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TRapped Ion Coherent Execution of Quantum Fourier Transform

Periodic Reporting for period 1 - TRICE QFT (TRapped Ion Coherent Execution of Quantum Fourier Transform)

Reporting period: 2015-04-01 to 2017-03-31

The overall scientific objective of the TRICE QFT project is to develop key ingredients necessary to realize an ion trap based large-scale quantum computer, for which it is imperative to have superior control over the efficiency and reliability of already available quantum operations. Despite certain advantages over other physical systems, qubits based on trapped atomic ion systems are susceptible to decoherence, which describes the phase randomization of a quantum superposition state. This unwanted and uncontrolled mechanism poses a serious obstacle in the realization of conditional quantum logic gates (e.g. CNOT), which are essential constituents of arbitrary quantum algorithms. The fidelity of such gates are reduced dramatically if the time required for the gate operation is significantly longer compared to the coherence time of the physical system that is capable of realizing such gates. While current experiments in the project are performed using a small quantum processor based on a linear string of up to three trapped ions, a longer string with a larger number of ions will be explored towards realization of a large-scale quantum computer. Therefore, as a key prerequisite for the technically challenging future experiments, the basic stability and reliability of the current experiments is required to be enhanced by a careful investigation of the systematic error sources. Noise sources that contribute towards systematic errors are mainly associated with the preparation and detection of states, conditional qubit rotation and decoherence owing to magnetic field fluctuation. The project aims at identification and elimination of these noise sources in order to enhance the fidelity of realizable quantum algorithms, such as a quantum Fourier transform, in the existing experimental setup. A critical aspect of the project, especially for experiments with large number of qubits, is to explore all possible ways to combat decoherence effects, thereby increasing the coherence time available for conditional quantum dynamics, and thus, leading to an improvement in the fidelity of conditional quantum logic operations.
The project began with a detailed investigation of decoherence in which potential noise sources were individually identified and characterized. As part of this investigation several components of the experimental setup were modified for better stability and reliability in their performance. Such technical modifications are concerned with frequency stabilization of optical cavities, minimization of stray laser light-induced decoherence of qubits, improvement in pointing stability of laser beams and improvement in detection fidelities. In addition, the microwave system was upgraded to generate more microwave power and multiple microwave fields, enabling to protect multiple qubits from decoherence effects using continuous dynamical decoupling. In order to increase the coherence time available for conditional dynamics using multiple qubits, the fluctuations in ambient magnetic field were actively compensated and robust dynamical decoupling pulses were implemented in various experimental sequences.

An adaptive correction of qubit resonance frequency was implemented in all experimental sequences. It enables to intermittently secure a precise knowledge of qubit addressing frequency while a long experimental sequence is in progress, which allows to minimize detuning of addressing frequency resulting from charging of trap electrodes and fluctuations in ambient magnetic field. This adaptive correction together with all other improvements resulting from various modifications in the experimental setup yields a significant improvement in the fidelities of quantum logic operation, such as fidelity of realizing entanglement between two ions.

Cooling of trapped ions, close to their motional ground state, was investigated for one and two ion systems using a static magnetic field gradient and a long-wavelength radiation in the microwave regime. This method features sideband cooling at a low secular frequency that is practical for trapping both ions and atoms. Both the axial modes of vibration are independently cooled and the thermal excitations of each mode are independently measured by observing one of the ions. Sympathetic cooling of a two ion crystal using microwave radiation was demonstrated for the first time.

The first proof-of-principle experiment showcasing the potential of a large-scale quantum computer in the field of quantum enhanced learning and artificial intelligence was performed. A learning agent can receive perceptual input from and react to the environment (Fig. 1). The learning aspect is facilitated by a reward system that prompts the agent to reinforce connections between the inputs and corresponding actions in its decision making process. The decision-making process of a quantum learning agent, modeled in a system of two ion qubits, was investigated following a novel approach based on projective simulation model for reinforcement learning. Here the agent’s reactions to the perceptual input were investigated by way of a quantum algorithm. The agent’s learning speed was quantified in terms of the average number of interactions with the environment until certain behavior (reactions triggering a reward) can be considered to have been learned. The result demonstrates that the decision-making process of quantum learning agent is quadratically faster compared to that of a classical learning agent. The experimental results are in excellent agreement with theoretically calculated and simulated predictions.

Apart from certain deviations from the originally proposed actions, the main objectives of the project were achieved. Major research results were acquired in the last quarter of the project. They are in the process of being written up, and will be appropriately disseminated within a few months after the project has ended. The project allowed the fellow to acquire various transferable skills in the context of career development. The project also allowed initiating and developing lasting collaborations with researchers
Final results of the project are expected to be beneficial for neighbouring research fields and will find applications in other communities and disciplines. The adaptive correction of qubit resonance frequency is certainly relevant for research in quantum computing. The sideband cooling method can be adapted to other physical systems, such as neutral atoms. The investigation of quantum artificial intelligence triggers further research on the integration of quantum computing and artificial intelligence platforms. The result of this investigation will undoubtedly receive a lot of attention and will be widely cited by both quantum computing and artificial intelligence communities. In general, the relevance of project results fits well within the development of essential ingredients for a large-scale quantum computer and therefore, the discoveries made in the project will likely inspire future studies in the emerging field of quantum information science. In addition, the novel experimental route for the demonstrated methods and results, employing the readily available low-cost and easy-to-use microwave technology, will complement the conventional approach of exclusively using laser radiation.
Figure 1