Circuit Optimization for Quantum State Preparation
田国敬，4 月 13 日 16:30
The Quantum State Preparation (QSP) aims to encode classical data \(v=(v_0,v_1,v_2,\ldots,v_{2^n-1})^T\in \mathbb{C}^{2^n}\) with \(\|v\|_2 = 1\) into the amplitudes of an \(n\)-qubit quantum state \(|\psi_v\rangle =\sum_{k=0}^{2^n-1}v_k|k\rangle\). QSP is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, and its circuit depth/size complexity needs to be studied. In this talk, we introduce our two recent results. The first one is the depth optimization for the most general QSP. That is, we construct, for any \(m\) ancillary qubits, circuits that can prepare \(|\psi_v\rangle\) in depth \(\tilde O\big(\frac{2^n}{m+n}+n\big)\) and size \(O(2^n)\), achieving the optimal value for both measures simultaneously. The second one is the size optimization for QSP with limited qubits connectivity architecture. We design quantum circuit for QSP and other essential circuit synthesis problems. For any architecture, the controlled NOT (CNOT) count is at most 5/3 times the state-of-the-art result on complete graph architecture, which illustrates that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era.