Quantum

Exact Unitary Synthesis: Simultaneously Optimal in Size and Depth-Ancilla Tradeoff

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 07/10/2026, 04:13:24 UTC.

Briefings

A 2026 arXiv preprint reports that any n-qubit unitary can be exactly implemented using O(4^n) CNOT and single-qubit gates in O(n + 4^n/(n+m)) layers, achieving the asymptotically optimal depth-ancilla tradeoff. This result applies to any budget m >= 0 of ancilla qubits, utilizing a Gaussian envelope encoding to convert unitary actions into shallow circuits with exact residual correction.

Key points

• Any n-qubit unitary can be exactly implemented using O(4^n) CNOT and single-qubit gates in O(n + 4^n/(n+m)) layers.
• The optimal depth-ancilla tradeoff is achieved simultaneously with optimal circuit size for any ancilla budget m >= 0.

Context and limitations

The study relies on a continuous encoding discretized with exact residual correction; the specific approximation error bounds and the exact residual correction method are not detailed in the provided evidence.

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