Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Understand

Quantum state preparation is an important subroutine for quantum computing.

• We show that any $n$-qubit quantum state can be prepared with a $\Theta(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits.
• On the other hand, for sparse quantum states with $d\geqslant2$ non-zero entries, we can reduce the circuit depth to $\Theta(\log(nd))$ with $O(nd\log d)$ ancillary qubits.
• The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size.