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Qutrits Bring Quantum Computers Closer
KentuckyFC writes "To do anything useful with quantum logic gates, you need dozens to hundreds of them, all joined together. And because of various errors and problems that creep in, that's more or less impossible with today's technology. Now an Australian group has built and tested logic gates that convert qubits into qutrits (three-level quantum states) before processing and then convert them back again. That makes them far more powerful. The group says that a quantum computer that might require 50 conventional quantum logic gates can now be built with just 9 of the new gates. What's more, the gates process photons using nothing more than standard linear optical components (abstract on the physics arxiv)."
Throughout the heyday of personal encryption, when Zimmerman was maintaining PGP and Bruce Schneier's Applied Cryptography was released, we kept hearing about how it would take thousands or millions of years to crack just one PGP message. Now we hear that computers that could break these messages might be relatively just around the corner. It's got to be a real disappointment and source of worry to people who did use PGP to encode the secrets that they are desparate to hide.
Oh it's simple. The cat could be not only alive or dead, but also could be on life support.
Or maybe the cat will be spinning because someone stapled a piece of bread with jam onto the cat's back.
i thought once I was found, but it was only a dream.
Naturally, I read that as "qutits" the first time.
How can I believe you when you tell me what I don't want to hear?
No fair, you changed the state of the cat by measuring it!
What this is basically saying is that instead of operating a quantum computer with 2 levels, 0 and 1, they are operating with 3, 0,1,2 lets say. According to my computer architecture prof 3 levels is the most efficient way of making computers, from a number of components standpoint. Its hard thinking in base-3, because things like inverters become meaningless. AND and OR gates still work with a reasonable amount of understanding. Things like multiplexers and decoders make sense. If you can get into the macroscopic level of design its pretty understandable. You can use 3 trit words to do base-27 in a similar way to using 4 bit words and hex.
Yes and No.
The word "gates" has almost the same meaning in quantum computing as in the classical computing. In classical computing a gate operates on a set of bits and changes them to another set of bits. In quantum computing it is the same with qubits playing the role of bits.
:)
Of course funny things are possible in quantum computing. For example it is possible to make a "square root of not" gate, that when applied *twice* to the qubit |1> produces |0> and vice versa. Applying once creates something else (the square root of not in some sense).
One particularly handy way to think of quantum gates is to think of them as a matrix (operator) that operates on a vector (input qubit) to produce another vector (output qubit) just by multiplication. So if A is some quantum gate (matrix) and u is input qubit (vector) the the output qubit (vector) v = A*u . The matrix A needs to satisfy some technical requirements that gives quantum computing some nice features (like every algorithm is fully reversible and so on), but those details are not needed to get a rough idea.
Too bad I lost my mod points yesterday. This is the kind of thing people actually come to Slashdot for. I'll just have to try to contribute instead.
:)
Here's some further detail for those interested: the |1> and |0> qubits are actually vectors of probabilities. (Well, probability "amplitudes". More on that later.) The |0> bit means [1 0] and the |1> bit means [0 1]. The "|.>" notation is a bit of convenient shorthand.
If you have two qubits, you'd represent them as |00>, meaning [1 0 0 0]. (That's four possibilities for the qubits, and all the probability mass on the first: both off.) |01> means [0 1 0 0], |000> means [1 0 0 0 0 0 0 0], and so on. Note the exponential growth.
A quantum gate is nothing more than an operator of the same type that governs all discrete quantum system evolution: a unitary matrix. Think of a rotation matrix of rank 2**(number-of-bits), but in complex space. It's got to be some kind of rotation - it must preserve length - to preserve the property that the qubit states and combined qubit states are probability (amplitude) distributions.
A "square root of NOT", IIRC, is an operator (rotation) that turns [1 0] (or |0>) into [sqrt(1/2) -sqrt(1/2)]. Do it again, and you get [0 1]. Again, and you get [-sqrt(1/2) sqrt(1/2)], and again yields the original [1 0]. (I may have some signs wrong.)
The reason this cycle works at all is that the states aren't probabilities per se, but sort of square roots of probabilities, which allows them to keep extra information. This is called "phase". Much of the exciting weirdness of computing with quantum gates is that phase isn't strictly real, but in general has imaginary components.
The other exciting weirdness is of the massively parallel sort. If I do a computation on [sqrt(1/2) -sqrt(1/2)], it's sort of like doing the same computation on [1 0] and [0 1] in parallel. The tricky part is that measuring the outcome restricts me to just one of the results! One way to express the dilemma is that I can compute an answer for every possible input simultaneously (which would be great for solving NP problems), but that I can't easily select the right answer.
Another way to express it is to say that the cat is in a superposition of dead/alive, which will localize when I observe the poor beast.
I got my Linux laptop at System76.