Qutrits Bring Quantum Computers Closer 66
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)."
Re:Wow (Score:3, Informative)
What it means (Score:4, Informative)
Re:Wow (Score:5, Informative)
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.
Re:IANAQCRoM (Score:3, Informative)
Re:What it means (Score:5, Informative)
Think of an SQL database, where a field can be TRUE or FALSE; however, if you didn't set up default values, it can also be NULL, neither true nor false. Or in mathematics, where a value can be GREATER THAN, LESS THAN, or EQUAL TO -- three mutually exclusive states. These aren't circuit-based examples, but it does illustrate how ternary logic can be routinely applied.
Re:Wow (Score:5, Informative)
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.