Quantum Computation with Ion Chains

Motivation

A promising path toward building scalable atom-photon networks uses a hierarchical architecture for quantum computation and communication. One version of this scheme envisions a network of elementary logic units (ELUs) that interact using photonic links via a heralded entanglement protocol. Each ELU is comprised of a chain of ions of a manageable size, in which individual qubits are entangled by applying local quantum gates that rely on the Coulomb interaction for spin-motion coupling.

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The beauty of using the motional modes of a chain of ions to entangle individual qubits is that the interaction between qubits can be engineered very precisely after the trapping potential and the resulting motional modes have been characterized. However, the same mechanism that allows qubit spins to interact is also a significant source of gate infidelity, especially for larger ion chains. As the number of ions increases, the number and complexity of these collective motional modes also increases, which makes it difficult to disentangle the qubit states from the motional state at the completion of the gate. This becomes a serious problem when performing gates at faster speeds.

The goal of this project is to demonstrate high fidelity quantum gates that entangle pairs of ions in chains of various lengths. By shaping of the light pulse that performs the quantum gate, we achieve acceptable gate fidelities at speeds higher than would be possible with a single, flat pulse protocol.

Method

Entanglement is performed by applying two high power laser beams to the target ions for a specific amount of time. By precise control of the beat note between the laser beams and the addition of sidebands near the motional mode frequencies, we drive stimulated Raman transitions that couple the internal qubit state to the collective motional mode. During this process, the ions execute a trajectory in phase space as the light field imparts momentum to the chain via a spin-dependent force. This trajectory is manipulated by modulating the light intensity in discrete steps during the gate. Optimizing these pulses results in the creation of a pure two-qubit entangled state useful for quantum computation with minimal decoherence.

Design

We trap a chain of Yb ions in a three-layered structure (previously used to demonstrate shuttling around a junction). The outer layers are the DC electrodes, with five segments available along the axial direction. It is thus possible to apply either a harmonic or anharmonic axial trapping potential. The middle layer provides the RF voltage required to confine the ion chain radially. The Raman beams are produced from a high power 355nm pulsed laser. Acousto-optic modulators in each beam path determine the beat note frequency as well as the applied beam power. Ions are individually addressed with focused laser beams, and an electro-optic deflector is used to select which pair will be entangled. Ion fluorescence is collected for qubit state detection using a high numerical aperture microscope objective and a multi-channel photo-multiplier tube array.