Solid-state quantum computing using spectral holes

Abstract

A quantum computer that stores information on two-state systems called quantum bits or qubits must be able to address and manipulate individual qubits, to effect coherent interactions between pairs of qubits, and to read out the value of qubits. 1,2 Current methods for addressing qubits are divided up into spatial methods, as when a laser beam is focused on an individual qubit 3,4,5 or spectral methods, as when a nuclear spin in a molecule is addressed using NMR. 6,7 The density of qubits addressable spatially is limited by the wavelength of light, and the number of qubits addressable spectrally is limited by spin linewidths. Here, we propose a method for addressing qubits using a method that combines spatial and spectral selectivity. The result is a design for quantum computation that provides the potential for a density of quantum information storage and processing many orders of magnitude greater than that afforded by ion traps or NMR. Specifically, this method uses an ensemble of spectrally resolved atoms in a spectral holeburning solid. The quantum coupling is provided by strong atom-cavity interaction. Using a thin disc of diamond containing nitrogen-vacancy color centers as an example, we present an explicit model for realizing up to 300 coupled qubits in a single spot. We show how about 100 operations can take place in parallel, yielding close to 4X10 4 operations before decoherence.The basic concept is illustrated in figure 1. Consider a small volume element of a crystal containing a set of impurity atoms. Each atom sees a unique surrounding, so that the resonance frequency for a given transition is different for different atoms. The number of spectrally resolvable bands, N R , is determined by the ratio of the spectral spread to the width of the individual resonance. We consider a situation where the number of atoms in the selected volume is less than N R, so that each atom can be addressed individually.We choose an effective density low enough to ignore the atom-atom direct coupling. Instead, we couple the atoms in a controlled fashion by placing them in an optical cavity with a strong vacuum Rabi frequency. Once two atoms are coupled by the

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