July 26, 2015

Currently Quantum computers might be where Rockets were at the time of Robert Goddard

There have been comparisons of current quantum computers to classical computers to the Wright Brothers flyer against lighter than air vehicles. The Wright brothers flyers had inferior performance and capabilities to the Zeppelins but would eventual later versions would prove more useful and more capable.

I think it might be better to look for an appropriate analogy in the history of rockets compared to conventional powered flight for a quantum to classical computing analogy.

Rocketry actually predates conventional powered flight. So this part of the analogy does not compare. If we were to condense the timescale of rocketry then we could make some comparison.

However, rocketry required several breakthroughs before they exceeded the capabilities of Wright brothers style vehicles for transporting humans.

If quantum computing is at the Goddard level that would be a good thing for quantum computing. This means that the major fundamental breakthrough that would put them over the top was in hand and merely a lot of investment, engineering and scaling was needed.

The goal of being able to solve NP-hard or NP-Complete problems with quantum computers is similar to being able to travel to the moon, mars or deeper into space with rockets. Conventional flight could not achieve those goals because of the lack of atmosphere in space. Current computing seems like they are very limited in being able to tackle NP-hard and NP Complete problems. Although clever work in advanced mathematics and approximations can give answers that are close on a case by case basis.

There was also recent progress with memcomputing against certain cases of NP-complete problems

So some unknowns with current quantum computing
1. will quantum computing take us areas of NP-hard and NP-Complete solutions that are radically different or radically more useful. In terms of rocketry - Can we get out of the atmosphere, to the moon to Mars or beyond but for quantum solutions ?

2. when will we get commercial applications that are the killer application for quantum computing. This will mean sustainable revenue is generated that will mean constant funding of research for improvement and to find more breakthroughs. Can we get communication and weather satellites or military applications that provide constant funding for better machines ?

3. Will the things that are not understood about quantum computing mean that there are fundamental, hard and time consuming research needed before we can get to items 1 and 2 above.

Let us consider four stages of rocket history.

* Ancient Rocketry

In the late 14th century, the Chinese had discovered how to combine the rocket launching tube with the fire lance. This involved three tubes attached to the same staff. As the first rocket tube was fired, a charge was ignited in the leading tube which expelled a blinding lachrymatory powder at the enemy, and finally the second rocket was fired. An illustration of this appears in the Huolongjing, which describes the effectiveness of this weapon to obfuscate the location of the rockets from the enemy. The Huolongjing also describes and illustrates two kinds of mounted rocket launchers that fired multiple rockets. There was a cylindrical, basket-work rocket launcher called the "Mr. Facing-both-ways rocket arrow firing basket", as well as an oblong-section, rectangular, box rocket launcher known as the "magical rocket-arrow block". Rockets described in the Huolongjing were not all in the shape of standard fire arrows because there some had artificial wings attached. An illustration shows that fins were used to increase aerodynamic stability for the flight path of the rocket, which according to Jiao Yu could rise hundreds of feet before landing at the designated enemy target.

* The Mysore Rocket

The first iron-cased and metal-cylinder rocket artillery, made from iron tubes, were developed by the weapon suppliers of Tipu Sultan, an Indian ruler of the Kingdom of Mysore, and his father Hyder Ali, in the 1780s. Tipu Sultan championed the use of mass attacks with rocket brigades within the army, and he wrote a military manual on it, the Fathul Mujahidin. He successfully used these metal-cylinder rockets against the larger forces of the British East India Company during the Anglo-Mysore Wars. The Mysore rockets of this period were much more advanced than what the British had seen, chiefly because of the use of iron tubes for holding the propellant; this enabled higher thrust and longer range for the missile (up to 2 km range). The effect of these weapons on the British during the Second, Third and Fourth Mysore Wars in 1792 was sufficiently impressive to inspire the British to develop their own rocket designs

* William Congreve was the son of the Comptroller of the Royal Arsenal, Woolwich, London. Under the influence of the Mysorean rockets from India, he developed the Congreve rocket. From there, the use of military rockets spread throughout Europe. At the Battle of Baltimore in 1814, the rockets fired on Fort McHenry by the rocket vessel HMS Erebus were the source of the rockets' red glare described by Francis Scott Key in The Star-Spangled Banner. Rockets were also used in the Battle of Waterloo.

