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arXiv:quant-ph/0506031 · New Journal of Physics

Trapped-ion qutrit spin molecule quantum computer

D. Mc Hugh, Jason Twamley

Published Aug 18, 2005• 50 citations
arXivHTMLPDF

Abstract

We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a 'spin–spin' type coupling, similar to the J-coupling observed in molecules, between the qutrits which allows conditional quantum logic to take place. We describe in some detail how one can execute specific one and two qutrit quantum gates, required for universal qutrit quantum computing.

DOI
10.1088/1367-2630/7/1/174

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We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a 'spin–spin' type coupling, similar to the J-coupling observed in molecules, between the qutrits which allows conditional quantum logic to take place. We describe in some detail how one can execute specific one and two qutrit quantum gates, required for universal qutrit quantum computing.
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Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -- analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a NNN-qubit molecule with adjustable coupling constants.
We propose a scheme to realize quantum logic and entanglement for qutrit systems via state-dependent forces on trapped ions. By exploiting the laser-ion coupling in the presence of Coulomb interactions, the set of quantum gate operations including the conditional phase shifts on two qutrits as well as arbitrary SU(3) rotations on single qutrits are derived for universal quantum manipulation. As an illustration, we demonstrate in detail how these gate resources could be used to generate the maximally entangled state of two qutrits. Besides being insensitive to vibrational heating of the trapped ions, the present scheme is also shown to be scalable through designing appropriately the pulse configuration of the laser-ion interactions.
We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.
We propose a design for a quantum-information processor where qubits are encoded into hyperfine states of ions held in a linear array of individually tailored linear microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single- and multiqubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the microtrap configurations we can tailor, in hardware, the qubit resonance frequencies and coupling strengths. We show that the system possesses a sideband transition structure which does not scale with the size of the processor, allowing scalable frequency discrimination between qubits. By using large magnetic field gradients, one can reset individual qubits in the ion chain via frequency selective optical pulses to implement quantum-error correction, thus avoiding the need for many tightly focused laser beams.
In this paper we describe one of the most promising platforms for the construction of a universal quantum computer, which consists of a chain of NNN ions trapped in a harmonic potential, whose internal states work out as qubits, and are coupled to collective vibrational modes of the chain. From such coupling, it is possible to build interactions between different ions of the chain, that is, qubit-qubit interactions that, together with individual operations on the ions, allow building a quantum computer as first proposed by Cirac and Zoller in the 1990s [Phys. Rev. Lett. 74, 4091 (1995)]. Here we discuss from the physics involved in trapping ions in electromagnetic potentials to the Hamiltonian engineering needed to generate a universal set of logic gates, fundamental for the execution of more complex quantum algorithms. Finally, we present the current state of the art of quantum computing in trapped ion systems, highlighting recent advances made by companies and government projects that use such architecture, such as IonQ and AQTION.