t matter for our purposes.
This gives us a system that goes from some known start state to some outcome state through a series of intermediate steps. If each of these steps is deterministic, then the entire system reaches the same outcome in all universes where it had the same starting point.
If those steps were stochastic, perhaps because there is chance of memory corruption in our computer or because of a random guess, than in some universes the system arrives as a different outcome, based on the probability of that branch of the intermediate states. This can produce many branches, but because each of these branches cannot affect the others the result is tree of intermediate states, leading to the outcomes of our computer and its program.
Now, both of these are classical computers, but it helps to know what a classical computer looks like in a many worlds interpretation, before mapping a quantum computer there. This is because all computers, classical or quantum share a property—they are computers. This means there must be a path from the starting state to the outcome state. We can influence that path in many ways, but the path is part of how we define and build a computer and a program.
In quantum mechanics, there is a phenomena called entanglement, which loosely means that the events in very similar worlds can affect the probabilities of events in all of those worlds. You can think of this as the boundaries between the many worlds smoothing out as you get to a small scale.
This means that unlike our stochastic tree of states, the quantum computer can have a more complex structure. It is even possible, for two branches to converge back into one and to have branches cancel out.* In practice, these are more approximate than precise, so you will find a dominant combination of two branches or a near cancellation. Using this interaction a skilled quantum algorithm designer can use a variety of tricks to make correct answers more likely, by canceling wrong answers, and by increasing the probability of correction ones.
There is no uniform solution to this problem, for example, the best known quantum algorithm, the Shor algorithm for prime factorization exploits frequency of a possible prime factorization using number theory. This works well on quantum computers because the frequency difference is also a critical value for determining the probability of the combination of two quantum variables.
In each case, a computer and its program produce a path of execution, but by exploiting the features of or needing to deal with the problems of non-determinism and quantum mechanics, the nature of that computation becomes more complex and difficult to see. Any one world’s view is not sufficient, especially in the case of quantum computing where the probabilities which govern a world’s execution are not derived solely from within that world.
I’m fairly sure one this, but I’m a little rusty, so I could be wrong.
First of all consider a computer is incomplete without a program, so lets just think of a programmed computer—whether in hardware or software doesn’t matter for our purposes.
This gives us a system that goes from some known start state to some outcome state through a series of intermediate steps. If each of these steps is deterministic, then the entire system reaches the same outcome in all universes where it had the same starting point.
If those steps were stochastic, perhaps because there is chance of memory corruption in our computer or because of a random guess, than in some universes the system arrives as a different outcome, based on the probability of that branch of the intermediate states. This can produce many branches, but because each of these branches cannot affect the others the result is tree of intermediate states, leading to the outcomes of our computer and its program.
Now, both of these are classical computers, but it helps to know what a classical computer looks like in a many worlds interpretation, before mapping a quantum computer there. This is because all computers, classical or quantum share a property—they are computers. This means there must be a path from the starting state to the outcome state. We can influence that path in many ways, but the path is part of how we define and build a computer and a program.
In quantum mechanics, there is a phenomena called entanglement, which loosely means that the events in very similar worlds can affect the probabilities of events in all of those worlds. You can think of this as the boundaries between the many worlds smoothing out as you get to a small scale.
This means that unlike our stochastic tree of states, the quantum computer can have a more complex structure. It is even possible, for two branches to converge back into one and to have branches cancel out.* In practice, these are more approximate than precise, so you will find a dominant combination of two branches or a near cancellation. Using this interaction a skilled quantum algorithm designer can use a variety of tricks to make correct answers more likely, by canceling wrong answers, and by increasing the probability of correction ones.
There is no uniform solution to this problem, for example, the best known quantum algorithm, the Shor algorithm for prime factorization exploits frequency of a possible prime factorization using number theory. This works well on quantum computers because the frequency difference is also a critical value for determining the probability of the combination of two quantum variables.
In each case, a computer and its program produce a path of execution, but by exploiting the features of or needing to deal with the problems of non-determinism and quantum mechanics, the nature of that computation becomes more complex and difficult to see. Any one world’s view is not sufficient, especially in the case of quantum computing where the probabilities which govern a world’s execution are not derived solely from within that world.
I’m fairly sure one this, but I’m a little rusty, so I could be wrong.