Documenting the Coming Singularity

Saturday, June 16, 2007

Qubit Calculations

Researchers at Delft University of Technology have succeeded in carrying out calculations with two quantum bits, the building blocks of a possible future quantum computer. ~ Science Daily

Quantum computing has the potential to increase computing power to an almost unimaginable level. The reasons for this amazing potential have to do with how matter behaves at very small scales, where the laws of quantum mechanics come into play.

Richard Feynman, one of the world's most respected and beloved physicists and Nobel prize-winner, famously said "I think it is safe to say that no one understands Quantum Mechanics." This is because the way particles behave at this scale makes no intuitive sense. They take every possible path from point A to point B. They are here and there at the same time. Until you look at them. Then they quickly settle down into one place and one path.

How does this strangeness translate into seemingly infinite computing power?
In a traditional computer, information is encoded in a series of bits, and these bits are manipulated via Boolean logic gates arranged in succession to produce an end result. Similarly, a quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. This similarity in calculation between a classical and quantum computer affords that in theory, a classical computer can accurately simulate a quantum computer. In other words, a classical computer would be able to do anything a quantum computer can. So why bother with quantum computers? Although a classical computer can theoretically simulate a quantum computer, it is incredibly inefficient, so much so that a classical computer is effectively incapable of performing many tasks that a quantum computer could perform with ease. The simulation of a quantum computer on a classical one is a computationally hard problem because the correlations among quantum bits are qualitatively different from correlations among classical bits, as first explained by John Bell. Take for example a system of only a few hundred qubits, this exists in a Hilbert space of dimension ~1090 that in simulation would require a classical computer to work with exponentially large matrices (to perform calculations on each individual state, which is also represented as a matrix), meaning it would take an exponentially longer time than even a primitive quantum computer.

Richard Feynman was among the first to recognize the potential in quantum superposition for solving such problems much much faster. For example, a system of 500 qubits, which is impossible to simulate classically, represents a quantum superposition of as many as 2500 states. Each state would be classically equivalent to a single list of 500 1's and 0's. Any quantum operation on that system --a particular pulse of radio waves, for instance, whose action might be to execute a controlled-NOT operation on the 100th and 101st qubits-- would simultaneously operate on all 2500 states. Hence with one fell swoop, one tick of the computer clock, a quantum operation could compute not just on one machine state, as serial computers do, but on 2500 machine states at once! Eventually, however, observing the system would cause it to collapse into a single quantum state corresponding to a single answer, a single list of 500 1's and 0's, as dictated by the measurement axiom of quantum mechanics. The reason this is an exciting result is because this answer, derived from the massive quantum parallelism achieved through superposition, is the equivalent of performing the same operation on a classical super computer with ~10150 separate processors (which is of course impossible)!! (Jacob West, 2000)
Didn't follow that? Not to worry. What it boils down to is that quantum computing, if fully realized, could easily perform calculations that a universe-sized classical machine would find impossible.

Is quantum computing only pie in the sky? No, it's not. Researchers are making solid progress towards its realization.
Now for the first time a 'controlled-NOT' calculation with two qubits has been realised with the superconducting rings. This is important because it allows any given quantum calculation to be realised.

The result was achieved by the PhD student Jelle Plantenberg in the team led by Kees Harmans and Hans Mooij. The research took place within the FOM (Dutch Foundation for Fundamental Research on Matter) concentration group for Solid State Quantum Information Processing.
Stay tuned.

Source: ScienceDaily

Via BetterHumans

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