Quantum description and dynamics of computer bits

Swati Karni, Arun Kumar Rajamandrapu

I. Bolesta, Олексій Кушнір, Serhiy Velhosh +1 more

Using the formalism of the Boolean algebra, the process of computation in quantum computers is analyzed.The description of quantum bits -qubits -in the Hilbert space is given, quantum logic elements, quantum networks and the structure of an ideal quantum computer are considered.Peculiarities of quantum mechanical calculations related to the superposition principle, the interference of complex amplitudes and the existence of entangled states are discussed.

Kenneth Wright

One of the fundamental problems of chemistry is the difficulty in determining full quantum mechanical descriptions of molecules. Molecules contain many degrees of freedom and as a result the classical description scales factorially with the number of electrons. One way to overcome this mismatch between quantum and classical pictures is to use one quantum system, a quantum computer, to simulate another. Quantum computation is based upon a two-level system, a qubit, which is analogous to a bit in classical computation. Unlike a classical bit, a qubit can exist in a superposition of quantum states. The interaction between a quantum system and its environment results in the decay of the superposition state of the system into a probability density of classical states [1]. This is known as decoherence. A realistic quantum computer requires qubits with long coherence times; with respect to the achievable gating times, for a formal relation refer to section 1.2.2. The spin echo effect in nuclear magnetic resonance (NMR) offers a way to increase the coherence time of a qubit and has been studied as a way to mitigate decoherence in quantum computation[2][3]. By applying an appropriate Π pulse to a system under the influence of a large external field, as in NMR, the interaction term of the Hamiltonian between the qubit and environment can be eliminated[3][4]. Periodic implementation of such pulses is known as periodic dynamic decoupling (PDD). Similar to PDD, concatenated dynamic decoupling (CDD) is a periodic pulse sequence which removes the interaction term of the Hamiltonian, however in CDD pulse sequences are recursively embedded within the overall pulse train. Such pulse sequences have been shown theoretically to work for model quantum systems such as GaAs quantum dots, and theoretically such pulse sequences vastly improve the coherence time of a qubit [5]. There have been many calculations showing that by progressively increasing the number of concatenated pulse sequences increasingly longer coherence times can be achieved [6][7]. These techniques have not been tested in the laboratory and experimental implementation of these promising techniques motivates current research. There also continues to be extensive work on developing novel pulse sequences which may improve coherence times even further. The goal of this research is to experimentally determine the coherence times which can be achieved with a trapped calcium atom by applying these pulse sequences.

I. Peterson

Pedram Khalili Amiri

Using atoms as digital bits will start a completely new era in computer design. Atoms cannot be simply manipulated and used like the bits built with transistors. The behavior of matter on the atomic scale follows the rules of modern physics. This behavior cannot be understood in terms of our classical description of the world (i. e. Newtonian mechanics or Maxwell's equations in electromagnetics). The physical theory dealing with such behavior is called quantum mechanics. Its use in the computer industry will most probably cause a revolution in the way we use and understand computers. The author describes how such a quantum computer-a computer based on the rules of quantum mechanics-may work, and how it is going to give incredible speed and problem-solving power.

V. Ravishankar