# Asymptotic Improvements to Quantum Circuits via Qutrits

## TL;DR

This paper introduces a novel qutrit-based quantum circuit design that achieves logarithmic depth for the Generalized Toffoli gate, significantly reducing circuit complexity and improving reliability over qubit-only approaches.

## Contribution

It presents a new qutrit circuit construction for the Generalized Toffoli gate with no ancilla and logarithmic depth, outperforming qubit-only methods in depth and gate count.

## Key findings

- Logarithmic depth decomposition of the Generalized Toffoli gate using qutrits.
- 70x reduction in two-qudit gate count compared to qubit-only circuits.
- Over 90% fidelity in noisy simulations, surpassing qubit-only baselines.

## Abstract

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 $\log_2(3)$ 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.

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Source: https://tomesphere.com/paper/1905.10481