## Qutrits Bring Quantum Computers Closer 66

Posted
by
kdawson

from the shortcut-through-higher-dimensions dept.

from the shortcut-through-higher-dimensions dept.

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: (Score:2)

...quantum logic gates...logic gates...qubits...qutrirts...quantum states...quantum computer...quantum logic gates...gates...gates...photons...linear optical components...

For some reason, this reminds me of this post [xkcd.com] on about blogs [xkcd.com] on xkcd.

## Re: (Score:3, Informative)

## Re: (Score:1, Funny)

A "gate" is roughly the equivalent of a transistor. Kind of. Think of it like a lot of transistors all put togetherAnd a transistor is kind of like a tube. (remember in the 1960s when they replaced all those tube radios with transistor radios?) So really, when it comes right down to it, the Internet IS really a bunch of tubes.

## Re:Wow (Score:4, Funny)

Or maybe the cat will be spinning because someone stapled a piece of bread with jam onto the cat's back.

## Re:Wow (Score:4, Funny)

## Re: (Score:1)

## 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: (Score:1)

## Re: (Score:1)

## 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

gotto be some kind of rotation - it must preservelength- 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

probabilitiesper se, but sort ofsquare rootsof 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 easilyselect 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.

## amplitude? analog? (Score:1)

(Actually, I guess, if my elliptical thinking here is anywhere close to meaningful, I guess the idea would be that a quantum processor would allow building complex reprogrammable filters (amplifiers) that don't require iterations. (Not talking about the simple analog filters, of course.)

My son seems enamored of analog computing these days. I remember when I was, as well. Maybe, the babbling above being completely wrong notwithst

## Re: (Score:1)

## Re: (Score:2)

## Personal cryptography users should be disappointed (Score:5, Interesting)

Applied Cryptography [amazon.com]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.## Re:Personal cryptography users should be disappoin (Score:2)

## Re:Personal cryptography users should be disappoin (Score:3, Insightful)

## Re:Personal cryptography users should be disappoin (Score:3, Insightful)

The real power of quantum computing will be in factoring primes. Which most certainly will affect public key crypto, but public key was never the FULL solution. Like anything in crypto different problems have different solutions.

Public key crypto is great in the web age because you can use it for establishing connections, exchanging private keys, etc.

One of the first things you learn in any crypto grad class is that creating the crypto schemes is only part o

## Re:Personal cryptography users should be disappoin (Score:2)

(Emphasis added)

You might die tomorrow. Hurricanes might devastate the western world. Aliens might show up and blow the planet to bits for housing such a greedy, self-centred species. Any number of progressively unlikely things might happen.

There's no real substance to the rumours of encryption-defeating quantum computers - it's a hypothesis somebody proposed a few years ago, which has never been proved or

## Re:Personal cryptography users should be disappoin (Score:2)

we kept hearing about how it would take thousands or millions of years to crack just one PGP message.

What were you reading?! Everything I ever read stressed the fact that there was something on the order of a 10-50 year expectation of privacy on anything you protected with current encryption mechanisms. That has pretty much been proven out, given that we're now on year 20 since I started using public key crypto.

As for quantum computing: don't get your hopes up. There's no proof of concept that shows that QC will ever scale up to practicality. Every 6 months someone announces a "breakthrough" and gains ple

## Re: (Score:1)

## Linux??? (Score:1, Funny)

## Re:Linux??? (Score:5, Funny)

## Re: (Score:1)

So like any other computer then?

## Re: (Score:2, Funny)

## Re: (Score:2)

Alright, enough of these qutrit jokes, they're awful.

## Re: (Score:2)

## convert qubits into qutrits...far more powerful (Score:4, Funny)

## Re: (Score:1, Funny)

## Re:convert qubits into qutrits...far more powerful (Score:5, Funny)

This would have brought many, many more female engineers into the field of computer science (hence accelerating the pace at which computers could do useful things besides transmit, compress, and enhance pornography), except that the same abbreviational logic that turned "binary digit" into "bit" turned "trinary digit" into "tit." This nomenclatural error set computing back nearly three hundred years, and two entire generations of promising computer scientists were lost trying to keep abreast of bad puns.

## Re: (Score:1)

## Re: (Score:1)

## All they need to do is.. (Score:2, Funny)

## What it means (Score:4, Informative)

## Re: (Score:2)

## 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: (Score:2, Interesting)

## Re: (Score:2)

Interesting, why is base-3 more efficient than base-2?

Because 3 is closer approximation of e than 2.

I remember learning this in telecommunications theory, but I don't remember why it is true. Wikipedia's article on weird number bases [wikipedia.org] mentions base-phi (golden ratio) [wikipedia.org], but there is no mention of base-e.

## Re: (Score:2)

## Re: (Score:2)

0 AND 0 = 0

0 AND 1 = 0

0 AND 2 = 0

1 AND 1 = 1

1 AND 2 = 1

2 AND 2 = 2

0 OR 0 = 0

0 OR 1 = 1

0 OR 2 = 2

1 OR 1 = 1

1 OR 2 = 2

2 OR 2 = 2

Where 0 means no, 1 means maybe, and 2 means yes?

## Re: (Score:2)

Fry: Don't worry, there's no such thing as 2.

There's a lot of different ways to use the extra value. If you treat it as "unknown", or the logical equivalent of NaN, then you can do NOT, AND, and OR with 0's and 1's, then use 2 as an exception case that can propagate.

## Re: (Score:1)

## Re: (Score:2)

## Re: (Score:3, Informative)

## I want to play Qutris (Score:2)

## Trinary Code (Score:2)

## Re: (Score:2)

## Qubits? Qutrits? BAH! (Score:2)

## Riiiiiiight (Score:2)

## Re: (Score:1)

## More science sensationalism (Score:1)

## The day is mine!!! (Score:2)

I'm a visionary!

3-State Bit [slashdot.org]## Trinary? (Score:2)

## Quantum Python (Score:2)

we were happy to have them!