Quantum computing with defects
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troduction A qubit is the basic unit of information in a quantum computer. In contrast to binary “bits” that can have only two values (0 or 1) and upon which Boolean logic is based, a qubit can be in any coherent superposition between two quantum states.1 The physical realization and control of qubits is very challenging. A range of qubit implementations is being explored, including in liquids,2 atoms,3 and in solids such as superconductors4 and semiconductors.5 Loss of coherence is a major issue: In principle, the qubit should be completely isolated from unwanted external fluctuations in its environment in order to maintain its quantum state. However, a completely isolated qubit would not allow for interactions, such as entanglement, that are necessary to perform quantum manipulations and computing. Even if a single qubit can be fabricated, scalability is a major issue. In principle, a wave function on an isolated atom would provide an intuitive, well-defined, and well-understood quantum state for use as a qubit. Unfortunately, isolated atoms do not easily lend themselves to incorporation in a quantum device; complex approaches such as ion traps or optical lattices3 are required to constrain the atoms or ions. It turns out, however, that point defects in semiconductors or insulators can display behavior that is very similar to that of isolated atoms, as illustrated in Figure 1. The electronic states associated with a vacancy, for instance, tend to have energies that lie within the
forbidden bandgap, and their wave functions are constructed out of atomic orbitals on the neighboring atoms and are hence very localized—on the scale of atomic dimensions. Invoking similarities with wave functions on isolated atoms is therefore quite appropriate. The advantage of point defects is that they are firmly embedded within the host material, and decades of investigation and characterization have provided us with many tools for controlling and manipulating such defects. Point defects tend to have a bad reputation. When unintentionally present in semiconductors, they can adversely affect the desired doping behavior and lead to degraded electronic or optical properties. The semiconductor community has therefore gone to great lengths to build a thorough understanding of such defects and to develop exquisitely precise characterization techniques,6–8 such as electron spin resonance and photoluminescence. This knowledge and toolset can now be constructively employed to design and manipulate point defects for use as qubits. The schematic provided in Figure 1 is a qualitatively correct but highly simplified description. A serious approach to designing defects needs to be based on a rigorous quantummechanical description. For isolated atoms, we would solve the Schrödinger equation. The electronic structure of a solid, however, presents a very complicated many-body problem. Density functional theory (DFT)9,10 provides an accurate and reliable approach to tackling this issue; it has become the
Luke Gordon, Materials Department, University of C
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