Curator's Take
AI Commentary
This article shows that on today’s noisy superconducting chips a six‑CX Toffoli decomposition, which is optimal in abstract circuit depth, can be outperformed by an eight‑CX version that respects the device’s linear nearest‑neighbor connectivity. By experimentally comparing both decompositions across many three‑qubit triples on IBM’s 156‑qubit processors, the authors demonstrate lower error rates and higher fidelity for the locality‑friendly circuit, highlighting how hardware topology can flip the usual “fewer gates = better” rule of thumb. The result underscores the need for compilers and algorithm designers to prioritize connectivity‑aware gate scheduling, a lesson that will become increasingly critical as quantum processors scale up.
— Mark Eatherly
Summary
The exact Toffoli gate admits a six-CX decomposition, denoted by $CCX_6$, that is optimal under unrestricted two-qubit connectivity. On a linear three-qubit topology, however, $CCX_6$ contains 4 nearest-neighbor CX gates and 2 non-nearest-neighbor CX gates. By contrast, an alternative exact decomposition, denoted by $CCX_8$, uses only 8 nearest-neighbor CX gates. Because CCX is locally equivalent to CCZ, we perform the experiments using the corresponding $\cczs$ and $\cczl$ circuits. We compare these circuits on sampled linear triples of the 156-qubit IBM Quantum Heron processors \texttt{ibm\_fez} and \texttt{ibm\_kingston}. Under the compilation protocol, the nominal $\cczs$ circuit becomes a twelve-CZ implementation, whereas the linear-nearest-neighbor circuit retains eight native CZ gates. Experimentally measured ensemble-feature-selection estimates favor the eight-CZ realization on nearly all retained triples. We test the same ordering by preparing a three-qubit hypergraph state, which probes the coherent conditional phase rather than only computational-basis populations. The measured hypergraph-state infidelity is lower for the $\cczl$ circuit for most triples on both processors. Phase-altered interleaved randomized benchmarking provides a complementary comparison of Clifford surrogates preserving the two compiled entangling structures. Within the scope of the tested circuits and phase-sensitive input state, the results demonstrate that hardware connectivity can reverse the operational ranking of exact decompositions: a circuit with more abstract two-qubit gates can yield the better physical implementation.