Quantum Computer - "A Major Project"

INTRODUCTION

A quantum computer is a computer that actively employs the principles of quantum mechanics. Fundamentally, all calculations done with conventional computers also can be done with a quantum computer. However, a quantum computer is not advantageous for all calculations. There are certain problems where the calculation time would increase exponentially with conventional computers, if one attempts to increase the scale of the problems.Those problems can be solved at extremely high speed with a quantum computer.

Factorization is one example. Basically,the only way to calculate is by checking whether or not the number can be factorized by each prime in order. As the number’s digits increase, a huge amount of calculation is needed. Actually, the safety of public key cryptography systems used on the Internet is based on the difficulty of such calculations.Therefore, the realization of quantum computers is fundamentally threatening the security of the network society. Factorization on the order of 256 figures would take about 10 million years even with IBM’s Blue-Gene which is announced to appear in 2005. However, by using a quantum computer, such calculation would take only several tens of seconds.Quantum cryptography using quantum mechanics is an example of technology for removing the uncertainty about security. Quantum computers also have the potential for performing, super quickly, such things as database searches of the vast ocean of the Internet,optimum design, and so on.

ORIGIN OF QUANTUM COMPUTER SPEED

Although there are some principles of quantum mechanics that can be applied to information processing, the most important one is the principle of superposition. Bit values permittedby conventional digital computers are only "0" and "1". However, besides these two, quantum computers can handle their superposition states of "0 and 1" also. The bits in quantum computers are called "qubits."
Actually, the same kind of superposition state of "0 + 1"can be formed by one bit in an analog computer, and it is possible to realize the superposition of the four states at equal probability by two bits. However, the nature of quantum computers is entirely different from classical physics on the point that any combination from the four states can be expressed with two qubits.

*For example, a superposition state of "11 + 00" cannot be realized classically,even if any classical superposition states are employed (This state is called quantum entanglement.). This is the origin of the superparallel nature of quantum computers that cannot be replicated by analog computers.
Likewise, using N qubits, any of 2N states can be formed with just one state. Therefore, it becomes possible to perform super-parallel processing of problems which need to have 2N input. The more the number of qubits increases, the greater becomes the effect exponentially.By means of quantum superposition and entanglement with N qubits, all 2N states can be expressed as one state.Here we have an example of N=3.
In quantum computers, each operation necessary for calculations can be performed simultaneously to the whole superposition state. This is the quantum-mechanical super-parallel nature that is the origin of tremendous calculating capacity. However, to get the answer, some kind of observation is needed. If the answer is also of a probabilistic nature, the answer tends to differ among different observations.To remove this kind of uncertainty, quantum interference is used, and operations are performed in order to get the answer with a probability of nearly one in a bit or a register for the answer. It can be said that the design for this process is a quantum computer algorithm.

ALGORITHMS AND HARDWARE

While algorithms are important as stated above, they are difficult to make. Only three kinds have been discovered up to now, and only two have any practical value.

#. Shor’s factorization - which is also applicable to discrete logarithm problems
#. Grover’s database search algorithm.
Since many information theory specialists are now entering the field of quantum information, we can expect discoveries of epoch-making algorithms concerning such things as optimization problems like the traveling salesman problem, optimum LSI design, optimum location of cellular phone ground stations, and others. Unfortunately, hardware is far behind the development of algorithms. The number of qubits necessary for practical factorization is said to be approximately 10,000. Even in the most advanced IBM experiment using NMR, only 5 to 7 qubits have been utilized. Besides NMR, many kinds of experiments have been reported, beginning with ion traps, cavity quantum electrodynamics, linear optics and so on. There have also been many proposals, such as the use of phosphorous nuclear spins in a silicon substrate. Among these, Yasunobu Nakamura and his colleagues at the NEC Fundamental Research Laboratories (FRL) have successfully demonstrated for the first time the control of a superposition state of a solid-state qubit for which there are growing expectations for integration.
**A very small super-conductive single electron box was made with Josephson junctions and its electronic superposition state was controlled at will by operating the gate. This result has been highly evaluated, consecutively winning several awards including the Nishina Memorial Prize, the most prestigious one in the world of physics in Japan.
Nevertheless, qubits for realistic quantum computations require much longer coherence time. We will continue to look for qubits with better conditions, and also try to develop applications appropriate for fewer qubits.

CONCLUSION

The principle of quantum computation and the forefront of algorithm and hardware have been briefly explained. Currently, the NEC FRL is developing qubits with the aforementioned Josephson junctions, and has started to develop quantum gates aiming at quantum cryptography. It is also working on applications with fewer qubits, and is strengthening theoretical research. It can be said that quantum mechanics has been transformed from a physical tool for interpretation of physical phenomena to a practical application tool for engineering.