Avoiding quantum chaos in quantum computation.

We study a one-dimensional chain of nuclear 1/2 spins in an external time-dependent magnetic field, considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos that can destroy the stability of quantum operations. The standard viewpoint is that the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits.

Delocalization border and onset of chaos in a model of quantum computation.

We study the properties of spectra and eigenfunctions for a chain of 1/2 spins (qubits) in an external time-dependent magnetic field and under the conditions of nonselective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transitions and show that for the interaction between nearest qubits, the transition is very different from that in quantum chaos.

Solid-state quantum computer based on scanning tunneling microscopy.

We propose a solid-state nuclear-spin quantum computer based on application of scanning tunneling microscopy (STM) and well-developed silicon technology. It requires the measurement of tunneling-current modulation caused by the Larmor precession of a single electron spin. Our envisioned STM quantum computer would operate at the high magnetic field (approximately 10 T) and at low temperature approximately 1 K.

Magnetic resonance force microscopy quantum computer with tellurium donors in silicon.

We propose a magnetic resonance force microscopy (MRFM)-based nuclear spin quantum computer using tellurium impurities in silicon. This approach to quantum computing combines well-developed silicon technology and expected advances in MRFM. Our proposal does not use electrostatic gates to realize quantum logic operations.

Influence of superpositional wave function oscillations on Shor's quantum algorithm.

We investigate the influence of superpositional wave function oscillations on the performance of Shor's quantum algorithm for factorization of integers. It is shown that wave function oscillations can modify the required quantum interference. This undesirable effect can be routinely eliminated using a resonant pulse implementation of quantum computation, but requires special analysis for nonresonant implementations.