Efficient phase-factor evaluation in quantum signal processing

Understand

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers.

• Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem.
• A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures.
• However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits.