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

Abstract

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