- Open Access
Unitary Synthesis with Fewer T Gates
PRX Quantum 7, 033058 – Published 16 September, 2026
DOI: https://doi.org/10.1103/pxhd-9s9q
Abstract
We present a simple algorithm that implements an arbitrary -qubit unitary operator using a Clifford + T circuit with T-count and ancilla-count . The previous best T-count for unitary synthesis was with ancillae by [Low et al., Quantum 8, 1375 (2024)]. There is a fundamental tradeoff between T gates and ancillae, and our algorithm extends the achievable regime of this tradeoff, reducing the exponent in T-count from to . The best known lower bound remains , so the optimal T-count for general unitary synthesis is still open. Our construction is based on a recursive application of the cosine-sine decomposition, together with a generalization of the optimal diagonal unitary synthesis method by [D. Gosset et al., Quantum 10, 2168 (2026)] to multi-controlled -qubit unitaries.
Physics Subject Headings (PhySH)
Popular Summary
Fault-tolerant quantum computers will rely on a small set of elementary gates to carry out computations, and among these, the so-called T gate is by far the most expensive to execute. A natural question is then: how many T gates does it take to compile an arbitrary quantum operation? For nearly a decade, the best known answer scaled as for an -qubit operation, and two independent methods hit the same wall. We break past this barrier by introducing a compilation strategy that groups operations into blocks sharing the same workspace, reducing the T-gate count to . The savings come from using additional ancillary qubits—exploiting a fundamental tradeoff between workspace and T-gate cost that prior methods could not access at this scale. Since the best known lower bound is , a significant gap remains open. Our result shows that the previous barrier was not fundamental and points toward what it would take to close the gap entirely.
Article Text
References (20)
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