Quantum state preparation with optimal T-count
David Gosset, Robin Kothari, Kewen Wu · Quantum · 2026
How many T gates are needed to approximate an arbitrary n -qubit quantum state to within error ε ? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is Θ ( 2 n log ( 1 / ε ) + log ( 1 / ε ) ) 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 ε . We describe applications in which a tensor product of many single-qubit unitaries can be synthesized in parallel for the price of one.