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QI: Fachverband Quanteninformation

QI 15: Quantum Computing Theory

QI 15.11: Vortrag

Mittwoch, 20. März 2024, 12:30–12:45, HFT-FT 101

Efficient Amplitude Encoding of Classical Data — •Vittorio Pagni — Deutsches Zentrum für Luft - und Raumfahrt (Dlr), Deutschland

Although the theoretical advantages associated to quantum computers have been proved, whenever we want to apply the most efficient quantum algorithms to classical data or initialize our quantum circuit in a specific state, an efficient state preparation algorithm can prevent us from wasting the quantum speed up because of a computational bottleneck effect, especially for large classical vectors.
We present an improved version of a pre-existing (PhysRevResearch.4.013091) quantum amplitude encoding procedure that encodes the real or complex entries of a properly normalized classical vector v^→=(v₁,..,v_N) of length N into the amplitudes of a quantum state. Our approach generalizes the protocol to complex entries and it shows a quadratic time speed up with respect to the original. Furthermore, the procedure also allows for some flexibility in the way the intermediate operations are performed, so that it is possible to customize the balance between memory and time cost for the specific application. Depending on the data density ρ(v^→)=∑_i=0^N−1||v_i/v_max||², 1/N≤ρ≤ 1 of the classical input vector of length N and on the parallelization parameter M, 1 ≤ M ≤ N, the number of qubits scales as O(Mlog₂N) while the time cost increases as O(1/√ρN/Mlog₂log₂N), which has an upper bound of O(√Nlog₂log₂N) in the worst case scenario.

Keywords: quantum amplitude encoding; state preparation; quantum machine learning