Marie Skłodowska-Curie Individual Fellowship

**TR**apped **I**on **C**oherent **E**xecution of **Q**uantum **F**ourier **T**ransform (TRICE QFT)

*Grant Agreement Number 657261*

## Summary

Quantum computers hold the promise to efficiently solve certain computational problems that would be, for all practical purposes, intractable using conventional computers. The latter are not able to efficiently incorporate quantum phenomena arising with superposition of states or entanglement. In order to realize a large-scale quantum computer, it is imperative to have superior control over the efficiency and reliability of already available quantum operations. Trapped ions, being a scalable quantum system, envisage the experimental realization of a large-scale universal quantum computer. The proposed project will demonstrate a novel route to implement a Quantum Fourier Transform (QFT), a crucial component of many quantum algorithms, in a small-scale quantum information processor based on a string of singly charged ytterbium ions confined in a linear Paul trap. In presence of a magnetic field gradient-induced coupling, simultaneous interaction between all pairs of qubits will be exploited for efficient execution of quantum algorithms. Thus, instead of decomposing a given quantum algorithm into its smallest possible elementary constituents (1- and 2-qubit gates), multi-qubit conditional quantum dynamics will be used to implement a QFT. Experiment and theory will collaborate at all stages to streamline the project. New collaborations will be established allowing to combine the tremendous knowledge and expertise already existing in the field.

The breakthroughs envisioned in the project are, to

The breakthroughs envisioned in the project are, to

- explore and implement simultaneous couplings between N ≥ 4 qubits allowing for efficient execution of quantum algorithms, and
- implement a Quantum Fourier Transform with N ≥ 4 qubits pointing into the future capability of realizing a large number factorization using a quantum factoring algorithm.

## Objective and OverviewThe overall objective of the proposed work focuses on the development of elements necessary for an ion trap based large-scale QC. The project will approach the question of implementing coherent QFT in a scalable system, and will give first and important insight into the development of a new experimental framework where simultaneous interaction between all pairs of qubits will be exploited to improve the performance of QFT. The specific scientific objectives to be pursed are:
Objective 1: To implement QFT with four or more qubits formed of ions in a linear chain. First, a QFT with three qubits will be realised and then will be extended to more qubits. QFT will be implemented with a sequence of precisely timed MW carrier π-pulses interspersed with free conditional evolution under long-range qubit coupling. Objective 2: To determine and analyse experimental fidelity of QFT and compare with theoretically estimated fidelity. Noise sources that contribute towards systematic errors are mainly associated with the preparation and detection of states, conditional qubit rotation and dephasing owing to magnetic field fluctuation. Such sources will be identified and eliminated to optimize experimental fidelity. Objective 3: To extend coherence time. This is critical for a large number of qubits. In particular, magnetic-field stabilization and shielding and/or sympathetic cooling may be necessary. Continuous17 and pulsed18 dynamical decoupling will be developed further and exploited during the conditional evolution times to combat decoherence effects. |
## PublicationsDistinguishing between statistical and systematic errors in quantum process tomography
New Journal of Physics 21, 013015 (2019) | arXiv:1808.10336 Speeding-up the decision making of a learning agent using an ion trap quantum processor Quantum Science and Technology 4, 015014 (2019) | arXiv:1709.01366 Radio frequency sideband cooling and sympathetic cooling of trapped ions in a static magnetic field gradient Journal of Modern Optics 65, 560 (2018) | arXiv:1710.09241Analog quantum simulation of (1 + 1) -dimensional lattice QED with trapped ions Physical Review A 94 052321 (2016) | arXiv:1604.03124 |