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arXiv · 2411.04790

Quantum state preparation with optimal T-count

David Gosset·Robin Kothari·Kewen Wu
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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.

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David Gosset, Robin Kothari, Kewen Wu. 2024-11-07. Quantum state preparation with optimal T-count. https://doi.org/10.22331/q-2026-07-22-2168

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