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Reports on Progress in Physics

Phonon-mediated entanglement for trapped ion quantum computing

K-A Brickman Soderberg, Christopher R. Monroe

Published Feb 23, 2010• 28 citations
Publisher

Abstract

Trapped ions are a near ideal system to study quantum information processing due to the high degree of control over the ion's external confinement and internal degrees of freedom. We demonstrate the key steps necessary for trapped ion quantum computing and focus on phonon-mediated entangling gates. We highlight several key algorithms implemented over the last decade with these gates and give a detailed description of Grover's quantum database search implemented with two trapped ion qubits.

DOI
10.1088/0034-4885/73/3/036401

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Trapped ions are a near ideal system to study quantum information processing due to the high degree of control over the ion's external confinement and internal degrees of freedom. We demonstrate the key steps necessary for trapped ion quantum computing and focus on phonon-mediated entangling gates. We highlight several key algorithms implemented over the last decade with these gates and give a detailed description of Grover's quantum database search implemented with two trapped ion qubits.
The scaling of controlled quantum systems to large numbers of degrees of freedom is one of the long term goals of experimental quantum information science. Trapped-ion systems are one of the most promising platforms for building a quantum information processor with enough complexity to enable novel computational power, but face serious challenges in scaling up to the necessary numbers of qubits. In this thesis, I present both technical and operational advancements in the control of trapped-ion systems and their juxtaposition with photonic modes used for quantum networking. After reviewing the basic physics behind ion trapping, I then describe in detail a new method of implementing Raman transitions in atomic systems using optical frequency combs. Several dierent experimental setups along with simple theoretical models are reviewed and the system is shown to be capable of full control of the qubit-oscillator system. Two-ion entangling operations using optical frequency combs are demonstrated along with an extension of the operation designed to suppress certain experimental errors. I then give an overview of how spatially separated ions can be entangled using a photonic interconnect. Experimental results show that pulsed excitation of trapped ions provide an excellent single photon source that can be used as a heralded entangling gate between macroscopically separated systems. This heralded entangling gate is used to show a violation of a Bell inequality while keeping the detection loophole closed and can be used a source private random numbers. Finally, the coherent Coulomb force-based gates are combined with the probabilistic photon-based gates in a proof of concept experiment that shows the feasibility of a distributed ion-photon network.
We propose an implementation of the Grover's search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions NNN. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with NNN ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.
Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long 1D ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. We devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor these modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits enable to perform entangling gates on these subsets in parallel.