Wednesday, June 20, 2012

Quantum computer for high school students



Recently some high school students contacted me for an interview. This motivated me to write the following short post on what does it mean to do a quantum computation.

1) What is the difference between a quantum and classical computer?

A)

Let me give you an example, if you want to sum 23 and 45 using classic computers, these numbers are first to be converted from decimal format to binary (0 and 1): 23 in decimal =10111 in binary, and 45=101101.

These two binaries must be written in left to right column order and they are linked together using a "summation" operator applied at each column. So we need 6 summation operators to work on the inputs. In quantum computers however, each number is represented by an angle and the summation of two number (no matter how large they are) needs at least one summation operator (that adds the angles).

What is the angle?

In quantum bits (qubit), we can have both states of 0 and 1 at the same time. So the state of a qubit can be 0 or 1 or a superposition of the two: a*(state 0)+b(state 1), where a and b are not independent coefficients, they are linked together by the relation a^2+b^2=1, so we have only one of them as an independent variable. You can assume state 0 is linka vector along the axis x and the state y is a vector along the axis y. Given the two states we can make any combination of the two vectors as a vector from the origin toward any direction in the xy plane. The angle between the vector and the axis x is related to the coefficient a (in fact the tangent of the angle is tan(theta)=b/a=sqrt(1-a^2)/a.)

This angle can be discretized in units (a unit is a small angle we can distinguish depending on the noise etc. in the system) and we can calibrate each unit to represent one in the decimal numbers.

This way adding two numbers means adding two angles. For this we need one summation operator and this saves a lot of resources in the computation. Similarly very complicated calculations can be achieved using smaller number computer resources compared to classical computers.

2) What are the main restrictions in making quantum computers, and how soon can we expect quantum computers to be put in use, and perhaps put on the market?


There are many different quantum computer version from ion trap to superconducting qubits and quantum optic. The smallest and most portable one is superconducting qubits, however they need to operate in low temperature (as low as 1 kelvin or lower). If we can achieve higher temperature less noisy system that may make a way into market.

Search for D-wave quantum computer to read about a 10million machine that was made recently.

3) How much faster is a quantum computer than an 8-bit computer?

People say exponentially faster. For the example I said earlier on the summation if each summation operator needs 0.1 second to take place, 6 of them in a row for summing 23 and 45 needs at least 0.6 second in classical computers, however only one of the operators is required in quantum computers and therefor 6 times faster (0.1 second). You can assume for large numbers the different becomes more pronounced. For instance a large factorial operator that takes years to compute on classical computers can be calculated in a few second.

To read more ... there are plenty of good references and book  online. A few of them are:

http://www.scottaaronson.com/writings/highschool.html

http://michaelnielsen.org/blog/quantum-computing-for-everyone/

Also at our institute you can find very interesting programs to attend
and learn more about qubits.

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