Quantum state preparation with optimal T-count

Quantum 10, 2168 (2026).

https://doi.org/10.22331/q-2026-07-22-2168

How many $T$ gates are needed to approximate an arbitrary $n$-qubit quantum state to within error $varepsilon$? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is

$Thetaleft(sqrt{2^nlog(1/varepsilon)}+log(1/varepsilon)right)$

if we allow ancilla qubits. We also show that this is the optimal $T$-count for implementing an arbitrary diagonal $n$-qubit unitary to within error $varepsilon$. We describe applications in which a tensor product of many single-qubit unitaries can be synthesized in parallel for the price of one.