Implementing a Ternary Decomposition of the Toffoli Gate on Fixed-FrequencyTransmon Qutrits

TL;DR

This paper demonstrates a novel ternary decomposition of a Toffoli gate on fixed-frequency transmon qutrits, reducing the number of operations and improving fidelity compared to binary methods.

Contribution

It introduces an experimental implementation of a ternary decomposition of a multi-qubit gate on superconducting transmons, leveraging qutrit states for efficiency.

Findings

Ternary decomposition outperforms binary in truth table fidelity on most transmons.

Achieved an average gate fidelity of 78.00% ± 1.93% with quantum process tomography.

Reduced the number of two-transmon operations from eight to four for the Toffoli gate.

Abstract

Quantum computation is conventionally performed using quantum operations acting on two-level quantum bits, or qubits. Qubits in modern quantum computers suffer from inevitable detrimental interactions with the environment that cause errors during computation, with multi-qubit operations often being a primary limitation. Most quantum devices naturally have multiple accessible energy levels beyond the lowest two traditionally used to define a qubit. Qudits offer a larger state space to store and process quantum information, reducing complexity of quantum circuits and improving efficiency of quantum algorithms. Here, we experimentally demonstrate a ternary decomposition of a multi-qubit operation on cloud-enabled fixed-frequency superconducting transmons. Specifically, we realize an order-preserving Toffoli gate consisting of four two-transmon operations, whereas the optimal order-preserving binary decomposition uses eight \texttt{CNOT}s on a linear transmon topology. Both decompositions are benchmarked via truth table fidelity where the ternary approach outperforms on most sets of transmons on \texttt{ibmq\_jakarta}, and is further benchmarked via quantum process tomography on one set of transmons to achieve an average gate fidelity of 78.00\% $\pm$ 1.93\%.