Deterministic, scalable, and entanglement efficient initialization of arbitrary quantum states
Prithvi Gundlapalli, Junyi Lee · arXiv (Cornell University) · 2021
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such quantum algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $| b\rangle$. However, efficient amplitude encoding of an arbitrary vector $\mathbf{b}$ in $| b \rangle$ is known to be a difficult problem that can reverse the gains of such algorithms. More importantly, an arbitrary quantum state of $Q$ qubits generally requires $\sim 2^Q$ number of entangling gates, which is problematic for today's Noisy-Intermediate Scale Quantum (NISQ) computers where large numbers of such error-prone gates will result in significant decoherence before initialization is completed. In this work, we demonstrate a deterministic and scalable initialization algorithm that allows for states with low entanglement to be initialized on actual quantum computers with more than an order of magnitude less entangling gates and significantly shallower circuits as compared to isometric decomposition. For states with higher entanglement, optimally approximate states with lower entanglement may be found and initialized with similar performance. We show this to be true for various cases of interest such as the normal and log-normal distributions. Unlike variational approaches, our method requires no classical optimizations in high dimensional spaces and is not plagued with exponentially vanishing gradients or a multitude of local minimas.