Polylogarithmic-depth controlled-NOT gates without ancilla qubits.

Controlled operations are fundamental building blocks of quantum algorithms. Decomposing n-control-NOT gates (C(X)) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces C(X) circuits outperforming previous methods in the asymptotic and non-asymptotic regimes.

Sparse Quantum State Preparation for Strongly Correlated Systems.

Quantum computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialization of the qubits to a high-quality approximation of the sought-after ground state. Quantum state preparation enables the generation of approximate eigenstates derived from classical computations but is frequently treated as an oracle in quantum information.

Quantum Spatial Search with Electric Potential: Long-Time Dynamics and Robustness to Noise.

We present various results on the scheme introduced in a previous work, which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field centered on the the node to be found. In such a walk, the electric term acts as the oracle of the algorithm, and the free walk (i.e.

Dirac Spatial Search with Electric Fields.

Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time.