The Signal
GKP Qubit Study Models Loss, Gates and Readout
A PRX Quantum study models how loss, dephasing, logical gates and inefficient measurements affect superconducting Gottesman-Kitaev-Preskill qubits. Its proposed decoder changes cut modeled gate infidelity by about two orders of magnitude un
Quantum.world Team · Written with AI · fact-checked ·
“We approximate the effect loss and dephasing on approximate GKP codestates using a random displacement channel, and show that this approximation matches well with numerics.”
Mackenzie H. Shaw, Andrew C. Doherty and Arne L. Grimsmo, authors of the PRX Quantum paper
The sentence captures a central aim of a new study of superconducting Gottesman-Kitaev-Preskill (GKP) qubits: recast hardware noise in a form quantum error-correction tools can handle, then account for errors that accumulate during gates and readout. The paper by Mackenzie H. Shaw, Andrew C. Doherty and Arne L. Grimsmo appeared in PRX Quantum on October 29, 2026.
From oscillator noise to a decoder
GKP codes store a logical qubit in the continuous position and momentum degrees of freedom of a harmonic oscillator, such as a superconducting microwave resonator. Their idealized error model focuses on small random displacements in those variables. Actual devices also lose energy, experience dephasing and make imperfect measurements; treating those effects directly can make larger-scale code simulations difficult.
The authors use a mathematical framework called the stabilizer subsystem decomposition to estimate how loss and dephasing affect encoded states. Their analytic approximation turns those channels into random displacements and, they report, agrees well with numerical calculations. The aim is not to claim that real hardware noise is literally uniform random motion, but to provide a tractable approximation for studying its impact on a GKP code.
Why a gate changes the error map
A logical Clifford gate can spread a displacement error across the oscillator’s phase space. If the decoder then uses the same correction region as before the gate, an error that was correctable beforehand can cross the boundary into a logical error. Shaw and colleagues propose changing that decoding region after each gate to account for the transformed error pattern.
For the square-code controlled-Z operation, their modeled gate reaches a 1% error rate at about 7.5 decibels of squeezing with the modified decoder, compared with about 9.8 dB without it, assuming ideal error correction and no gate noise. At fixed 12 dB squeezing, the modification improves average gate infidelity by roughly two orders of magnitude in the ideal-correction analysis. With approximate correction, the gain falls to about one order of magnitude; reaching 1% controlled-Z infidelity then requires roughly 11 dB of squeezing in the square code.
Microwave readout sets a separate limit
The paper also quantifies the cost of inefficient homodyne measurement, which reads an oscillator’s position or momentum. Its cited state-of-the-art microwave measurement efficiencies sit around 60% to 75%. In the square GKP model, a 70% efficient measurement leaves a minimum logical readout error of about 5.6%, even as the encoded state’s squeezing increases without bound.
For a square GKP state at 12 dB squeezing, the model requires approximately 85% measurement efficiency to reach 1% readout error, or 92% to reach 0.1%. The authors analyze two ways to raise effective efficiency: squeeze the measured mode before detection, or couple it to a separate, low-quality-factor readout mode and measure that ancilla. In their example, starting from 70% physical efficiency, about 4 dB of squeezing raises effective efficiency to 85%; about 7 dB raises it to 92%.
A model, not a hardware demonstration
The results are theoretical estimates, not a reported experiment implementing the decoder changes or improved readout. The paper also marks a gap in its gate analysis: modeled error spreading does not necessarily capture noise from imperfect gate execution, and the authors leave a full estimate of those implementation errors to future work.
The ancilla readout proposal brings its own engineering conditions. It adds a physical mode, depends strongly on the coupling between the storage resonator and ancilla, and requires a large on-off ratio to limit unwanted leakage. The authors say whether experimentally feasible coupling strengths can meet the proposal’s needs remains unresolved. For now, the study’s clearest hardware-facing result is a quantitative one: at 70% measurement efficiency, its square-code model bottoms out at 5.6% logical readout error.