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ePaper created 2012-09-28, 09:46:25 | version 1.24.0
2|2012 Research in Jülich 17 RESEARCH AT THE CENTRE | Models tum computer,” says Neuhaus. Since the Jülich theoreticians did not have a D-Wave quantum computer at their dis- posal they simulated the sequences on the Jülich supercomputers, which was extremely time-consuming. They achieved a spectacular if rather sobering result. The problem was just as unman- ageable on a quantum computer as on any other computer. “Our research is al- so intended to continue to help assess the usefulness of quantum computers more realistically in the future,” says Neuhaus. However, the Jülich physicist is still convinced that the adiabatic quantum computer does have a future. If D-Wave should succeed in increasing the num- ber of qubits in their quantum computer to 512, then this could already exceed the performance of a present-day super- computer. “And in doing so it would only consume about one thousandth of the energy required by a conventional super- computer,” adds Neuhaus. :: The user of an adiabatic quantum com- puter would first radically simplify the travelling salesman problem (see article) by, for example, arranging all the towns on a circle. This simplified problem would then be formulated mathematically with the aid of a Hamiltonian function, named after the Irish mathematician and physi- cist William Rowan Hamilton (1805– 1865). This function describes the ener- gy state of a quantum mechanical system. The familiar solution of the sim- plified travelling salesman problem cor- responds to the energy minimum of such a quantum mechanical system, which is the central component of a quantum computer. If the adiabatic quantum computer is to solve the travelling salesman problem for a real arrangement of towns then the original Hamiltonian function must be modified in controlled steps until it de- scribes the problem. Due to a natural law, the quantum mechanical system is always in the lowest energy state at each step. If the system arrives at the Hamilto- nian function that describes the real trav- elling salesman problem then the solu- tion has been found, which is the energy minimum of the quantum mechanical state that has been reached. Even the adiabatic quantum computer cannot solve problems without real ef- fort. On the way to a real arrangement of towns, the computer comes across a quantum phase transition at which it has to perform a large number of small steps in order to remain in the minimum ener- gy state. Travelling Salesman for Quantum Computers tum computer, has been implemented in practice by D-Wave – with 128 qubits ac- cording to the company’s information. “An adiabatic quantum computer does not need to make any calculations, that is to say it doesn’t need to solve equa- tions or multiply anything in order to solve a difficult mathematical problem,” says Prof. Kristel Michielsen, head of the research group at the Jülich Institute for Advanced Simulation. She admits that the functioning of an adiabatic quantum computer (see “Travelling Salesman for Quantum Computers”) is rather mind- boggling. SOLUTION FOR THE UNMANAGEABLE Many experts hoped that quantum computers would outstrip conventional computers above all in solving those mathematical problems that are regard- ed as “unmanageable”. The classical ex- ample of this is the travelling salesman problem. The problem is to find the shortest route connecting finitely many points such that the traveller should visit each town just once and return to the starting point. This problem cannot be solved with mathematical precision. A solution can only be found that is as close as possible to the optimum. For such a problem, computing time on a conventional computer explodes with the number of towns to be included. “We investigated a special unmanage- able problem to discover how effectively it can be treated with an adiabatic quan- The Way to the Goal The standard PC solves a single math- ematical operation in several operations in which the bits are switched between 0 and 1. The quantum computer can in principle perform a very large number of mathematical operations (qubit spins) at once with each switching operation. The adiabatic quantum computer determines the lowest point of an ener- gy function that describes the problem to be solved. It approaches this function stepwise – starting from a simplified problem. 1 0 1+1=2 2+2=4 3.5=15 8-1=7 0 1