Spacetime-Efficient Low-Depth Quantum State Preparation with Applications

Understand

We propose a novel deterministic method for preparing arbitrary quantum states.

• When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $O(N)$, which are both optimal.
• When compiled into the $\{\mathrm{H,S,T,CNOT}\}$ gate set, we show that it requires asymptotically fewer quantum resources than previous methods.
• Specifically, it prepares an arbitrary state up to error $\epsilon$ with optimal depth of $O(\log(N) + \log (1/\epsilon))$ and spacetime allocation $O(N\log(\log(N)/\epsilon))$, improving over $O(\log(N)\log(\log (N)/\epsilon))$ and $O(N\log(N/\epsilon))$, respectively.