Early Fault-Tolerant Magic State Synthesis and Spacetime Efficient Analog Rotations with Color Code on a Superconducting Quantum Processor

Abstract

With recent improvements to syndrome extraction scheduling and decoding, and the availability of complete transversal Clifford operations and lattice surgery, color code is an especially promising platform for quantum processors with local connectivity. The key ingredient for universal computation is thus generating useful magic states with limited resources. Space-Time Efficient Analog Rotations (STAR) and Fault-tolerant magic state synthesis (MSS) are two such methods for magic state generation, targeted for near-term and long-term quantum computing, respectively. In this work, we perform the first implementations of both magic state paradigms on a superconducting quantum processor. We present a STAR-type injection protocol on the color code, with favorable error rate and spacetime costs versus prior protocols on both the color and surface codes. We then implement a MSS factory by performing multi-patch magic state cultivations, interleaved with transversal Clifford operations, and lattice-surgery magic state teleportation. Under post-selection, we achieve a kickback tomography correct sign probability of $99.9859\%$ on cultivated $T_L$ states, $96\%$ tomographic fidelity on logical analog rotation states, and $91\%$ fidelity on synthesized logical magic states consuming 3 cultivated $T_L$ states, 3 transversal Hadamard operations, and real-time feed-forward $S_L$ corrections during magic state teleportation. We compare the efficacy of post-selection, Most-Likely-Error (MLE) decoding, and concatenated-matching decoding throughout, highlighting the potential of end-to-end color code computation.