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arXiv:1410.6720 · New Journal of Physics

Universal set of gates for microwave dressed-state quantum computing

Gatis Mikelsons, Itsik Cohen, Alex Retzker, Martin Bodo Plenio

Published May 22, 2015• 21 citations
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Abstract

We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.

DOI
10.1088/1367-2630/17/5/053032

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•Apr 8, 2015•14 citations
We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.
Abstract We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.
The key research aim of the present thesis is the building of a universal set of quantum gates for a long wavelength trapped-ion quantum information processor. It is desired to realise quantum computation using microwave and radio wave sources in a linear ion trap, where a static magnetic field gradient has been added to enhance motional and atomic state coupling. Furthermore, the qubit is constructed with the intrinsic use of superposition states generated with the help of constant microwave fields in the background: dressed states. This technique is essential for the shielding of the quantum operations against the unavoidable effects of magnetic noise. After reviewing the preliminary results and discussing briefly an auxiliary experimental technique intrinsic to the set-up, we introduce the magnetic gradient coupling and the dressed state scheme. We then proceed to illustrate how single and multi-qubit gates can be realised within such a system. Theoretical arguments are supplemented by numerical simulation and sources of experimental noise are taken into account.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.
A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.
A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.