Regressions on quantum neural networks at maximal expressivity.

Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decomposition of the generated output and systematically benchmarked with the aid of a teacher-student scheme. While the maximal expressive power increases with the depth of the network and the number of qubits, it is fundamentally bounded by the data encoding mechanism.

Quantum neural networks with multi-qubit potentials.

We propose quantum neural networks that include multi-qubit interactions in the neural potential leading to a reduction of the network depth without losing approximative power. We show that the presence of multi-qubit potentials in the quantum perceptrons enables more efficient information processing tasks such as XOR gate implementation and prime numbers search, while it also provides a depth reduction to construct distinct entangling quantum gates like CNOT, Toffoli, and Fredkin. This simplification in the network architecture paves the way to address the connectivity challenge to scale up a quantum neural network while facilitating its training.

Tailored ion beam for precise colour centre creation.

We present an invariant-based quantum control scheme leading to a highly monochromatic ion beam from a Paul trap. Our protocol is implementable by supplying the segmented electrodes in the trap with voltages of the order of volts. This mitigates the impact of fluctuations in previous designs and leads to a low-dispersion beam of ions.

Large Quantum Delocalization of a Levitated Nanoparticle Using Optimal Control: Applications for Force Sensing and Entangling via Weak Forces.

We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles.

Speeding up quantum perceptron via shortcuts to adiabaticity.

The quantum perceptron is a fundamental building block for quantum machine learning. This is a multidisciplinary field that incorporates abilities of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where a control field on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function.

Modulated Continuous Wave Control for Energy-Efficient Electron-Nuclear Spin Coupling.

We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts.

Vibrational mode multiplexing of ultracold atoms.

Sending multiple messages on qubits encoded in different vibrational modes of cold atoms or ions along a transmission waveguide requires us to merge first and then separate the modes at input and output ends. Similarly, different qubits can be stored in the modes of a trap and be separated later. We design the fast splitting of a harmonic trap into an asymmetric double well so that the initial ground vibrational state becomes the ground state of one of two final wells, and the initial first excited state becomes the ground state of the other well.

Quest for absolute zero in the presence of external noise.

A reciprocating quantum refrigerator is analyzed with the intention to study the limitations imposed by external noise. In particular we focus on the behavior of the refrigerator when it approaches the absolute zero. The cooling cycle is based on the Otto cycle with a working medium constituted by an ensemble of noninteracting harmonic oscillators.

Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity.

A Schrödinger equation may be unitarily transformed into dynamical equations in different interaction pictures which describe a common physical process, i.e., the same underlying interactions and dynamics.