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European Quantum Electronics Conference (EQEC)

Quantum information processing with spatially delocalized qubits

J. Mompart, K. Eckert, Maciej Lewenstein, Wolfgang A. Ertmer, G. Birkl

Published Jan 1, 2003• 0 citations
Publisher

Abstract

A qubit is implemented by using two adjacent optical microtraps and a single atom initially stored in the vibrational ground state of the left trap. This configuration represents |0>, while having the atom in the ground state of the right trap represents |1>. As the computational basis states have different localizations in space, this concept is referred as spatially delocalized qubits.

DOI
10.1109/eqec.2003.1314249

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A qubit is implemented by using two adjacent optical microtraps and a single atom initially stored in the vibrational ground state of the left trap. This configuration represents |0>, while having the atom in the ground state of the right trap represents |1>. As the computational basis states have different localizations in space, this concept is referred as spatially delocalized qubits.
We analyze the operation of quantum gates for neutral atoms with qubits that are delocalized in space, i.e., the computational basis states are defined by the presence of a neutral atom in the ground state of one out of two trapping potentials. The implementation of single-qubit gates as well as a controlled phase gate between two qubits is discussed and explicit calculations are presented for rubidium atoms in optical microtraps. Furthermore, we show how multiqubit highly entangled states can be created in this scheme.
Many approaches have been proposed towards the realization of practical quantum information processing. They include laser manipulation of the energy states in atomic or ion traps, nuclear magnetic resonance in molecules, quantum computation in optical lattices, and in Bose-Einstein condensates. For any of these system to be viable quantum computation, it should have stable and long-lived internal states. In addition it should be possible to quantum- mechanically entangle two or more qubits and the entangled states should be capable of non-local realism phenomena. The ground state and metastable states of low Z atoms especially the single and two-electron atoms and their ions are the most commonly used qubits for quantum information processing systems. Efforts to exhibit these phenomena in high Z elements has been much more challenging. In part because of the high energy needed to ionize the high Z elements into effective one- or two-electron system suitable for quantum information processing. Furthermore the energy difference between two stable states of the High Z elements that are possible qubits states turn to be very high. Preferably the energy difference of two qubits levels should be in the meV to a few tens of electron volts for practical realization of a quantum computing system. In general any two stable terms of an atomic or molecular system with low to moderate energy separation, that do not violate term rules for selection and symmetry, may be viable qubits states.
To begin with, we need a quantum register made of many qubits to store information. Recall that a classical computer also requires memory to store information. The simplest way to realize a qubit physically is to use a two-level quantum system. For example, an electron, a spin 1/2 nucleus or two mutually orthogonal polarization states (horizontal and vertical, for example) of a single photon can be a qubit. We may also employ a two-dimensional subspace, such as the ground state and the first excited state, of a multi-dimensional Hilbert space, such as atomic energy levels. In the latter case, special care must be taken to avoid leakage of the state to the other part of the Hilbert space. In any case, the two states are identified as the basis vectors, |0〉 and |1〉, of the Hilbert space so that a general single qubit state takes the form |ψ〉 = α|0〉 + β|1〉, where |α|2 + |β|2 = 1. A multiqubit state is expanded in terms of the tensor products of these basis vectors. Each qubit must be separately addressable. Moreover it should be scalable up to a large number of qubits. The two-dimensional vector space of a qubit may be extended to be three-dimensional (qutrit) or, more generally, d-dimensional (qudit). A system may be made of several different kinds of qubits. Qubits in an ion trap quantum computer, for instance, may be defined as: (1) hyperfine/Zeeman sublevels in the electronic ground state of ions (2) a ground state and an excited state of a weakly allowed optical transition and (3) normal mode of ion oscillation. A similar scenario is also proposed for Josephson junction qubits, in which two flux qubits are coupled through a quantized LC circuit. Simultaneous usage of several types of qubits may be the most promising way to achieve a viable quantum computer.
Classical information processing is performed using bits , which are just two-state systems, with the two states called 0 and 1. By grouping bits togetherwe can represent arbitrary pieces of information, and by manipulating these bits we can perform arbitrary computations. The corresponding basic element used in quantum information is the quantum bit, or qubit . This is simply a quantum system with two orthonormal basis states, which we shall call |0⧽ and |1⧽. There are many possible physical implementations of a qubit, such as spin states of electrons or atomic nuclei, charge states of quantum dots, atomic energy levels, vibrational states of groups of atoms, polarization states of photons, or paths in an interferometer. At this stage the physical implementation is not important: the idea of a qubit is to abstract the discussion away from physical details. Taking the standard approach of quantum information theory, we shall begin by not worrying too much about the properties of these states, or even what their energies are; we shall simply assume that they are eigenstates of the system's Hamiltonian with known eigenvalues (that is, known energies). This approach allows us to concentrate on the fundamental properties of the system, without considering all the tedious details. We can in principle perform classical information processing on our quantum system by using the two states |0⧽ and |1⧽ as our logical states 0 and 1 and proceeding in the usual fashion, giving rise to the field of reversible computing , which will be explored briefly in Part II. This, however, misses the point.