Efficient unitary preparation of non-trivial quantum states
Wen Wei Ho, Timothy H. Hsieh · arXiv (Cornell University) · 2018
We provide a route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Specifically, we find explicit unitary circuits which exactly prepare (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical ground state, and (iii) a topologically ordered ground state, all with circuit depth $O(L)$, where $L$ is the linear dimension of the system. We obtain these circuits both numerically, using a variant of the 'Quantum Approximate Optimization Algorithm' (QAOA) [E. Farhi et al., arXiv:1411.4028], and analytically, in the case of GHZ and topological order. Our results are practically useful for achieving non-trivial states in synthetic quantum systems and illustrate the utility of QAOA-type circuits as variational wavefunctions for non-trivial phases of matter.