Quantum Phase Processing and its Applications in Estimating Phase and Entropies

Understand

Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space.

• Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts.
• Based on this unique principle of quantum computing, we develop a new algorithmic toolbox "quantum phase processing" that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator.
• The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled-unitaries, typically using only one ancilla qubit.