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Quantum state preparation with optimal T-count
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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.
Forward citations
Cited by 6 Pith papers
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Search-based approximate diagonalization followed by analytical inversion yields high-precision multi-qubit Clifford+T circuits with 95% fewer non-Clifford gates on real-algorithm benchmarks.
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