Optimization and Decoding QEC

Qudits are d-level quantum mechanical systems, capable of storing and processing the same amount of information as log2(d) qubits. This implies that conducting fault-tolerant quantum computations using qudits rather than qubits might entail less overhead. We test this hypothesis by creating and simulating the quantum circuitry for small qudit error correction codes. More specifically, we add general higher-dimensional quantum gates to the Cirq simulation framework, create general encoding circuits for arbitrary prime dimensions, and extract realistic syndrome measurements using a circuit-level noise model. We then feed these syndromes to adapted versions of well-known qubit decoders, of which one is the minimum-weight-perfect-matching decoder, and perform an in-depth analysis of their error correction performance with respect to their qubit counterparts. After appropriate rescaling, we find that the fidelities of executing quantum algorithms with higher-dimensional qudits are generally higher than those with qubits.