Scott, maybe you can explain where so many people come from, SO a priori hostile to AI or aliens? (I combine these themes because I have observed that there is a high correlation between a priori hostility towards AI and towards aliens.) By this I don’t mean fear of a “paperclip maximizer” or anything like that, but of “super-intelligent, self-reflective, high-level AI with behavior at least as complex as that of humans”.

P.S. I recommend reading George Yuri Right’s short story “The Duel” (“Поединок”), written as an answer to “Arena”. You may have to use a translator as the story is in Russian and I don’t know if there is an English translation.

]]>You may have seen the recent post by Gil Kalai. Any comments?

https://gilkalai.wordpress.com/2022/05/26/waging-war-on-quantum/

]]>If China suddenly goes dark then the international community needs to launch an immediate full spectrum strike against their AI research centers. There can be no hesitation. The AI must be contained in a reasonably sized subsystem and interred in a Faraday cage. These measures will allow a safe trial before the World Court in the Hague for crimes against humanity. Otherwise all organic life on Earth will be eradicated except in the Harlan Ellison scenario (I Have No Mouth, and I Must Scream) where one person is retained by the AI and modified physically and then tortured for eternity.

An example must be made of this AI Adam.

]]>thanks, very interesting.

]]>You’ll probably just end up with whatever the initial state was.

For example, if the QC starts in the all-zero state and we then apply one Hadamard gate to each qubit, we get an even superposition over all possible states.

If we then apply a second Hadamard gate to each qubit, we’ll get back to the all-zero state – that’s because these are unitary operations (so HH=I).

But we can also interpret this circuit as causing every non-zero state to cancel out via destructive interference.

Ultimately, interference is another way by which a QC can manipulate a probability distribution, but it still needs to add up to 1.

After all, if you consider a QC algorithm that’s supposed to solve some problem on n qubits, and, at the end, you measure those n qubits, what happens when the problem you’re solving has no solution?

It depends on the problem and what the circuit is doing. E.g. you might just get a random useless string.

Here’s a concrete example of how i tried (and failed) to solve Graph Isomorphism with a QC – maybe it’s helpful.

I started with the observation that if two graphs A and B are isomorphic, then the set of graphs we get from permuting A is the same as what we get for B (they’re just in a different order).

That means that we can assemble a circuit that implements a c-to-1 function (where c is even) when A and B are isomorphic, and 1-to-1 otherwise.

The circuit just implements f(m,i) and outputs the ith permutation of A when m==0 and the ith permutation of B when m==1.

The states will be of the form |m,i,o>, where m is a single bit, i is the permutation index and o is the output (the permuted graph).

When A and B are isomorphic, we get pairs like this:

|0,0001001,00011>

|1,0100101,00011>

So the output register (o) is the same, but the input registers (m and i) are different.

That seems perfect, when A and B are isomorphic we can pair up states for destructive interference.

One way to get interference is by adding Hadamard gates to the input register (right at the end).

But independently of how we do it, we want the pairs to interfere consistently and predictably.

Let’s say that, after interference, the input register always has an even number of 1s.

Then we’ll know that A and B are *not* isomorphic if we see an odd number of 1s in the register.

If it’s always even (over a number of runs) then we’ll have high confidence that the graphs are isomorphic.

Unfortunately, the kind of interference we get (e.g. by just adding Hadamard gates at the end) is not consistent or predictable (at least not in a trivial way).

It’s like sampling positions from a random double-slit experiment, of many, where their interference patterns are totally different.

In that case, we’re just getting random useless values.

That’s why it’s important to orchestrate a *pattern* of interference.

Ultimately, there needs to be some exploitable structure.

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]]>I know that a qubit can be either 0 or 1, and anywhere “in between”, and always measured as 0 or 1 (just like a classic bit).

But, in the case of qubits, isn’t it possible to “extend” the model to account for the fact that a qubit could have no value at all? I.e. neither 0 or 1?

Imagine we have 3 qubits in state {001}, isn’t it possible to create 3 other qubits also in state {001}, but with a sort of opposite “phase” to the first triplet (like “anti-qubits”), so that, at the point of final measurement, the wave functions of the two triplets cancel out and nothing is measured? And, if the second triplet is encoding the entire solution space, then we end up with a wave function encoding the complementary solution space?

After all, if you consider a QC algorithm that’s supposed to solve some problem on n qubits, and, at the end, you measure those n qubits, what happens when the problem you’re solving has no solution? So that the final measurement would lead to no answer at all, i.e. no string of 0s or 1s? Do you always have to account for this with an extra qubit encoding whether the solution is valid or not (there is no solution)?

I see, thanks so much!

That makes sense, otherwise I think it would be easy to use this to build an efficient quantum algorithm to solve NP hard problems.