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Alice and Bob dive into January 2026's quantum computing breakthroughs, exploring phantom codes that achieve "impossible" gates, hybrid approaches minimizing quantum resources, and realistic benchmarks showing when quantum advantage actually arrives. From error correction innovations to practical chemistry simulations, this month reveals a field maturing from theory to implementation. *Key Innovations Explored:* *Phantom Codes: Entangling Logical Qubits Without Physical Operations* Jin Ming Koh, Anqi Gong, Andrei C. Diaconu et al. Achieves perfect-fidelity entangling gates purely through qubit relabeling during compilation, reducing logical infidelity by 1-2 orders of magnitude for 2D product codes without spatial or temporal overhead. https://arxiv.org/abs/2601.20927v1 *Hierarchical Quantum Decoders* Nirupam Basak, Ankith Mohan, Andrew Tanggara et al. Uses Sum-of-Squares optimization hierarchy to bridge the gap between fast heuristic decoders and optimal-but-slow methods, with low levels performing nearly as well as exact decoding. https://arxiv.org/abs/2601.21715v1 *In-Situ Benchmarking of Fault-Tolerant Quantum Circuits* Xiao Xiao, Dominik Hangleiter, Dolev Bluvstein et al. Characterizes both physical and logical errors using only syndrome data during algorithm execution, enabling real-time calibration with exponential sample-efficiency advantages. https://arxiv.org/abs/2601.21472v1 *Learning Under Quantum Privileged Information (LUQPI)* Vasily Bokov, Lisa Kohl, Sebastian Schmitt et al. Proves quantum advantages are possible even when quantum computers only extract features from individual data points during training, minimizing quantum resource requirements. https://arxiv.org/abs/2601.22006v1 *AlphaSyndrome: Syndrome Measurement Circuit Scheduling* Yuhao Liu, Shuohao Ping, Junyu Zhou et al. Reduces logical error rates by 80.6% on average through optimized scheduling of syndrome measurements that shapes error propagation away from logical operators. https://arxiv.org/abs/2601.12509v1 *Why This Matters:* Phantom codes and hierarchical decoders advance fault tolerance with practical resource constraints. Hybrid quantum-classical frameworks and minimal-quantum-use methods show realistic paths to near-term advantage. In-situ benchmarking enables real-world deployment while chemistry applications provide concrete utility targets. *Subscribe for monthly quantum deep dives with Alice & Bob—where cutting-edge research meets accessible insights!* *** For the full research landscape → https://quantuminfo.app