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arXiv:quant-ph/0508123 · Physical Review A

Entanglement of trapped-ion clock states

P. C. Haljan, P. J. Lee, Kathy-Anne Brickman, M. Acton, Louis Deslauriers, Christopher R. Monroe

Published Dec 9, 2005• 124 citations
arXivHTMLPDF

Abstract

A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped $^{111}\mathrm{Cd}^{+}$ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.

DOI
10.1103/physreva.72.062316

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A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped 111Cd+^{111}\mathrm{Cd}^{+}111Cd+ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.
High-fidelity two-qubit entangling gates play an important role in many quantum information processing tasks and are a necessary building block for constructing a universal quantum computer. Such high-fidelity gates have been demonstrated on trapped-ion qubits; however, control errors and noise in gate parameters may still lead to reduced fidelity. Here we propose and demonstrate a general family of two-qubit entangling gates which are robust to different sources of noise and control errors. These gates generalize the renowned Mølmer-Sørensen gate by using multitone drives. We experimentally implemented several of the proposed gates on ^{88}Sr^{+} ions trapped in a linear Paul trap and verified their resilience.
Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.
To date, the highest-fidelity quantum logic gates between two qubits have been achieved using the geometric-phase gate in trapped ions, with the two leading variants being the M\o{}lmer-S\o{}rensen gate and the light-shift (LS) gate. Both of these approaches have their respective advantages and challenges. For example, the latter is technically simpler and is natively insensitive to optical phases, but it has not been made to work directly on a clock-state qubit. We present a technique for implementing the LS gate that combines the best features of these two approaches: By using a small ($\ensuremath{\sim}\mathrm{MHz}$) detuning from a narrow (dipole-forbidden) optical transition, we are able to operate an LS gate directly on hyperfine clock states, achieving gate fidelities of 99.74(4)99.74(4)%99.74(4) using modest laser power at visible wavelengths. Current gate infidelities appear to be dominated by technical noise, and theoretical modeling suggests a path toward gate fidelity above 99.9999.99%99.99.
Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.
We demonstrate universal quantum control over chains of ions in a surface-electrode ion trap, including all the fundamental operations necessary to perform algorithms in a one-dimensional, nearest-neighbor quantum computing architecture. We realize both single-qubit operations and nearest-neighbor entangling gates with Raman laser beams, and we interleave the two gate types. We report average single-qubit gate fidelities as high as 0.970(1) for two-, three-, and four-ion chains, characterized with randomized benchmarking. We generate Bell states between the nearest-neighbor pairs of a three-ion chain, with fidelity up to 0.84(2). We combine one- and two-qubit gates to perform quantum process tomography of a cnot gate in a two-ion chain, and we report an overall fidelity of 0.76(3).