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Physical Review Letters

Quantum Logic Gates for Hot Ions without a Speed Limitation

Shi-Biao Zheng

Published May 28, 2003• 38 citations
Publisher

Abstract

We propose a scheme for realizing two-qubit quantum phase gates with trapped ions in thermal motion. In the scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier, which virtually excites several vibrational modes. The scheme puts no limitations on the intensity of the laser field, allowing the production of a quantum logic gate for hot ions with an arbitrarily high speed as long as a laser field of sufficiently high intensity is available.

DOI
10.1103/physrevlett.90.217901

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We propose a scheme for realizing two-qubit quantum phase gates with trapped ions in thermal motion. In the scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier, which virtually excites several vibrational modes. The scheme puts no limitations on the intensity of the laser field, allowing the production of a quantum logic gate for hot ions with an arbitrarily high speed as long as a laser field of sufficiently high intensity is available.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.
We propose a scheme to generate a superposition of motional coherent states with arbitrary coefficients on a line in phase space and implement a quantum controlled phase-gate for multiple trapped ions with a single standing-wave laser pulse whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave, which is very important from viewpoint of experiment. Furthermore, our scheme may allow the generation of a superposition of coherent states with large mean phonon number for a large number of trapped ions in a fast way by choosing suitable laser intensity. We show that it can also be used to generate maximally entangled states of multiple trapped ions.
Based on the scheme of ``hot'' trapped-ion quantum computation proposed by Sϕrensen and Mϕlmer, we construct a set of multi-mode excited logic gates on trapped ions, which may be operated on arbitrary even number of ions selected randomly from a string of ions trapped in a linear trap. The gate speed may be made faster than that of the corresponding one-mode excited logic gate by adjusting appropriately the detunings of driving lasers with respect to the sidebands of vibrational modes and can be demonstrated in current experimental techniques.
Based on the scheme of hot trapped-ion quantum computation proposed by Sφrensen and Mφlmer, we construct a set of multi-mode excited logic gates on trapped ions, which may be operated on arbitrary even number of ions selected randomly from a string of ions trapped in a linear trap. The gate speed may be made faster than that of the corresponding one-mode excited logic gate by adjusting appropriately the detunings of driving lasers with respect to the sidebands of vibrational modes and can be demonstrated in current experimental techniques.