# Asymptotic Improvements to Quantum Circuits via Qutrits

**Best Poster Award at QIP 2019. ****Poster Link****.**

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu*trits*. Past work with qutrits has demonstrated only constant factor improvements, owing to the lg(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla–a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.

*Gokhale, Pranav; Baker, Jonathan; Duckering, Casey; Brown, Natalie; Brown, Kenneth R., Chong, Frederic*