Generalized Quantum Singular Value Transformation

Understand

The quantum singular value transformation has revolutionised quantum algorithms.

• By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms.
• However, polynomials are restricted to definite parity and real coefficients, and finding the circuit (the phase factors) has proven difficult in practice.
• Recent work has removed these restrictions and enabled faster computation of phase factors, yet only for unitary matrices.