Alfréd Rényi Institute of Mathematics
An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2^n-dimensional, Hilbert space, which is a major source of quantum speed-ups. We show how Quantum Singular Value Transformation can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. The transformations are realized by quantum circuits with a very simple structure – typically using only a constant number of ancilla qubits – leading to optimal algorithms with appealing constant factors. We show that this framework allows describing and unifying many quantum algorithms on a high level, and enables remarkably concise proofs for many prominent quantum algorithms, ranging from optimal Hamiltonian simulation to quantum linear equation solving (i.e., the HHL algorithm) and advanced amplitude amplification techniques. Finally, we also prove a quantum lower bound on spectral transformations.
The purpose of the Team-Net Quantum Computing Colloquium series is to expose Polish and international researchers, as well as interested peers, to the most important recent achievements and trends in the field of quantum computing. Seminars will be taking place on a monthly basis, on Wednesdays at 16:00 CET. Topics of the colloquium include, but are not limited to:
Webpage of the project: nisq.pl