What is a quantum computer?

Transcription

1 What is a quantum computer? Lucas Paresqui Berruezo lucaspberruezo@gmail.com 3 de julho de Introduction Many people may have heard the words quantum computer, but only a few have actually seen one. Today we ll show you what it really is, some of its advantages, and some of its flaws, so that by the end of the day, you ll know what this marvelous piece of technology is. We shall discuss topics such as what is a quantum computer, how does a quantum computer work, why build a quantum computer, what s wrong with my regular computer, and many other questions that may have troubled the reader. Of course you won t become an expert, but I assure you that you ll be enlightened. 2 Why build a quantum computer? Well, the best answer is, why not? During the whole history of mankind, we never stopped building new kinds of machines, so there is no need to stop 1

2 now; but that is not the only motive. All the manipulation and transmission of information, before the development of quantum information(q.i.), was made using classical mechanics. After the development of Q.I., following the laws of quantum mechanics, nothing more logical than the appearance of a quantum physical system, a.k.a. a quantum computer. Another pertinent question would be: is it worth building one? Maybe so, maybe not... fortunately quantum computers have a greater computational power than classical ones; we ll discuss this topic later. Does this mean you ll have to throw your classical computer away? No! Of course not (at least not for now). Quantum computers [1] are only advantageous at some types of operations; iteration processes, such as summation or intersection operations, for example, are not sped up. 3 Classical x Quantum The most critical difference between these two systems are the Bits. I ll start with a simple example. Suppose we have only a single bit; then for a classical computer, it can assume the values 0 or 1, frequently called states 0 and 1 of your system. This is a good notation, because as we add more bits they are easily represented by 01 (two bits, the former at 0 and the latter at 1), 101 (three bits), (n bits). Back to our one bit example: Expressing in general terms: Bit = a 0 + b 1 ; a and b can only assume the values 0 or 1, beside being mutually exclusive (if a=1, then b=0, so the bit is at position 0). For a quantum bit, there is a slight difference: QuBit = a 0 +b 1 ; some 2

3 of you must be wondering what is the difference between those two equations. There is no explicit difference, but this time, the values a and b can assume are no longer fixed, they only need to obey the relation a 2 + b 2 = 1. This may not look like a big change, but it certainly means more than it looks like. Things become even more interesting when more bits are added to the system; for two Qubits: QuBits = a 00 +b 01 +c 10 +d 11. These states are usually entangled, meaning they can t be written by a product of two independent bits. In larger systems the size of the operation someone can perform with a classical computer scales with 2n while quantum computer scales with 2 n (n is the number of bits the system possesses), this means that for an effective 1024 bit operation, a classical computer will need 512 bits, while a quantum one, need only 10 qubits. 4 Inside a quantum computer In order to create a productive quantum computer, we need a system with well characterized qubits. Some physical systems meet these requirements, such as an ion-trap [2], [3], nuclear magnetic resonance [4], quantum dots [5], [6], et. al. Superconducting techniques are also frequently used in a quantum computer due to extremely low energy dissipation and ultra-sensitive electrometers and magnetometers (state detectors) [8].. Unfortunately all the qubits in these system have some decoherence time. This is not something we desire, since once this time reaches zero the capability of a quantum computer does not outpace a classical one. This means we need a constant supply of qubits with a decoherence time greater than the time that takes to 3

4 perform an operation; yet another problem is that quantum operations cannot be perfectly implemented. Fortunately most of these problems can be corrected using ancillary qubits and quantum error correction [7], and if an operation is not yet ensured, the process is repeated a few times to enhance the probability. 5 Discussion The development of Q.I. is also applied in other systems, such as quantum communication (with a very good outcome by the way), but since today s topic is about quantum computers, we shall leave that for another time. For those who yet do not believe the concept of quantum computers may be a tangible reality, researchers form D-wave systems have already made a real quantum computer with effective 512 bit capacity. [9], [10]. This may not seem a lot, but it already performs some operations better than its classical version; besides, the first microcomputers ever made were not a big deal, but nowadays they are an essential part of our lives, something that a quantum computer may also one day become. 6 Bibliography [1] D. P. DiVincenzo, quant-ph/ v3 13 Apr 2000; [2] J.I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); [3] P. M. Platzman and M. I. Dykman, Science 284, 1967 (1999); [4] N. Gershenfeld and I. Chuang, Science 275, 350 (1997); 4

5 [5] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998); [6] B. Kane, Nature 393, 133 (1998); [7] J. Preskill, Proc. R. Soc. Lond, quant-ph/ (1998); [8] K. K. Berggren. PROC. of the IEEE, VOL. 92,n10, (2004) [9] [10] 5