2.11 - High-Level Circuit, Precision & Complexity

The lecture slides are available here Download here.

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This lecture focuses on practical aspects of phase estimation in quantum computing. We begin by emphasizing the use of phase estimation to determine eigenphases associated with a QPU operation's eigenstates.

The high-level circuit of phase estimation is introduced, explaining key components such as the input register (qin), the output register (qout), and the controlled version of the QPU operation (cont_u).

An example is presented, demonstrating how phase estimation works by applying it to find the eigenphase of the Hadamard gate. The importance of choosing the right size for the output register to ensure precision is highlighted, with insufficient resolution leading to probabilistic estimates. The lecture concludes by discussing the complexity of phase estimation, indicating that it depends on the output register size (m) and emphasizing the inverse Quantum Fourier Transform (invQFT) role.