We investigate the time T a quantum computer requires to factorize a given number
dependent on the number of bits L required to represent this number. We stress the fact that …

In the last few years, theoretical study of quantum systems serving as computational devices
has achieved tremendous progress. We now have strong theoretical evidence that quantum …

We argue that the halting problem for quantum computers which was first raised by Myers, is
by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties …

A lower bound on the amount of energy needed to carry out an elementary logical operation
on a quantum computer, with a given accuracy and in a given time, is derived. The bound …

As quantum computers are based on the laws of quantum mechanics, they are capable of
solving certain problems faster than their classical counterparts. However, quantum …

We consider how to optimize memory use and computation time in operating a quantum
computer. In particular, we estimate the number of memory quantum bits (qubits) and the …

We analyse dissipation in quantum computation and its destructive impact on the efficiency
of quantum algorithms. Using a general model of decoherence, we study the time evolution …

Recently it has become clear, that a key issue in quantum computation is understanding
how interaction with the environment, or" decoherence", affects the computational power of …

Recent theoretical results confirm that quantum theory provides the possibility of new ways
of performing efficient calculations. The most striking example is the factoring problem. It has …

The Church-Turing thesis says that a digital computer is a universal computational device;
that is, it is able to simulate any physically realizable computational device. It has generally …