Thread: Quantum Computers

Originally Posted by Sound

From Ray Kurzweils book "The Singularity is Near" (2005).

Note that this excerpt is talking not about quantum computing, but ordinary, classical computing on a really small scale.

Quantum computers are 4 states rather than two, this is what makes them so powerful. A q-bit can be on, off, neither, or both.

The following assumes that the modern standard model holds. If it doesn't, all bets are off.

IIRC, this is not exactly true. A qubit (quantum bit) doesn't simply have four distinct states of off/on/both/neither. For starters, it can't really be neither. It can be in states representing 0 or 1, or, crucially, in a quantum superposition of both states. Wikipedia probably explains this better than I can, but it means that the state of the qubit in a superposition of states 0 and 1 can be thought of as a a combination of each state multiplied by its respective probability amplitude. The value of these probability amplitudes are complex numbers with the sum of the squares of the moduli being equal to 1.

However, this doesn't mean that a qubit is like a regular bit, but with more states. Qubits are a lot more complicated to manipulate and read.

For example: Measuring a qubit will not simply reveal the probability amplitudes. You'll actually measure the state of it as either 0 or 1, with the probability of each being equal to the square of the modulus of its probability amplitude (this is why these values need to sum to 1).

Quantum computation is really interesting.

Originally Posted by archdreamer

The value of these probability amplitudes are complex numbers with the sum of the squares of the moduli being equal to 1.

Actually the probability amplitudes are real numbers and are calculated as the mod-squared of the wavefunction, which is complex. /end nitpick

But yeah, I don't think quantum computers will ever be a replacement for classical computers because of the way they work. The programming is essentially the hardware itself, and it finds the answer by settling into the most probable set of positions. The areas will quantum computers will be useful are when a MASSIVE NP calculation has to be done that would take a classical computer weeks or more to do. Then it's worth building a quantum computer to do that calculation.

The biggest problem is that even if quantum chips are faster than regular ones, it doesn't really matter. Chips have reached the limit of how fast they can go because they are dependent on RAM. CPUs have gotten so fast that they now have to slow down and wait for the RAM.

Wanna make a billion dollars? Invent a superfast RAM chip.

I just got back from visiting my friend at Cornell, she and her PhD adviser are currently doing research on M-RAM. It's fast but they can't keep it stable outside of super cold temperatures.

Originally Posted by drewmandan

Actually the probability amplitudes are real numbers and are calculated as the mod-squared of the wavefunction, which is complex. /end nitpick

Are you sure? From my understanding, the value of the wavefunction (function that maps from a space representing the possible states of the system, to the complex numbers) at any particular point is the probability amplitude (complex), and squaring the modulus of that will give you the probability of the system being measured as being in that state (real). What you describe sounds like this value of probability. Call me on this if I am wrong, though, I'm no quantum physicist, just an interested amateur.

The biggest problem is that even if quantum chips are faster than regular ones, it doesn't really matter [because of current RAM speeds]

This is way off, as far as I know. Quantum computing doesn't rely on traditional RAM. You initialise the system, allow its components to interact, then measure some of them (like a regular computer, dohohoho). You might use traditional RAM to store input and output data, but it isn't going to significantly impact the speed of your quantum computation. You may need, however, some sort of quantum analogue to ordinary RAM, but the design of something like that would be very different to the design of RAM today.

Originally Posted by archdreamer

Are you sure? From my understanding, the value of the wavefunction (function that maps from a space representing the possible states of the system, to the complex numbers) at any particular point is the probability amplitude (complex),

It's not probability, it's the wavefunction amplitude. Probability is a real number between 0 and 1.

Originally Posted by archdreamer

and squaring the modulus of that will give you the probability of the system being measured as being in that state (real). What you describe sounds like this value of probability. Call me on this if I am wrong, though, I'm no quantum physicist, just an interested amateur.

Probability amplitude is a different term for probability. Same thing.

Originally Posted by drewmandan

Probability amplitude is a different term for probability. Same thing.

I hate to be that guy, but, I don't think this is the case. Sources follow.

Probability amplitude: A complex number, the squared norm of which gives a probability.

this URL is long, it's a physics dictionary on google books

The probability distribution itself is obtained by squaring the probability amplitude.

http://www.chemistry.mcmaster.ca/esa...section_2.html

Note that this probability amplitude is quite distinct from the probability itself; to repeat, the probability is proportional to the modulus squared of the probability amplitude.

QM textbook on google books, awful scan

Originally Posted by archdreamer

Are you sure? From my understanding, the value of the wavefunction (function that maps from a space representing the possible states of the system, to the complex numbers) at any particular point is the probability amplitude (complex), and squaring the modulus of that will give you the probability of the system being measured as being in that state (real). What you describe sounds like this value of probability. Call me on this if I am wrong, though, I'm no quantum physicist, just an interested amateur.



This is way off, as far as I know. Quantum computing doesn't rely on traditional RAM. You initialise the system, allow its components to interact, then measure some of them (like a regular computer, dohohoho). You might use traditional RAM to store input and output data, but it isn't going to significantly impact the speed of your quantum computation. You may need, however, some sort of quantum analogue to ordinary RAM, but the design of something like that would be very different to the design of RAM today.

They would have the same implementation, but they would be qubits instead of bits. They still need a way to increase the bus speed though, that's what is restraining computer speed right now. I don't think the laws of quantum physics allow for quantum RAM anyway, it's too volatile and the information will degrade too quickly.

Quantum CPU speeds will not matter, even for huge calculations if the RAM bus speed is still slow. Most CPUs have 32 registries and about 32MB of cache, huge calculations require gigabytes to do, so it'll have to swap to quantum RAM a lot, which restricts the speed of the calculations.