Phantom Codes: Entangling Logical Qubits without Physical Operations by Koh Jin Ming

Abstract
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes—quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all 27 billion inequivalent CSS codes up to n = 14 and identify additional instances up to n = 21 via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed-Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.

About the Speaker
Jin Ming received his BS in physics and computer science from Caltech in 2023, and is in his second year pursuing a PhD in physics at Harvard University, advised by Prof. Norman Yao. He received numerous institutional awards at Caltech, including the Richard Feynman and George W. Housner prizes for his academic achievements and research. At the national level, he received the prestigious APS LeRoy Apker award, an accolade given to two students in the United States annually, in 2024 for his work on measurement-induced entanglement phase transitions. His research has spanned quantum simulation and condensed-matter physics, and he is currently most interested in quantum error correction and fault-tolerant quantum computation.