Quantum State Preparation with Optimal T-Count
Abstract
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 \(\Theta\left(\sqrt{2^n \log(1/\varepsilon)} + \log(1/\varepsilon)\right)\) 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.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Quantum Information and Cryptography
Quantum many-body systems
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Publisher
- Society for Industrial and Applied Mathematics
- Pages
- 3378–3406
- Publication date
- 1 January 2026
- Language
- EN