Reducing the Overhead of Quantum Error Correction
Quantum error correction is essential for large-scale quantum computing, but current methods introduce substantial overhead. A recent focus of ours has been developing strategies to reduce this overhead, with particular emphasis on fault-tolerant logical gate implementation. In one line of work, we introduced phantom codes: a class of codes in which logical entangling gates between all pairs of logical qubits in a code block are realized purely via qubit relabelling during compilation, incurring zero space-time overhead and perfect fidelity — and demonstrated one-to-two orders of magnitude improvements in logical fidelity over surface-code baselines for entanglement-dense tasks such as GHZ state preparation and Trotterized many-body simulation. In a complementary line of work, we introduced tricycle codes — a class of quantum LDPC codes supporting constant-depth physical circuits implementing logical CCZ gates — enabling single-shot fault-tolerant magic state generation without multiple rounds of distillation, with a circuit-noise threshold exceeding 0.5% and logical error rates below 6×10⁻¹⁰ with modest post-selection.