Yasser Omar

The question of the energetic efficiency of quantum computers has gained increasing attention recently. A precise understanding of the resources required to operate a quantum computer with a targeted computational performance and how the energy requirements can impact the scalability is still missing. In this work, one implementation of the quantum Fourier transform algorithm in a trapped-ion setup was studied. The main focus was to obtain a theoretical characterization of the energetic costs of quantum computation, based on actual experimental measurements performed on a similar trapped-ion setup.The energetic cost of the computation was estimated by analyzing the components of the setup and all the steps involved, from the cooling and preparation of the ions to the execution of the algorithm and readout of the result. In the Noisy Intermediate-Scale Quantum regime, a potential scaling of the energetic costs was argued and used to find a possible threshold for an energetic quantum advantage against state-of-the-art classical supercomputers. Remarkably, this threshold appears to be lower than the one for which computational time advantage is expected.

Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be reversible. In this work, we provide a proof-of-principle of classical logical gates running on quantum technologies. In particular, we propose, and realise experimentally, Toffoli and Half-Adder circuits suitable for classical computation, using radiofrequency-controlled $^{171}$Yb$^+$ ions in a macroscopic linear Paul-trap as qubits. We analyse the energy required to operate the logic gates, both theoretically and experimentally, with a focus on the control energy. We identify bottlenecks and possible improvements in future platforms for energetically-efficient computation, e.g., trap chips with integrated antennas and cavity QED. Our experimentally verified energetic model also fills a gap in the literature of the energetics of quantum information, and outlines the path for its detailed study, as well as its potential applications to classical computing.

Quantum phase estimation is a paradigmatic problem in quantum sensing andmetrology. Here we show that adaptive methods based on classical machinelearning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ramsey-fringe visibility due to decoherence. We discuss their robustness against noise in connection with real experimental setups such as Mach-Zehnder interferometry with optical photons and Ramsey interferometry in trapped ions,superconducting qubits and nitrogen-vacancy (NV) centers in diamond.