Topological Quantum Computing

Other Unique Engineering Ideas

Quantum computers promise to perform calculations believed to be impossible for ordinary computers. Some of those calculations are of great real-world importance. A certain widely used encryption methods could be cracked given a computer capable of breaking a large number into its component factors within a reasonable length of time. Virtually all encryption methods used for highly sensitive data are vulnerable to one quantum algorithm or another.

1. Description

2. Why

3. How

4. Future Trends

5. Related Links

Useful Links Topological Quantum Computing 

Description 

In conventional computing these zeroes and ones are created by switching an electric current on and off. Spins are less affected by the environment than electric charges and take longer to decay. Also, keeping an electric charge in position requires continuous power; when computers lose power, the charge goes away. With a magnetic device the memory stays put when the power shuts off.As a bonus - and it's a fairly major bonus - if you take electricity out of the equation, you get rid of the overheating problem that is undercutting Moore's law.At first sight, a topological quantum computer does not seem much like a computer at all. It works its calculations on braided strings—but not physical strings in the conventional sense.Rather, they are what physicists refer to as world lines, representations of particles as they move through time and space. (Imagine that the length of one of these strings represents a particle’s movement through time and that its thickness represents the particle’s physical dimensions.) Moreover, even the particles involved are unlike the electrons and protons that one might first imagine.They are instead quasiparticles—excitations in a two-dimensional electronic system that behave a lot like the particles and antiparticles of high-energy physics. And as a further complication, the quasiparticles are of a special type called anyons, which have the desired mathematical properties. 

Why

The extra power of a quantum computer comes about because it operates oninformation represented as qubits, or quantum bits, instead of bits. 

  • An ordinary classical bit can be either a 0 or a 1, and standard microchip architectures enforce that dichotomy rigorously.
  • A qubit, in contrast, can be in a so-called superposition state, which entails proportions of 0 and 1 coexisting together.
  • One can think of the possible qubit states as points on a sphere.
  • The north pole is a classical 1, the south pole a 0, and all the points in between are all the possible superpositions of 0 and 1

A few researchers are pursuing a very different way to build a quantum computer. 

  • If qubits are not carefully isolated from their surroundings, such disturbances will introduce errors into the computation.
  • Most schemes to  design a quantum computer therefore focus on finding ways to minimize the interactions of the qubits with the environment.
  • If the error rate can be reduced to around one error in every 10,000 steps, then error-correction procedures can be implemented to compensate for decay of individual qubits.
  • Constructing a functional machine that has a large number of qubits isolated well enough to have such a low error rate is a daunting task that physicists are far from achieving. 

Topological quantum computers are equivalent in computational power to other standard models of quantum computation, in particular to the quantum circuit model and to the quantum Turing machine model. That is, any of these models can efficiently simulate any of the others.Nonetheless, certain algorithms may be a more natural fit to the topological quantum computer model. For example, algorithms for evaluating the Jones polynomial were first developed in the topological model, and only later converted and extended in the standard quantum circuit model

How 

The freedom that qubits have to roam across the entire sphere helps to give quantum computers their unique capabilities. Unfortunately, quantum computers seem to be extremely difficult to build. The qubits are typically expressed as certain quantum properties of trapped particles, such as individual atomic ions or electrons.But their superposition states are exceedingly fragile and can be spoiled by the tiniest stray interactions with the ambient environment,  which includes all the material making up the computer itself.In their approach the delicate quantum states depend on what are known as topological properties of a physical system.Topology is the mathematical study of properties that are unchanged when an object is smoothly deformed, by actions such as stretching, squashing and bending but not by cutting or joining. It embraces such subjects as knot theory. Small perturbations do not change a topological property.For example, a closed loop of string with a knot tied in it is topologically different from a closed loop with no knot. The only way to change the closed loop into a closed loop plus knot is to cut the string, tie the knot and then reseal the ends of the string together.Similarly, the only way to convert a topological qubit to a different state is to subject it to some such violence. Small nudges from the environment will not do the trick.Here is a what a computation might look like:

  • First, create pairs of anyons and place them along a line.
  • Each anyon pair is rather like a particle and its corresponding antiparticle, created out of pure energy.
  • Next, move pairs of adjacent anyons around one another in a carefully determined sequence.
  • Each anyon’s world line forms a thread, and the movements of the anyons as they are swapped this way and that produce a braiding of all the threads.
  • The quantum computation is encapsulated in the particular braid so formed. 

The final states of the anyons, which embody the result of the computation, are determined by the braid and not by any stray electric or magnetic interaction. And because the braid is topological— nudging the threads a little bit this way and that does not change the braiding—it is inherently protected from outside disturbances.  

Future Trends

Tangible evidence of the quantum revolution hit the market, when Freescale Semiconductor (Charts), a Motorola spinoff, began commercial shipments of magnetic random-access memory (MRAM) chips. The U.S. certainly isn't alone in this race; the Europeans and Japanese are funding huge research efforts. India and China are getting onboard as well.Beyond the actual creation of a quantum computer, our chief limitations are the imaginations of software engineers. This will be the major challenge of the Google geniuses of tomorrow: to take computing and networking power that is effectively infinite and create interfaces that are simple enough for mere mortals to understand. 

Keywords

Quantum computers, anyons, qubits, Topological quantum computing, Spin Networks and Anyonic Topological Quantum Computing

Related Articles

Related Links