Early rockets were very, very inaccurate. Without the use of spinning or any gimballing of the thrust, they had a strong tendency to veer sharply off course from the desired trajectory. The early British Congreve rockets reduced this somewhat by attaching a long stick to the end of a rocket (similar to modern bottle rockets) to make it harder for the rocket to change course. The largest of the Congreve rockets was the 32-pound (14.5 kg) Carcass, which had a 15-foot (4.6 m) stick.

* Modern rockets were born when Goddard attached a supersonic (de Laval) nozzle to a liquid-fueled rocket engine's combustion chamber. These nozzles turn the hot gas from the combustion chamber into a cooler, hypersonic, highly directed jet of gas, more than doubling the thrust and raising the engine efficiency from 2% to 64%. Early rockets had been grossly inefficient because of the thermal energy that was wasted in the exhaust gases. In 1926, Robert Goddard launched the world's first liquid-fueled rocket in Auburn, Massachusetts

The specs of the D-Wave machine are given in the center column, using a technique called quantum annealing, which is the subject of some controversy with regards to whether or not it is a true quantum computer. At some level, if the machine can solve a particular hard problem, the distinction will not matter so much and perhaps, given the nature of the mathematical problems at hand, perhaps a better name for such devices would be topological computing or topographical computing. The third column in the chart above represents the coherent Ising machine technique that Yamamoto and his team have come up with, which uses quantum effects of coherent light operating at room temperature to store data and perform calculations, specifically a class of very tough problems called NP Hard and using a mathematical technique called Max-Cut.

When will we see a quantum computer, of any kind, that can solve at least one hard problem that we care about?

“We can build a 10,000 spin quantum Ising machine in four years’ time, and the particular problems here with Max-Cut are, at least with the computational time, probably four orders of magnitude faster than the best approach possible by GPUs,” said Yamamoto. “Then the question becomes what is the application of Max-Cut can be applied to. We don’t have a focus on any specific target right now, but some sort of reasonable combinatorial optimization problems should be solved by this machine.”

“We can build a 10,000 spin quantum Ising machine in four years’ time, and the particular problems here with Max-Cut are, at least with the computational time, probably four orders of magnitude faster than the best approach possible by GPUs,” said Yamamoto. “Then the question becomes what is the application of Max-Cut can be applied to. We don’t have a focus on any specific target right now, but some sort of reasonable combinatorial optimization problems should be solved by this machine.”

When asked to put a more precise number on it, Vandersypen had this to say: “For the circuit model of quantum computing, the one based on quantum error correction codes and so forth, I think that in the next five years there is no realistic prospect of solving relevant problems unless there is a breakthrough in solving a few qubit algorithms. We are hopeful that on a ten to fifteen year timescale this is going to be possible, and even that is ambitious.”

Smelyanskiy changed the nature of the question away from time and towards money, which was an unexpected shift. Here is what he said:

“We did an analysis at Google recently in what it would take to implement a Grover’s algorithm for extremely hard problems where classical algorithms fail beyond 40 or 50 bits and with 70 bits you would not be able to do it. Grover’s algorithm is a search algorithm that provides a quadratic speedup for extremely hard problems; if you have 2n steps to find the solution on structured search, you would need only n/2 steps to find a solution with that algorithm on a quantum machine. For a problem of size 60, you would need about 3.5 billion qubits and it would take about three hours with a speed up over a single CPU of over 1.4 million times. For the problem of size 70, the speedup would be 34 million and you would need only a little bit more qubits at 5.9 billion. If it is about $1 per qubit, and you spend another $500 million to bid down the price, roughly with a $2 billion investment you would be able to build a decent supercomputer with several millions of CPUs.”

In terms of the rocket history analogy for the state of quantum computers :

* do we need to find the metal tube of the mysore rocket
* do we need the long stick of the Congreve rocket
* do we need Goddard's nozzle and liquid fuel ?
* is one of the dozen or so approaches now good enough and we just need to scale ?
* are we stuck in ancient rocketry with no killer app and missing fundamental knowledge in science and engineering
* is the physics against achieving truly useful results ?

Getting 1.4 million times speedup over a single CPU is possible now with a Google data center. In ten to 15 years it could be inside one rack of future conventional computers. If that rack of computers could not solve your NP-hard problem you could use it for many other revenue generating and useful applications.

SOURCES- the Platform, Wikipedia, Dwave

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