Error semitransparent universal control of a bosonic logical qubit

Bosonic codes offer hardware-efficient quantum error correction, recently achieving beyond-breakeven quantum memory. However, fault-tolerant logical operations remain a critical bottleneck. While error transparent (ET) gates offer a pathway to resolve this, experimental demonstrations remain limited to phase gates. Here, we introduce a dynamic encoding subspaces framework that enables simple linear drives to accomplish universal logical gates that are error semi-transparent (EsT) to oscillator photon loss. Our EsT logical gate set of {X, H, T} exhibited a five-fold reduction in infidelity conditioned on photon loss, extended active-manipulation lifetimes with quantum error correction, and enabled a composite EsT non-Clifford operation using an eight-gate sequence. Our approach is compatible with methods for detectable ancilla errors and is readily extensible to other rotation-symmetric codes, offering an approach to error-mitigated universal control of bosonic logical qubits with the standard quantum control toolkit and a coherent framework for incorporating more sophisticated quantum control methods. Error transparency is an alternative approach to quantum fault-tolerance relying on multi-body Hamiltonians whose evolution is unaffected - to first order - by noise. Here, the authors show a dynamic encoding subspace framework achieving universal control of Bosonic logical qubits with error semitransparent gates, correcting most single-photon loss errors in the Bosonic mode during logical gate operations.

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