Remote CZ meets modular fault tolerance (10/06/26)

TL;DR Across two dilution cryostats linked by a 30-m cryogenic microwave line, a microwave photon emitted from node A acquires a state-dependent phase upon reflection from node B, realizing a tunable-phase controlled-Z (CZ) entangling gate—a two-qubit gate that applies a phase only when both qubits are excited. The same interaction enables single-shot remote readout of B from A without synchronizing or actively driving the remote node, a practical primitive for distributed circuit QED.

• Setup: Two superconducting circuit-QED nodes in separate dilution cryostats communicate over a 30-m cryogenic quantum link using traveling microwave photons.
• Protocol: Bidirectional photon transfer emits a photon from the communication qubit at A; upon reflection at B the photon picks up a conditional phase set by B’s computational state.
• Main result: Tuning the communication-photon frequency sets that conditional phase, implementing an arbitrary-phase CZ gate between the spatially separated nodes.
• Remote readout: The same entangling reflection maps B’s state onto a locally measurable observable at A in a single shot, with no active pulse sequence required on the remote node.
• Hardware implication: Distributed gates and readout need not rely on tight inter-fridge timing lock; the idle remote node can stay passive while the active node drives the interaction.

TL;DR A modular graph-recurrent decoder—local syndrome encoders reused across patches, with only lightweight spatial aggregation retuned per experiment—transfers from simulation to superconducting hardware and across memory, stability, and lattice-surgery observables. On IBM Nighthawk-generation data it beats minimum-weight perfect matching (MWPM; pairing detection events by lowest total edge weight) at distances 3 and 5, and on Google below-threshold memory it approaches AlphaQubit, showing neural decoding need not be memory-only or device-locked.

• Architecture: Reusable local syndrome encoders feed a graph-recurrent backbone; only a thin spatial aggregator is adapted when changing device, noise, or logical observable, so one pretrained model covers qualitatively different surface-code tasks.
• Memory benchmarks: On an IBM Nighthawk-generation processor the decoder outperforms MWPM at code distances $d=3$ and $d=5$; on Google's below-threshold hardware data it closely approaches AlphaQubit (Google's neural surface-code decoder).
• Noise-robust stability: In an $X$-type stability experiment—repeated checks that $X$-type stabilizers remain consistent over time—a single jointly trained decoder matches or beats MWPM across a continuous sweep of effective measurement error set by a variable pre-readout rotation, without per-setting recalibration.
• Logical operation: On a $ZZ$-merge lattice-surgery experiment (merging two distance-3 surface-code patches so their joint $ZZ$ parity becomes a logical observable), the decoder improves the decoded correlation between the merge outcome and the final $ZZ$ parity relative to MWPM on the same IBM device.
• Practicality: The full pipeline—simulation pretraining plus hardware fine-tuning—runs on single-GPU academic resources, lowering the barrier to portable neural decoding beyond memory experiments.

TL;DR Any quantum low-density parity-check (QLDPC) code can fault-tolerantly measure a transversal logical Clifford by deforming onto ancillas so a stabilizer product enacts that measurement. The deformed, Clifford-stabilized code stays LDPC with distance reduced only by an $n$-independent constant factor, and the measurement's fault distance (minimum weight of data-plus-measurement errors that flip the logical outcome undetected) grows linearly with the original code distance $d$—opening a scalable route to logical non-Cliffords and magic-state preparation inside QLDPC architectures.

• Main result: A general code-surgery protocol measures any transversal logical Clifford on an arbitrary QLDPC code by deforming the code across ancillas until a product of stabilizers equals that logical operator.
• LDPC and distance: The deformed, Clifford-stabilized code remains LDPC, and its distance is preserved up to a constant factor independent of the number of physical qubits $n$.
• Fault tolerance: Against data-qubit and measurement errors, the Clifford measurement has a fault distance that scales linearly with the original code distance $d$.
• Non-Clifford payoff: Measuring logical Cliffords supplies the resource for logical non-Clifford gates in algorithmically relevant subroutines and for preparing magic states (resource states that teleport non-Cliffords) in stabilizer codes.