Efficient state preparation for quantum amplitude estimation

A Carrera Vazquez, S Woerner - Physical Review Applied, 2021 - APS
Physical Review Applied, 2021APS
Quantum amplitude estimation (QAE) can achieve a quadratic speedup for applications
classically solved by Monte Carlo simulation. A key requirement to realize this advantage is
efficient state preparation. If state preparation is too expensive, it can diminish the quantum
advantage. Preparing arbitrary quantum states has exponential complexity with respect to
the number of qubits, and thus, is not applicable. Currently known efficient techniques
require problems based on log-concave probability distributions, involve learning an …
Quantum amplitude estimation (QAE) can achieve a quadratic speedup for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, and thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum arithmetic. In this paper, we introduce an approach to simplify state preparation, together with a circuit optimization technique, both of which can help reduce the circuit complexity for QAE state preparation significantly. We demonstrate the introduced techniques for a numerical integration example on real quantum hardware, as well as for option pricing under the Heston model, i.e., based on a stochastic volatility process, using simulation.
American Physical Society